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The perimeter of each circle is *aπ*.\r\n\r\n\u003c\u003chttp://imgfz.com/i/UzgCJut.png\u003e\u003e\r\n\r\nGiven *a*, obtain the area of ​​the square.\r\n","description_html":"\u003cp\u003eFour circles are inscribed in the square ABCD. The perimeter of each circle is \u003cb\u003eaπ\u003c/b\u003e.\u003c/p\u003e\u003cimg src = \"http://imgfz.com/i/UzgCJut.png\"\u003e\u003cp\u003eGiven \u003cb\u003ea\u003c/b\u003e, obtain the area of ​​the square.\u003c/p\u003e","function_template":"function y = squartArea(a)\r\n y = a;\r\nend","test_suite":"%%\r\na = 0;\r\ny = 0;\r\nassert(isequal(squartArea(a),y))\r\n%%\r\na = 8;\r\ny = 256;\r\nassert(isequal(squartArea(a),y))\r\n%%\r\na = 1;\r\ny = 4;\r\nassert(isequal(squartArea(a),y))\r\n%%\r\na = 10;\r\ny = 400;\r\nassert(isequal(squartArea(a),y))\r\n%%\r\na = 50;\r\ny = 10000;\r\nassert(isequal(squartArea(a),y))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":446926,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":95,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-05-18T03:09:51.000Z","updated_at":"2026-02-05T12:03:10.000Z","published_at":"2020-05-18T03:09:51.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/media/image1.JPEG\"}],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFour circles are inscribed in the square ABCD. The perimeter of each circle is\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eaπ\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e 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\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eDetermine the ratio of the area of a circle to the area of a square, Given the side of the square = radius of the circle.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = area_ratio(x)\r\n y =\r\nend","test_suite":"%%\r\nx = 6.76;\r\ny_correct = pi;\r\nassert(isequal(area_ratio(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":564784,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":113,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-12-05T15:46:44.000Z","updated_at":"2026-02-14T16:21:13.000Z","published_at":"2020-12-05T15:46:44.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDetermine the ratio of the area of a circle to the area of a square, Given the side of the square = radius of the circle.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":49657,"title":"Determine the area of square if length of the diagonal is given","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 21px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 10.5px; transform-origin: 407px 10.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eWe have to find the area of square if the length of the diagonal of a square is given.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = your_fcn_name(x)\r\n y = x;\r\nend","test_suite":"%%\r\nx = 4;\r\ny_correct = 8;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":822117,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":72,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-12-29T15:05:52.000Z","updated_at":"2026-02-06T15:13:38.000Z","published_at":"2020-12-29T15:05:52.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWe have to find the area of square if the length of the diagonal of a square is given.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":50447,"title":"Calculate Triangle Area, A, B and Gamma is given.","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 359px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 179.5px; transform-origin: 407px 179.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eCalculate Triangle Area:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e A\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eB \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eand\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e Gamma\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e [degree] is given as follows:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 209px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 104.5px; text-align: left; transform-origin: 384px 104.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cimg 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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eRound the answer to four decimal places\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = AreaTriangle(A, B, Gamma)\r\n\r\nend","test_suite":"%% \r\nA = 4; B = 6; Gamma = 56.45; % [degree]\r\ny_correct = 10.0008\r\nassert(isequal(AreaTriangle(A, B, Gamma),y_correct))\r\n\r\n%%\r\nA = 5.7; B = 8.9; Gamma = 132; % [degree]\r\n\r\ny_correct = 18.8499\r\nassert(isequal(AreaTriangle(A, B, Gamma),y_correct))\r\n\r\n%%\r\nA = 48.3; B = 643; Gamma = 8; % [degree]\r\n\r\ny_correct = 2161.1425\r\nassert(isequal(AreaTriangle(A, B, Gamma),y_correct))\r\n\r\n%%\r\nA = pi; B = 2*pi; Gamma = 43; % [degree]\r\n\r\ny_correct = 6.7311\r\nassert(isequal(AreaTriangle(A, B, Gamma),y_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":487522,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":31,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-02-18T16:05:19.000Z","updated_at":"2026-03-21T09:29:10.000Z","published_at":"2021-02-18T16:05:19.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate Triangle Area:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e A\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eB \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eand\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e Gamma\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e [degree] is given as follows:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e 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12.5;\r\nassert(abs(square_area(x)-y_correct)\u003c1e-4)","published":true,"deleted":false,"likes_count":4,"comments_count":4,"created_by":134267,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":247,"test_suite_updated_at":"2017-05-31T18:18:43.000Z","rescore_all_solutions":true,"group_id":1,"created_at":"2017-05-16T16:59:29.000Z","updated_at":"2026-02-25T17:47:50.000Z","published_at":"2017-05-16T17:01:02.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind the area of a square whose diagonal length is given as x.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":46948,"title":"area","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 20.8px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 10.4px; transform-origin: 407px 10.4px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.4px; text-align: left; transform-origin: 384px 10.4px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003efind the area of a cube of side \"x\"\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = your_fcn_name(x)\r\n y = x;\r\nend","test_suite":"%%\r\nx = 1;\r\ny_correct = 6;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 2;\r\ny_correct = 24;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":430136,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":215,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-10-19T15:10:51.000Z","updated_at":"2026-02-11T18:22:05.000Z","published_at":"2020-10-19T15:10:51.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003efind the area of a cube of side \\\"x\\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":44391,"title":"For a rectangle, if x is the length and 2x is width. Then find out x from the area of the rectangle?","description":"For a rectangle, if x is the length and 2x is the width. Then find out x from the area of the rectangle?\r\n\r\nif the area is equal to 200 then the length of the rectangle is 10.","description_html":"\u003cp\u003eFor a rectangle, if x is the length and 2x is the width. Then find out x from the area of the rectangle?\u003c/p\u003e\u003cp\u003eif the area is equal to 200 then the length of the rectangle is 10.\u003c/p\u003e","function_template":"function y = length_of_rect(A)\r\n y = A;\r\nend","test_suite":"%%\r\nA = 200;\r\ny_correct = 10;\r\nassert(isequal(length_of_rect(A),y_correct))\r\n\r\n%%\r\nA = 32;\r\ny_correct = 4;\r\nassert(isequal(length_of_rect(A),y_correct))\r\n\r\n%%\r\nA = 18;\r\ny_correct = 3;\r\nassert(isequal(length_of_rect(A),y_correct))\r\n\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":93545,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":109,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2017-10-26T09:21:07.000Z","updated_at":"2026-02-06T18:21:25.000Z","published_at":"2017-10-26T09:21:07.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor a rectangle, if x is the length and 2x is the width. Then find out x from the area of the rectangle?\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eif the area is equal to 200 then the length of the rectangle is 10.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":44505,"title":"Calculating Ring Area","description":"In two-dimensional space, a ring can be constructed by using two concentric circles. Determine the area of a ring which has r1 as the inner radius and r2 as the outer radius.","description_html":"\u003cp\u003eIn two-dimensional space, a ring can be constructed by using two concentric circles. Determine the area of a ring which has r1 as the inner radius and r2 as the outer radius.\u003c/p\u003e","function_template":"function area = RingArea(r1,r2)\r\n area = r1+r2;\r\nend","test_suite":"%%\r\nr1 = 4;\r\nr2 = 5;\r\ny_correct = 28.27433;\r\nassert(abs(RingArea(r1,r2)-y_correct)\u003c1e-5)\r\n%%\r\nr1 = 7.5;\r\nr2 = 8.25;\r\ny_correct = 37.11006;\r\nassert(abs(RingArea(r1,r2)-y_correct)\u003c1e-5)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":180632,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":107,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2018-01-24T18:16:13.000Z","updated_at":"2026-02-06T12:07:01.000Z","published_at":"2018-01-24T18:16:13.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn two-dimensional space, a ring can be constructed by using two concentric circles. Determine the area of a ring which has r1 as the inner radius and r2 as the outer radius.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":2378,"title":"Area of a triangle","description":"A triangle is given with base *'b'* ,vertical hight *'h'* . then find it's area.","description_html":"\u003cp\u003eA triangle is given with base \u003cb\u003e'b'\u003c/b\u003e ,vertical hight \u003cb\u003e'h'\u003c/b\u003e . then find it's area.\u003c/p\u003e","function_template":"function A = trg_area(b,h)\r\n A=f(b,h);\r\nend","test_suite":"%%\r\nb = 1;\r\nh=5\r\ny_correct = 2.5;\r\nassert(isequal(trg_area(b,h),y_correct))\r\n\r\n%%\r\nb = 1;\r\nh=10\r\ny_correct = 5;\r\nassert(isequal(trg_area(b,h),y_correct))","published":true,"deleted":false,"likes_count":4,"comments_count":0,"created_by":22553,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":984,"test_suite_updated_at":"2014-07-07T12:31:13.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2014-06-18T17:40:40.000Z","updated_at":"2026-04-14T21:14:43.000Z","published_at":"2014-06-18T17:40:40.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA triangle is given with base\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e'b'\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e ,vertical hight\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e'h'\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e . then find it's area.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":51173,"title":"Squares inside a square! ","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 99.7778px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.5px 49.8889px; transform-origin: 406.5px 49.8889px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 40.8889px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 20.4444px; text-align: left; transform-origin: 383.5px 20.4444px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eIf you have a square has a side (x) that is divided into four squares. Two of those squares carries smaller squares inside them. Each side carries 5 squares. Find the area of one of these small squares. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.4444px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 10.2222px; text-align: left; transform-origin: 383.5px 10.2222px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.4444px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 10.2222px; text-align: left; transform-origin: 383.5px 10.2222px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = squares_inside_square(x)\r\n y = ;\r\nend","test_suite":"%%\r\nx = 500;\r\ny_correct = 2500;\r\nassert(isequal(squares_inside_square(x),y_correct))\r\n\r\n%%\r\nx = 100;\r\ny_correct = 100;\r\nassert(isequal(squares_inside_square(x),y_correct))\r\n\r\n%%\r\nx = 50;\r\ny_correct = 25;\r\nassert(isequal(squares_inside_square(x),y_correct))\r\n\r\n%%\r\nx = 30;\r\ny_correct = 9;\r\nassert(isequal(squares_inside_square(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":4,"created_by":995198,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":70,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-03-24T11:45:55.000Z","updated_at":"2025-12-25T11:51:40.000Z","published_at":"2021-03-24T11:45:55.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf you have a square has a side (x) that is divided into four squares. Two of those squares carries smaller squares inside them. Each side carries 5 squares. Find the area of one of these small squares. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":45195,"title":"Calculate the area of a circle","description":"Given a circle of diameter x calculate its area","description_html":"\u003cp\u003eGiven a circle of diameter x calculate its area\u003c/p\u003e","function_template":"function y = areaOfCircle(x)\r\n y = x;\r\nend","test_suite":"%%\r\nx = 1;\r\ny_correct = pi * 0.25;\r\nassert(isequal(areaOfCircle(x),y_correct))\r\n%%\r\nx = 15;\r\ny_correct = pi * 56.25;\r\nassert(isequal(areaOfCircle(x),y_correct))\r\n%%\r\nx = 20;\r\ny_correct = pi * 100;\r\nassert(isequal(areaOfCircle(x),y_correct))\r\n%%\r\nx = 100;\r\ny_correct = pi * 2500;\r\nassert(isequal(areaOfCircle(x),y_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":348097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":144,"test_suite_updated_at":"2019-11-05T16:44:06.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2019-11-05T16:37:48.000Z","updated_at":"2026-02-12T19:03:56.000Z","published_at":"2019-11-05T16:44:06.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a circle of diameter x calculate its area\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":60750,"title":"Area of a rectangle","description":"FInd the area of a rectangle with a length L and width W. Round to the nearest integer.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 21px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 10.5px; transform-origin: 407px 10.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFInd the area of a rectangle with a length L and width W. Round to the nearest integer.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function A = your_fcn_name(L,W)\r\n A = ;\r\nend","test_suite":"%%\r\nL = 1;\r\nW = 1;\r\nA_correct = 1;\r\nassert(isequal(your_fcn_name(L,W),A_correct))\r\n%%\r\nL = 3;\r\nW = 6;\r\nA_correct = 18;\r\nassert(isequal(your_fcn_name(L,W),A_correct))\r\n%%\r\nL = 4.5;\r\nW = 5;\r\nA_correct = 23;\r\nassert(isequal(your_fcn_name(L,W),A_correct))\r\n%%\r\nL = 482.2;\r\nW = 572.34;\r\nA_correct = 275982;\r\nassert(isequal(your_fcn_name(L,W),A_correct))\r\n%%\r\nL = 3542113582974;\r\nW = 0;\r\nA_correct = 0;\r\nassert(isequal(your_fcn_name(L,W),A_correct))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":4700639,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":31,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-10-18T20:19:06.000Z","updated_at":"2026-02-09T16:28:46.000Z","published_at":"2024-10-18T20:19:06.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFInd the area of a rectangle with a length L and width W. Round to the nearest integer.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":45333,"title":"Area-01","description":"Given the radius of the circle inscribed in a square, find the area that is not bounded by the circle but inside the square.\r\n\r\n","description_html":"\u003cp\u003eGiven the radius of the circle inscribed in a square, find the area that is not bounded by the circle but inside the square.\u003c/p\u003e","function_template":"function y = inscribed_circle(r)\r\n y = x;\r\nend","test_suite":"%%\r\nr = 1;\r\ny_correct = 0.8584;\r\nassert(abs(inscribed_circle(r)-y_correct)\u003c0.01)\r\n%%\r\nr = 5;\r\ny_correct = 21.4602;\r\nassert(abs(inscribed_circle(r)-y_correct)\u003c0.01)\r\n%%\r\nr = 0;\r\ny_correct = 0;\r\nassert(isequal(inscribed_circle(r),y_correct))\r\n%%\r\nr = 12.1;\r\ny_correct = 125.6794;\r\nassert(abs(inscribed_circle(r)-y_correct)\u003c0.01)\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":363598,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":67,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-02-16T18:24:27.000Z","updated_at":"2026-02-09T14:23:49.000Z","published_at":"2020-02-16T18:24:41.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven the radius of the circle inscribed in a square, find the area that is not bounded by the circle but inside the square.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":2402,"title":"Area of a Square ","description":"Inside a square is a circle with radius r.\r\n\r\nWhat is the area of the square?\r\n\r\n","description_html":"\u003cp\u003eInside a square is a circle with radius r.\u003c/p\u003e\u003cp\u003eWhat is the area of the square?\u003c/p\u003e","function_template":"function A = area_sqr(r)\r\n A= ;\r\nend","test_suite":"%%\r\nr = 2;\r\ny_correct = 16;\r\nassert(isequal(area_sqr(r),y_correct))\r\n\r\n%%\r\nr = 3;\r\ny_correct = 36;\r\nassert(isequal(area_sqr(r),y_correct))\r\n\r\n%%\r\nr = 25;\r\ny_correct = 2500;\r\nassert(isequal(area_sqr(r),y_correct))","published":true,"deleted":false,"likes_count":10,"comments_count":1,"created_by":22553,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":857,"test_suite_updated_at":"2014-07-02T18:36:38.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2014-07-02T18:34:11.000Z","updated_at":"2026-04-06T22:48:48.000Z","published_at":"2014-07-02T18:36:38.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eInside a square is a circle with radius r.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWhat is the area of the square?\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":44308,"title":"Component area","description":"Find the area of the component below, all measurements are in mm\r\n\r\n\u003c\u003chttps://image.ibb.co/hocruF/Component.png\u003e\u003e","description_html":"\u003cp\u003eFind the area of the component below, all measurements are in mm\u003c/p\u003e\u003cimg src = \"https://image.ibb.co/hocruF/Component.png\"\u003e","function_template":"function A = your_fcn_name(h,w,r)\r\n A = h,w,r;\r\nend","test_suite":"%%\r\nh = 50;\r\nw = 20;\r\nr = 12;\r\nA_correct = 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column-rule-color: rgb(60, 60, 60); font-family: Helvetica, Arial, sans-serif; font-size: 20px; font-weight: 700; line-height: 20px; margin-block-end: 5px; margin-block-start: 3px; margin-bottom: 5px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 3px; outline-color: rgb(60, 60, 60); perspective-origin: 384px 10px; text-align: left; text-decoration: none; text-decoration-color: rgb(60, 60, 60); transform-origin: 384px 10px; white-space: pre-wrap; margin-left: 4px; margin-top: 3px; margin-bottom: 5px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eArea between curves - Problem 1\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 24.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 12.25px; text-align: left; transform-origin: 384px 12.25px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFind the area between the curves \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"89\" height=\"24\" style=\"width: 89px; height: 24px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"89.5\" height=\"19\" style=\"width: 89.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e over the interval [0 2] for different \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ea\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eb\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e coefficients:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; 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woWee+6///6VK1equCSohRQBuqHbi8xbLBYOatA9agT/DR06VK//3OmGJickgBQB+qPho+xgWNQI0CUmJGgJKQJ0jAkJmkGNAH1jQoIGkCLACAgSpMYJUhEqHGInP4IEeTEYAYZCkCAjBiPAgAgSpMNgBBgTQYJEGIwAIyNIkAWDEWBw/B0S1GcyUSOEHddDkh8TElRGigC4ESSohneMAHgjSFAHgxGAJggSlMZgBKBFBAmKYjAC0BqCBIUwGAHwjSBBCQxGAK6IICG8GIwA+IkgIYwYjAD4jyAhLEgRZMP1kOTHqYMQetQIQACYkBBKpAhAwJiQEDLUCEAwmJAQAqQIQPCYkBAsagQgJJiQEDhSBA0xmUwcaCc5JiQEiBoBCC0mJLQZKQIQDkxIaBtqBCBMmJDgL1IEIKwIEq6ME6QCUABBwhUwGAFQBkFCqxiMACiJIKFlDEYAFEaQ0BSDEQBVECT8CoMR9IrTNMiPIOG/GIwAqIsgQQgGIwASIEhGx2AEQBIEydAYjADIgyAZFIMRANkQJCNiMIIBcT0k+REkY2EwAiAtgmQgDEYAZEaQDIHBCID8ZA+S1WodPXp08/vtdnt5ebnnZr9+/bp27argurSEwQiAJkgdpOzs7O3bt1ut1uaf2r1798aNGzt27Oi+mZWVNWrUKGVXpwGkCICGSBqkurq6devWffLJJ507d27xAUVFRenp6ffdd5/CC9MQagRAW8xqL6BlmZmZ0dHRa9eube0BxcXFffv2tdvtDQ0NrT3G4iU8y5SUydRCjY4dK6BGAGQm6YS0cuVKs9l86NChFj/rdDrPnDmzZs0au91eV1c3Y8aMjIyM5g8rKSkJ8zJlxGAEQKMknZDMZl8Ls9lsSUlJW7Zsyc/Pz83NtVqt27dvV2xt0mIwAqBpkgbJt7i4uKysrLi4OCFETEzMhAkTCgqM/m8ugxHgG6dpkJ8mg1RRUbFz507PTYfDERERoeJ61MVgBEAftBSkEydOVFdXCyHq6+tXrVpVVlYmhLDZbAcOHJgyZYraq1MHgxEA3ZD0oIYWZWZmTp48OSUlxWKxpKenp6amDhw4sLCwcMmSJQb8IyRSBEBndHv6W4vFouOj7KgR0FaJiYlqLwFXoKUJCYIUAdAvLb2HBGoEBMzU2jmGIQ0mJG0gRQB0jyDJjitHADAIgiQ1BiMAxkGQJMVgBMBoCJKMGIwAGBBBkguDEQDDIkgSYTACYGQESQoMRgBAkNTHYAQAgiCpi8EIUIxez9upJwRJNQxGAOCNIKmAwQgAmiNISmMwAoAWESTlMBgBgA8ESSEMRgDgG0EKO1IEyMBk0u0FsnWDC/SFFzUCAD8xIYULKQKANmFCCgtqBABtxYQUYqQIAALDhBRK1AgAAsaEFBqkCACCxIQUAtQIAILHhBQUUgQAocKEFDhqBAAhxIQUCFIEaA6naZAfE1KbUSMACAcmpDYgRQAQPgTJL1w5AgDCjSBdGYMRACiAIPnCYAQAiiFIrWIwAvSE6yHJjyC1gMEIAJRHkJpiMAIAVRCk/2EwAgAVEaT/YjACAHURJAYjAJCC0YPEYAQAkjBukBiMAEAqBg0SgxEAyMZwQWIwAgA5GStIDEaAYXGaBvkZJUikCAAkZ4gL9FEjAJCf5oNktVp9fNZkaqFGx44VUCMAkI22g5Sdnf3UU0+19lkGIwDQEK2+h1RXV7du3bpPPvmkc+fOLT6gtLSkyT2kCABkptUJKTMzMzo6eu3ata09oF8/i/dNagQYnKm1v/mANLQ6Ia1cudJsNh86dMjHY44dKxg6NJEUAYAmaHVCMpv9Wjk1AgCt0GqQAAA6Q5AAAFLQbZBKS0vVXgIAoA10GyQAgLaY9HrCQZPJdOzYMbVXAUAWQ4cO1es/d7rBhAQAkAJBAgBIgSABMAT218mPIAEApECQAABSIEgAACkQJACAFHQbpH79+qm9BABAG+g2SADgjeshyY8gAQCkQJAAAFIgSAAAKRAkAIAUdBskrocEANqi2yABALSFIAEApECQAABSIEgAACkQJACGwPWQ5EeQAABSIEgAACkQJACAFAgSAEAKug0S10MCAG3RbZAAwBvXQ5IfQQIASIEgAQCkQJAAAFIgSAAAKeg2SFwPCQC0RbdBAgBoC0ECAEiBIAEApECQAABSIEgADIHrIcmPIAEApECQAABSIEgAACkQJACAFHQbJK6HBADaotsgAYA3rockP4IEAJACQQIASIEgAQCkQJAAAFLQbZC4HhIAaEs7tRfQqsrKypKSkl69elksluaftdvt5eXlnpv9+vXr2rWrgqsDAISYpEHat2/fCy+8cNtttxUUFEydOnXp0qVNHrB79+6NGzd27NjRfTMrK2vUqFGKLxMAEDIyBsnpdK5ateq9996Lj4+32+3jx4+fOnVq7969vR9TVFSUnp5+3333qbRGAECIyfge0ueffx4VFRUfHy+EiI6OHjNmzOHDh5s8pri4uG/fvna7vaGhQY01AgBCTMYJqa6urn///p6bXbp0aXKEgtPpPHPmzJo1a+x2e11d3YwZMzIyMhRfJgAt4XpI8pNxQnI6nWbz/xZmNptdLpf3A2w2W1JS0pYtW/Lz83Nzc61W6/bt2xVfJgAglGQMUseOHZ1Op+emy+Vq1+5Xk1xcXFxWVlZcXJwQIiYmZsKECQUFBUqvEgAQUjIG6brrrvv22289N2traxMTE70fUFFRsXPnTs9Nh8MRERGh3PoAAGEgY5CGDRsmhDh06JAQ4tSpU/n5+SNGjBBCnDhxorq6WghRX1+/atWqsrIyIYTNZjtw4MCUKVNUXTIAIFgyHtRgNpvXr1+/fPny+Pj4oqKidevWXXvttUKIzMzMyZMnp6SkWCyW9PT01NTUgQMHFhYWLlmypPkfIXE9JADQFpNejzyxWCzbtm1TexUAZDF06FC9/nOnGzLusgMAGBBBAgBIgSABAKRAkAAAUtBtkLgeEgBoi26DBADQFhn/Dgnwx1XPh/6voS8+uS/kzwnATwQJ8gpHcoL5juQKCCuCBFkon5+2anGFVAoIFYIEdcifHz813xASJSdO0yA/ggTlhDZC/XaeDeGzuZWmxAX/JCQKCIxuz2VnMpmOHTum9iqMLsgChSM5wQhJrgR9UkmTq9hAQgQJIRZwhGTLj5+CrxR9UgZBkh9BQmgE0CGNFuiKgkkUcQofgiQ/3b6HxPWQFNDWCOm1QE0030z/E+X9IyVOMBrdBgnh06YO6SlCFRUV77//flVVVVJS0sSJE/3/wiY/BB99suyqLvl/se6PiVNomUy63SGkGwQJ/vK/Q3qKkEdtbe2uXbuWL1/e2Ng4cuTIysrK+fPnB/ZU3j+fJnHy1KiJJj98+gRd0u3/MnDF2FDxs0O6jJC3PXv2PPzww+fPnxdCbNmyJScn58iRIyH/LgG8/0Sc/MQVY+XHhISWqdghm822adOmsrKy66+/fvbs2QkJCSH/FgFISkrKyclxf1xfX9+9e/dwfBcfw1NrPP+lKBO0jiDhV1Sfh4qLizds2PDcc8/Fxsbm5OQMHDjw1VdfXbRoUZi+nf+6dOmSnJwshHC5XJs2bdq6dWu4v2Nb48R7TtA63e6y47DvNlG9Qx533HHHm2++2bNnT/fNxYsXv/rqq4WFhZLMSUKIxx9//Lbbbps2bZpaC2jrbj3i5MYuO/kRJKPzJ0VKvj/Url27a665xv1WjRBiz54906dPz8jISE9PV2wNPuTk5MTHx48ePbqysrJXr15qL4c4tQFBkh+77AxKtg55zJs3z2xuet1Il8ul5Bpyc3N//PHHO++8s2vXrl9//XV5eXlSUlLXrl0//fTTm266afjw4Y2NjR988MHChQuVXFWL2K0HPSFIxiJthzyavDdTUFAghLj77ruV+e4ul+vxxx+fNWtW9+7dBw8evGzZspiYmAsXLgwePHjXrl3JyckNDQ3uRy5btkyZJfmPOEHr2GVnFFdMkYTHbV+4cKFv37733HPP66+/rsx3XL9+/axZs9z74vr06XPXXXdlZ2cnJyfX1NSE4yBvZbBbz41ddvJjQtI5LXbIIy0tbeTIkZs3bw7mSVwu1+XLl30/pkuXLu4Pevbs6a5RY2NjZWWlezLbs2dP872IGuL5T9zW48iFvuJEjeTHhKRP8u+au6Lnn3++vLw8+KOrjx49mp2d7fsxmZmZ11xzjfc9H3/8cXJy8qVLlyIjI4NcgJwMODZxclX5MSHpjaZHIo+cnJz6+np3jVwuV3FxccCHfQ8fPnz48OFt/Sqr1XrLLbfotUaCN5wgJYKkE/rokNuHH35YU1Pz7LPPum9+9913RUVFVwySy+VqbGzs0KFDMN/aarUOGzYsMjLy4MGDt956q/vOsrKy48ePz5w5M5hnllkwcRL0CaFDkDRPKymqra199tlny8rKamtrk5KSnnnmmfr6+qeeeqqqqurixYsLFixw/4t/5MiRRx99dOLEiYsXL3a5XA0NDWVlZStXrvTxzEePHl2xYoXZbI6Lizt+/PigQYM2btwYExPT1hV+/PHHd911165duxITEwsKChYsWOC+Pzs7e+3atYFtteYEc+4iQZwQHN0GSffXQ9JKh9zOnz9/7733vvzyywkJCfX19TfffHNNTU1VVdXq1av79+8/f/781NTUqqqqnj173nPPPT/++OOpU6e8v/yTTz5p7Zm3b9/+wAMPvP766w8++KAQorGxccKECUOGDPnqq6/a2qQePXokJiaazeZXXnll7969zz//fLdu3Y4ePTp37lwd77vzgThBYbo9qEGvZ/vW6NEKKSkpa9eu9fxfwuzZs9955x33+Rd27NiRmpoaERHxww8/tDUh33777ZAhQ0aPHn3gwAHPnd99992AAQPS0tKueCxDcw6Ho7Cw0P3ut8PhKCgoGD58uKYPsQsHjZ6SnMO+5afbCUl/tDUSefvmm2969OjhPbOePXtWCDF37lwhxNixY9PS0pKTkwPYybZixYqG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0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = AreaCurves(a, b)\r\n \r\nend","test_suite":"%%\r\nfiletext = fileread('AreaCurves.m');\r\nfor ii = [3.5773, 6.1773, 5.5773, 11.2970]\r\n assert(isempty(strfind(filetext, num2str(ii))), ... \r\n 'Do NOT use provided answers in your solution')\r\nend\r\n%%\r\na = 1; \r\nb = 1;\r\n\r\ny_correct = 3.5773;\r\nassert(abs(AreaCurves(a,b)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = 3; \r\nb = 0.3; \r\n\r\ny_correct = 6.1773;\r\nassert(abs(AreaCurves(a,b)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = -1;\r\nb = 4;\r\n\r\ny_correct = 5.5773;\r\nassert(abs(AreaCurves(a,b)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = pi;\r\nb = exp(1);\r\n\r\ny_correct = 11.2970;\r\nassert(abs(AreaCurves(a,b)-y_correct)\u003c1e-4)\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":487522,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":25,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-02-19T12:36:27.000Z","updated_at":"2026-01-23T10:01:56.000Z","published_at":"2021-02-19T12:40:47.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"heading\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eArea between curves - Problem 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind the area between the curves \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ef(x) = x^2\\\\, \\\\mathrm{e}^{- x^2}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":48000,"title":"Lateral Area of a Right Rectangular Pyramid","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 42px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 21px; transform-origin: 407px 21px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eGiven the length (l) and width (w) of the rectangular base along with the height (h) of a pyramid, determine the lateral area of a right rectangular pyramid.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = area(l,w,h)\r\n y = l^2+w^2+h^2;\r\nend","test_suite":"%%\r\nl = 1; w=1; h=1;\r\ny_correct = 2.2361;\r\nassert(isequal(area(l,w,h),y_correct))\r\n%%\r\nl = 2; w=2; h=12;\r\ny_correct = 48.1664;\r\nassert(isequal(area(l,w,h),y_correct))\r\n%%\r\nl = 12; w=3; h=1;\r\ny_correct = 39.8816;\r\nassert(isequal(area(l,w,h),y_correct))\r\n\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":180632,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":36,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-12-17T03:05:41.000Z","updated_at":"2026-02-17T08:25:19.000Z","published_at":"2020-12-17T03:05:41.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven the length (l) and width (w) of the rectangular base along with the height (h) of a pyramid, determine the lateral area of a right rectangular pyramid.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61157,"title":"Scaling vertically parabola by evaluating its area over an interval","description":"Let p be a quadratic polynomial, with its axis of symmetry being the y-axis. Considering the vertical shift of its vertex to the origin, find the positive constant, k, that scales the shifted parabola such that its area over the interval [-a; a] (a\u003e0) will be equal to the area under the original parabola (see figure below).\r\ninput: (p, a)\r\noutput: k\r\n\r\n\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 447.8px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 408px 223.9px; transform-origin: 408px 223.9px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eLet \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ep\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e be a quadratic polynomial, with its axis of symmetry being the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ey\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e-axis. Considering the vertical shift of its vertex to the origin, find the positive constant, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ek\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, that scales the shifted parabola such that its area over the interval \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[-a; a] (a\u0026gt;0)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e will be equal to the area under the original parabola (see figure below).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003einput: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(p, a)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eoutput: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ek\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 255.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 127.9px; text-align: left; transform-origin: 384px 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\" alt=\"Scale parabola\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function k = scale_parabola(p, a)\r\n k = x;\r\nend","test_suite":"%%\r\np = [1 0 1];\r\na = 2;\r\nk_correct = 7/4;\r\nassert(isapprox(scale_parabola(p,a),k_correct))\r\n\r\n%%\r\np = [1 0 -1];\r\na = 2;\r\nk_correct = 0.25;\r\nassert(isapprox(scale_parabola(p,a),k_correct))\r\n\r\n%%\r\np = [5 0 0];\r\na = 0.5;\r\nk_correct = 1;\r\nassert(isequal(scale_parabola(p,a),k_correct))\r\n\r\n%%\r\nfiletext = fileread('scale_parabola.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\np = [-3 0 1];\r\na = 1;\r\nk_correct = 0;\r\nassert(isequal(scale_parabola(p,a),k_correct))\r\n\r\n%%\r\np = [-3 0 2];\r\na = 1;\r\nk_correct = -1;\r\nassert(isequal(scale_parabola(p,a),k_correct))\r\n\r\n%%\r\np = [-3 0 2];\r\na = 3;\r\nk_correct = 7/9;\r\nassert(isapprox(scale_parabola(p,a),k_correct))\r\n\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":2,"created_by":4993982,"edited_by":4993982,"edited_at":"2026-01-16T14:57:57.000Z","deleted_by":null,"deleted_at":null,"solvers_count":12,"test_suite_updated_at":"2026-01-16T14:57:57.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2026-01-10T14:36:03.000Z","updated_at":"2026-03-29T13:27:42.000Z","published_at":"2026-01-15T14:52:59.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eLet \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e be a quadratic polynomial, with its axis of symmetry being the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e-axis. Considering the vertical shift of its vertex to the origin, find the positive constant, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, that scales the shifted parabola such that its area over the interval \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[-a; a] (a\u0026gt;0)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e will be equal to the area under the original parabola (see figure below).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003einput: 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":50462,"title":"Calculate quadrilateral Area: sides and diagonals given","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 352px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 176px; transform-origin: 407px 176px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eCalculate quadrilateral Area: sides (a,b, c, d) and diagonals (e, f) are given\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 232px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 116px; text-align: left; transform-origin: 384px 116px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"269\" height=\"226\" style=\"vertical-align: baseline;width: 269px;height: 226px\" 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\" 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9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e Round the answer to four decimal places.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eHint: use Bretschneider's formula\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = AreaQuadrilateral(a,b,c,d,e,f)\r\n\r\nend","test_suite":"%%\r\na = 4; b = 4; c = 4; d = 4; \r\ne = 4*sqrt(2); f = 4*sqrt(2);\r\n\r\ny_correct = 16;\r\nassert(isequal(AreaQuadrilateral(a,b,c,d,e,f),y_correct))\r\n\r\n%%\r\na = 3; b = 3; c = 3; d = 3; \r\ne = 3*sqrt(3); f = 3;\r\n\r\ny_correct = 7.7942;\r\nassert(isequal(AreaQuadrilateral(a,b,c,d,e,f),y_correct))\r\n\r\n%%\r\na = 5; b = 5; c = 8; d = 8;\r\ne = 4+sqrt(55); f = 6;\r\n\r\ny_correct = 34.2486;\r\nassert(isequal(AreaQuadrilateral(a,b,c,d,e,f),y_correct))\r\n\r\n%%\r\na = 97.7; b = 76.6; c = 110; d = 66.5; \r\ne = 151.7; f = 91.6;\r\n\r\ny_correct = 6341.4175;\r\nassert(isequal(AreaQuadrilateral(a,b,c,d,e,f),y_correct))\r\n\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":487522,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":20,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-02-18T20:12:44.000Z","updated_at":"2026-03-04T22:07:29.000Z","published_at":"2021-02-18T20:25:42.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate quadrilateral Area: sides (a,b, c, d) and diagonals (e, f) are given\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"226\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"269\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e Round the answer to four decimal places.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHint: use Bretschneider's 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a Polyshape_01 (ps) Return its Perimeter, Area, and Centroid.","description":"Return the perimeter (P) of a polyshape object, which is the sum of the lengths of its boundaries.\r\nReturn the total area (A) of a polyshape object, which is the sum of the areas of the solid regions that make up the polyshape.\r\nReturn the x-coordinate (Cx) and the y-coordinate (Cy) of the centroid of a polyshape. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 104.667px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407.5px 52.3333px; transform-origin: 407.5px 52.3333px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21.6667px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 10.8333px; text-align: left; transform-origin: 384.5px 10.8333px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eReturn the perimeter (P) of a polyshape object, which is the sum of the lengths of its boundaries.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 43.3333px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 21.6667px; text-align: left; transform-origin: 384.5px 21.6667px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eReturn the total area (A) of a polyshape object, which is the sum of the areas of the solid regions that make up the polyshape.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.6667px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 10.8333px; text-align: left; transform-origin: 384.5px 10.8333px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eReturn the x-coordinate (Cx) and the y-coordinate (Cy) of the centroid of a polyshape. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"%%\r\nfunction [P, A, Cx, Cy] = PolyShape_01(ps)\r\n % Return the perimeter (P) of a polyshape object, which is the sum\r\n % of the lengths of its boundaries.\r\n \r\n % Return the total area (A) of a polyshape object, which is the sum\r\n % of the areas of the solid regions that make up the polyshape.\r\n \r\n % Return the x-coordinate (Cx) and the y-coordinate (Cy) of the\r\n % centroid of a polyshape. \r\n end","test_suite":"%% Test 1\r\n ps = nsidedpoly(13,'Center',[17, 47],'SideLength', 101);\r\n [P, A, Cx, Cy] = PolyShape_01(ps);\r\n assert(isequal(round(P,4),1313))\r\n assert(isequal(round(A,4),134508.0227))\r\n assert(isequal(round(Cx,4),17))\r\n assert(isequal(round(Cy,4),47))\r\n\r\n \r\n%% Test 2\r\n ps = nsidedpoly(13,'Center',[17, 47],'SideLength', 101);\r\n ps = translate(ps,[237,-1723]);\r\n [P, A, Cx, Cy] = PolyShape_01(ps);\r\n assert(isequal(round(P,4),1313))\r\n assert(isequal(round(A,4),134508.0227))\r\n assert(isequal(round(Cx,4),254))\r\n assert(isequal(round(Cy,4),-1676))\r\n\r\n \r\n%% Test 3\r\n ps = nsidedpoly(13,'Center',[17, 47],'SideLength', 101);\r\n ps = translate(ps,[237,-1723]);\r\n ps = scale(ps,0.135);\r\n [P, A, Cx, Cy] = PolyShape_01(ps);\r\n assert(isequal(round(P,4),177.255))\r\n assert(isequal(round(A,4),2451.4087))\r\n assert(isequal(round(Cx,4),34.29 ))\r\n assert(isequal(round(Cy,4),-226.26))\r\n\r\n \r\n%% Test 4\r\n ps = nsidedpoly(13,'Center',[17, 47],'SideLength', 101);\r\n ps = translate(ps,[237,-1723]);\r\n ps = scale(ps,0.135);\r\n ps = subtract(ps,nsidedpoly(17,'Center',[43, -220],'SideLength', 1.7));\r\n [P, A, Cx, Cy] = PolyShape_01(ps);\r\n assert(isequal(round(P,4),206.155))\r\n assert(isequal(round(A,4),2385.7031))\r\n assert(isequal(round(Cx,4),34.0501))\r\n assert(isequal(round(Cy,4),-226.4324))\r\n\r\n \r\n%% Test 5\r\n ps = nsidedpoly(13,'Center',[17, 47],'SideLength', 101);\r\n ps = translate(ps,[237,-1723]);\r\n ps = scale(ps,0.135);\r\n ps = subtract(ps,nsidedpoly(17,'Center',[43, -220],'SideLength', 1.7));\r\n ps = subtract(ps,nsidedpoly(17,'Center',[20, -220],'SideLength', 1.7));\r\n [P, A, Cx, Cy] = PolyShape_01(ps);\r\n assert(isequal(round(P,4),235.055))\r\n assert(isequal(round(A,4),2319.9976))\r\n assert(isequal(round(Cx,4),34.448))\r\n assert(isequal(round(Cy,4),-226.6146))\r\n\r\n \r\n%% Test 6\r\n ps = nsidedpoly(13,'Center',[17, 47],'SideLength', 101);\r\n ps = translate(ps,[237,-1723]);\r\n ps = scale(ps,0.135);\r\n ps = subtract(ps,nsidedpoly(17,'Center',[43, -220],'SideLength', 1.7));\r\n ps = subtract(ps,nsidedpoly(17,'Center',[20, -220],'SideLength', 1.7));\r\n ps = subtract(ps,polyshape([20 30.1 40.1 45.1 50 45.2 40.2 30.2 27.2],[-235 -239 -239 -237 -235 -239 -241 -240.5 -240]));\r\n [P, A, Cx, Cy] = PolyShape_01(ps);\r\n assert(isequal(round(P,4),300.0489))\r\n assert(isequal(round(A,4),2274.2476))\r\n assert(isequal(round(Cx,4),34.4235))\r\n assert(isequal(round(Cy,4),-226.367))\r\n \r\n \r\n ","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":20795,"edited_by":20795,"edited_at":"2024-06-28T13:41:58.000Z","deleted_by":null,"deleted_at":null,"solvers_count":10,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-06-26T18:00:30.000Z","updated_at":"2026-03-18T15:16:22.000Z","published_at":"2024-06-26T18:18:37.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eReturn the perimeter (P) of a polyshape object, which is the sum of the lengths of its boundaries.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eReturn the total area (A) of a polyshape object, which is the sum of the areas of the solid regions that make up the polyshape.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eReturn the x-coordinate (Cx) and the y-coordinate (Cy) of the centroid of a polyshape. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61070,"title":"Square area to triangle area","description":"Given the area, A, of a square with side length, c, if a right angle triangle has the same area A and the hypothenuse length 2c (two times the square side), then find the height, h, of the triangle.\r\nForbidden functions / expressions\r\nregexp\r\nassignin\r\nstr2num\r\necho","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 163.75px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 81.875px; transform-origin: 408px 81.875px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven the area, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, of a square with side length, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ec\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, if a right angle triangle has the same area \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and the hypothenuse length \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e2c \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e(two times the square side), then find the height, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eh\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, of the triangle.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eForbidden functions / expressions\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.75px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 392px 40.875px; transform-origin: 392px 40.875px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2125px; text-align: left; transform-origin: 364px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eregexp\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2125px; text-align: left; transform-origin: 364px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eassignin\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2125px; text-align: left; transform-origin: 364px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003estr2num\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2125px; text-align: left; transform-origin: 364px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eecho\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function h = find_height(A)\r\n h = A;\r\nend","test_suite":"%%\r\nA = 8;\r\nh_correct = 4;\r\nassert(isequal(find_height(A),h_correct))\r\n\r\n%%\r\nfiletext = fileread('find_height.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\nA = 9;\r\nh_correct = 3*sqrt(2);\r\ntolerance = 1e-12;\r\nassert(abs(find_height(A)-h_correct)\u003ctolerance)\r\n\r\n%%\r\nA = 15;\r\nh_correct = sqrt(30);\r\ntolerance = 1e-12;\r\nassert(abs(find_height(A)-h_correct)\u003ctolerance)\r\n\r\n%%\r\nA = 16;\r\nh_correct = 4*sqrt(2);\r\ntolerance = 1e-12;\r\nassert(abs(find_height(A)-h_correct)\u003ctolerance)\r\n\r\n%%\r\nA = 18;\r\nh_correct = 6;\r\nassert(isequal(find_height(A),h_correct))\r\n\r\n%%\r\nA = 32;\r\nh_correct = 8;\r\nassert(isequal(find_height(A),h_correct))\r\n\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":5,"created_by":4993982,"edited_by":4993982,"edited_at":"2025-11-09T16:09:35.000Z","deleted_by":null,"deleted_at":null,"solvers_count":22,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-11-09T13:39:12.000Z","updated_at":"2026-04-12T13:53:34.000Z","published_at":"2025-11-09T16:09:35.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven the area, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, of a square with side length, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ec\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, if a right angle triangle has the same area \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and the hypothenuse length \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2c \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e(two times the square side), then find the height, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, of the triangle.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eForbidden functions / expressions\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eregexp\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eassignin\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003estr2num\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eecho\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":45538,"title":"Find the area of ​​the square","description":"There are *n²* circles inscribed in the square ABCD. The perimeter of each circle is *aπ*\r\n\r\n\u003c\u003chttp://imgfz.com/i/3wzCeAT.png\u003e\u003e\r\n\r\nGiven *n* and *a*, find the area of ​​the square.","description_html":"\u003cp\u003eThere are \u003cb\u003en²\u003c/b\u003e circles inscribed in the square ABCD. The perimeter of each circle is \u003cb\u003eaπ\u003c/b\u003e\u003c/p\u003e\u003cimg src = \"http://imgfz.com/i/3wzCeAT.png\"\u003e\u003cp\u003eGiven \u003cb\u003en\u003c/b\u003e and \u003cb\u003ea\u003c/b\u003e, find the area of ​​the square.\u003c/p\u003e","function_template":"function y = squartArea(n,a)\r\n y = n+a;\r\nend","test_suite":"%%\r\na = 8;\r\nn = 5;\r\ny = 1600;\r\nassert(isequal(squartArea(n,a),y))\r\n%%\r\na = 0;\r\nn = 10;\r\ny = 0;\r\nassert(isequal(squartArea(n,a),y))\r\n%%\r\na = 100/pi;\r\nn = 6;\r\ny = 36476;\r\ntolerance = 1e-12; \r\nassert(abs(36476-y)\u003ctolerance)\r\n%%\r\na = 15;\r\nn = 0;\r\ny = 0;\r\nassert(isequal(squartArea(n,a),y))\r\n%%\r\na = 10;\r\nn = 2;\r\ny = 400;\r\nassert(isequal(squartArea(n,a),y))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":446926,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":60,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-05-18T03:38:49.000Z","updated_at":"2026-03-05T11:06:44.000Z","published_at":"2020-05-18T03:38:49.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/media/image1.png\"}],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThere are\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en²\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e circles inscribed in the square ABCD. The perimeter of each circle is\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eaπ\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, find the area of the square.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray 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the Area of the Ring","description":"\r\nYou have Ring which consist of inner and outer Circles with Radius r and R which are not given but you'll be given Hprizontal distance d which is Tangent to inner circle .\r\nCalculate the Area of the Ring","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 312.033px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.5px 156.017px; transform-origin: 406.5px 156.017px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 231.033px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 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\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 21px; text-align: left; transform-origin: 383.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 192.067px 7.81667px; transform-origin: 192.067px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou have Ring which consist of inner and outer Circles with \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 126.742px 7.81667px; transform-origin: 126.742px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eRadius r and R which are not given \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 59.1833px 7.81667px; transform-origin: 59.1833px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ebut you'll be given Hprizontal distance d which is Tangent to inner circle .\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 10.5px; text-align: left; transform-origin: 383.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 96.5917px 7.81667px; transform-origin: 96.5917px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCalculate the Area of the Ring\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function area = your_fcn_name(d)\r\n area = d;\r\nend","test_suite":"%%\r\nd = 3;\r\narea_correct = 28.2743;\r\ntolerance = 1e-4;\r\nassert(abs(your_fcn_name(d)-area_correct)\u003ctolerance)\r\n%%\r\nd = 5;\r\narea_correct = 78.5398;\r\ntolerance = 1e-4;\r\nassert(abs(your_fcn_name(d)-area_correct)\u003ctolerance)\r\n%%\r\nd = 8;\r\narea_correct = 201.0619;\r\ntolerance = 1e-4;\r\nassert(abs(your_fcn_name(d)-area_correct)\u003ctolerance)\r\n%%\r\nd = 15;\r\narea_correct = 706.8583;\r\ntolerance = 1e-4;\r\nassert(abs(your_fcn_name(d)-area_correct)\u003ctolerance)\r\n%%\r\nd = 17;\r\narea_correct = 907.9203;\r\ntolerance = 1e-4;\r\nassert(abs(your_fcn_name(d)-area_correct)\u003ctolerance)","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":4033021,"edited_by":223089,"edited_at":"2024-06-12T15:22:45.000Z","deleted_by":null,"deleted_at":null,"solvers_count":21,"test_suite_updated_at":"2024-06-12T15:22:45.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2024-04-07T14:03:59.000Z","updated_at":"2026-03-05T11:47:22.000Z","published_at":"2024-04-07T14:20:37.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"225\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"225\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou have Ring which consist of inner and outer Circles with \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eRadius r and R which are not given \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003ebut you'll be given Hprizontal distance d which is Tangent to inner circle .\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate the Area of the 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":44742,"title":"Find the area of a triangle having vertices (A,B), (C,D), and (E,F)","description":"Find the area of a triangle using if we have the three vertices of the triangle","description_html":"\u003cp\u003eFind the area of a triangle using if we have the three vertices of the triangle\u003c/p\u003e","function_template":"function A = triarea(x1,y1,x2,y2,x3,y3)\r\nA=b*h/2","test_suite":"%%\r\nx1 = 1;y1=1;x2=0;y2=0;x3=2;y3=0;\r\ny_correct = 1;\r\nassert(isequal(triarea(x1,y1,x2,y2,x3,y3),y_correct))\r\n%%\r\nx1 = 2;y1=1;x2=5;y2=1;x3=4;y3=3;\r\ny_correct = 3;\r\nassert(isequal(triarea(x1,y1,x2,y2,x3,y3),y_correct))\r\n%%\r\nx1 = 4;y1=0;x2=7;y2=2;x3=2;y3=3;\r\ny_correct = 6.5;\r\nassert(isequal(triarea(x1,y1,x2,y2,x3,y3),y_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":38144,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":44,"test_suite_updated_at":"2018-10-04T21:31:40.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2018-10-04T21:07:54.000Z","updated_at":"2026-03-05T11:56:43.000Z","published_at":"2018-10-04T21:31:40.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind the area of a triangle using if we have the three vertices of the triangle\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":50452,"title":"Calculate Triangle Area: A, B and Beta is given","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 275px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 137.5px; transform-origin: 407px 137.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eCalculate Triangle Area: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eA\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eB\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eBeta\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e [degree] is given as follows:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 215px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; 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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e Round the answer to four decimal places\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = AreaTriangle(A, B, Beta)\r\n\r\nend","test_suite":"%% \r\nA = 4; B = 4; Beta = 45; % [degree]\r\n\r\ny_correct = 8\r\nassert(isequal(AreaTriangle(A, B, Beta),y_correct))\r\n\r\n%%\r\nA = 6.39; B = 4.9; Beta = 32.9; % [degree]\r\n\r\ny_correct = 15.3134\r\nassert(isequal(AreaTriangle(A, B, Beta),y_correct))\r\n\r\n%%\r\nA = 257; B = 567; Beta = 23.8; % [degree]\r\n\r\ny_correct = 41099.6329\r\nassert(isequal(AreaTriangle(A, B, Beta),y_correct))\r\n\r\n%%\r\nA = 2*pi; B = 3*pi; Beta = 56.3; % [degree]\r\n\r\ny_correct = 29.6088\r\nassert(isequal(AreaTriangle(A, B, Beta),y_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":487522,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":24,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-02-18T16:37:21.000Z","updated_at":"2026-03-14T18:27:52.000Z","published_at":"2021-02-18T16:44:29.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate Triangle Area: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eB\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eBeta\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e [degree] is given as follows:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"209\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"269\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e Round the answer to four decimal 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VI0ye8Wwvox5Ea9Q9MsPnkNUtFXBWYBfSi6zbfa3LnDTU66ytvIOp91OBS4L1SEVcIshfal5q/8vZtB0qvPf6oyZOvffLOsw/cEvSU8Qaq0AORAisFuvF/dM/bB7bd+cWqVJh/9dfvff79R2dOH/nPel4RX4VlQQ32GnflP/7hw4fP2Qq5/O4jR+4J5rRRmlfEd0hFXDGMbvy//+///cX5Hxmu2/bhff4PbrNJgYekIq4cxkPgv/z27+bcLl7+5Ftfw0ufyHSQFw8hwzFUxGE3/itHnrYs93wg2yVSYPVxOnT6wnvfvx0v62Uxr4h3SmIoyTIqNjmxgL767YohYz3YpMBSEVcVN0Onl7zxEF55J7+DV8Sl8Kkqi+lGDSKswcUv1ekSXxgWKXBccGUBnUotevr5Oqqjq7gU2PH8SSECMvQ8OIqwNvOffByvXMOlwDulIq427rvxi17ztk9p3Ef/KUKkwKoDC+hxhI64+tRKvHJOukWkwDED3Xh3VgAbrFkaTsls5FLgZVgXFIb+lp0PnSYed/W4YZMC90lFPA6gG9+E0CmLjjjvp2R7TtJ/xOSkVMRjAm0ZHFpAV3HLq3hRi1yfSIFjyRq6Y20InTP/LUfqnmW8Ir5REiM2UAHKoQU047tVw+rPh00K3CIV8fgAC+guhG5Y9P5VeHU+CmPVibFPKuKxwp0FNOe+uYetNOw0vzcQKXDMyNGfdR9Cdyz5cI4TBuu4FNipv5+gCu4soO388rxHoLkUeFgq4rEjS2YzboZOV/PQfXjBsUmBpSIeR6gbf9brvfvaS3hRTaaDV8Sl8BlHPAydZiz5aNbpg2wnlwIvxroQL2AB7f202BGbH6NtOEaXVMRjilsL6Nk8uhkvTLgU+JhUxOMLLKDrmMZ5b5VnfH5IpMCJwVs3vpqZ1CjwinijJEacWUe30bEF9DmwUoMPx9gtFfGY47UbX8XtZmpwKfAuqYjHnVV0J90NnbaxoZwajeb4BQuRAicA7934GTb8eTOXAi/HF4QYk6e76W7otI3Mn/09fReTqX6piCcCsoA+XUdRKtMx8bv/Mr+LwaRUxBOCt6HTVWR7Js6e/Z/fmt/FqIhL4TMp9Jl31I0FNCO31ayI//7fzG8jUuAE4cECuoqlqIj/6++N/324TRIjQXSZt9aNBfQMM1Lg3/732bP7pSKeKOroxhdGZyri//k7GY6RNNro1q5B6JwGXhH/AywLScFrN34tlwK7zyxBdTxYQJfhUuARqYgnEQ/d+HQrjbcnZDhGQnFvAZ1pFymwFoybN9i5BXSWD8fokcRIKi4toG1S4G6piCeXUfMeTzorYeb66RQTcVwq4knGjQV0flCkwBoxaN7mKQdnh1ZwKXCTJEaycdyN51LgPVIRTzywgK41m7GBtjFgXKTAyQfd+BoW0I17zH8FRAqsBQ6GTqebuBTYU+deiBvoxu9EeA5swzEGpCKuCcwC+hzwqcCnpSKuD/SOsBeRnWw3r4hL4VMf5uzG53pZRbxjIdYFHaAziIcQMWw+ee1SEdeK83fj+VTgg1IR1w2a8Tox674XRlhFXAqf2nGebvwaLgV2Z5kjJIJh897bhk7z4RhjUhHXEXTjexGacCnwqFTE9WTW0Ol060FziRApsLbAAnoAYSrTxqXAXk9GC7GHW0Av5FLgXqmI6wssoEfMwCYFloq41lR143P9vCIuhU+tSR8382C8vFEZECmwUIXVjV/OpcDNkhjaQ9vUv2aFz71SEResbnw14pMnGDAZsIFIgQUTWEBbTO+QxBCIv0JOmEwNSkVcACuQFAYyHEOoAh5rZUQKLHAKI/9sJMZEhySGYOdPzp79G6mIC+cgveuPpfApcFKp/wfUk0GGNJB3NQAAAABJRU5ErkJggg==\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":2284,"title":"Find the area of the four walls ","description":"If length, breadth and height of the walls are given, find the area of the four walls.","description_html":"\u003cp\u003eIf length, breadth and height of the walls are given, find the area of the four walls.\u003c/p\u003e","function_template":"function a = your_fcn_name(l,b,h)\r\n %your code\r\nend","test_suite":"%%\r\nl = 1;\r\nb = 1;\r\nh = 1;\r\ny_correct = 4;\r\nassert(isequal(your_fcn_name(l,b,h),y_correct))\r\n\r\n%%\r\nl = 20;\r\nb = 10;\r\nh = 15;\r\ny_correct = 900;\r\nassert(isequal(your_fcn_name(l,b,h),y_correct))\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":2,"created_by":22816,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":292,"test_suite_updated_at":"2014-04-14T15:16:41.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2014-04-14T05:59:25.000Z","updated_at":"2026-03-05T16:44:02.000Z","published_at":"2014-04-14T05:59:25.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf length, breadth and height of the walls are given, find the area of the four walls.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":56255,"title":"Area under the curve","description":"Compute area under the curve specified by points stored in y, where y is in range (0,inf) and x time step is 1. \r\nnote: please round the result to 4 decimals.\r\nexample: y=[1 2 3 5 8 9 10]\r\n area=32.5000","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 111px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 55.5px; transform-origin: 407px 55.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eCompute area under the curve specified by points stored in \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003ey, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003ey\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e is in range (0,inf) and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003ex\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e time step is 1. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; \"\u003enote: please round the result to 4 decimals.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eexample: y=[1 2 3 5 8 9 10]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e area=32.5000\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function area = your_fcn_name(y)\r\n area= 'Your solution'\r\nend","test_suite":"%%\r\nx = [1 2 3 5 8 9 10];\r\ny_correct = 32.5000;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\n\r\nx = [43 10 27 16 29 45 53 46 88 52 95 64 96 25 68 29 68];\r\ny_correct = 798.5000;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\n\r\nx=[70 7 26 23 67 85 35 79 68 1];\r\ny_correct = 425.5000;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\n\r\nx=[0.993183755212665 0.480756369506705 0.827750131864470 0.603238265822881 0.817841681068066 0.955547170535556 0.650378193390669 0.627647346270777 0.646563331304310 0.062133128691720];\r\ny_correct = 6.1374;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":3,"created_by":1739584,"edited_by":1739584,"edited_at":"2022-10-10T12:14:42.000Z","deleted_by":null,"deleted_at":null,"solvers_count":26,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-10-10T12:13:31.000Z","updated_at":"2026-03-05T14:10:14.000Z","published_at":"2022-10-10T12:14:42.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCompute area under the curve specified by points stored in \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e is in range (0,inf) and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e time step is 1. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003enote: please round the result to 4 decimals.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003eexample: y=[1 2 3 5 8 9 10]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e area=32.5000\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":425,"title":"ranch area?","description":"Your friend has a ranch with four distinct boundary lines. Three boundary lines are ideal straight roads: (1) North Club Road, (2) East Cathedral Road, and (3) North Market Road. The fourth boundary line is the Threadwater Canal. The length of the second boundary line is exactly one mile. You have visualized that any point on the Threadwater Canal is defined by cartesian coordinates x and y in miles, where x is its distance from North Club Road, and y is its distance from East Cathedral Road. A surveyor has found the function y(x) for you. She also told you that one square mile is 640 acres. She wants you to calculate the area of this ranch in acres.","description_html":"\u003cp\u003eYour friend has a ranch with four distinct boundary lines. Three boundary lines are ideal straight roads: (1) North Club Road, (2) East Cathedral Road, and (3) North Market Road. The fourth boundary line is the Threadwater Canal. The length of the second boundary line is exactly one mile. You have visualized that any point on the Threadwater Canal is defined by cartesian coordinates x and y in miles, where x is its distance from North Club Road, and y is its distance from East Cathedral Road. A surveyor has found the function y(x) for you. She also told you that one square mile is 640 acres. She wants you to calculate the area of this ranch in acres.\u003c/p\u003e","function_template":"function acres = ranch(y)\r\n acres=y(1)^2;\r\nend","test_suite":"%%\r\ny=@(x)1+x/10^10;\r\nacres=round(ranch(y));\r\nacres_correct = 640;\r\nassert(acres==acres_correct)\r\n%%\r\ny=@(x)0.5+x/10^10;\r\nacres=round(ranch(y));\r\nacres_correct = 320;\r\nassert(acres==acres_correct)\r\n%%\r\ny=@(x)1+x;\r\nacres=round(ranch(y));\r\nacres_correct = 960;\r\nassert(acres==acres_correct)\r\n%%\r\ny=@(x)2+sin(x);\r\nacres=round(ranch(y));\r\nacres_correct = 1574;\r\nassert(acres==acres_correct)\r\n%%\r\ny=@(x)3+cos(x);\r\nacres=round(ranch(y));\r\nacres_correct = 2459;\r\nassert(acres==acres_correct)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":166,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":52,"test_suite_updated_at":"2012-02-29T07:24:36.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-02-29T03:37:08.000Z","updated_at":"2026-03-19T18:32:18.000Z","published_at":"2012-02-29T07:24:36.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYour friend has a ranch with four distinct boundary lines. Three boundary lines are ideal straight roads: (1) North Club Road, (2) East Cathedral Road, and (3) North Market Road. The fourth boundary line is the Threadwater Canal. The length of the second boundary line is exactly one mile. You have visualized that any point on the Threadwater Canal is defined by cartesian coordinates x and y in miles, where x is its distance from North Club Road, and y is its distance from East Cathedral Road. A surveyor has found the function y(x) for you. She also told you that one square mile is 640 acres. She wants you to calculate the area of this ranch in acres.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":60166,"title":"Recursive triangle area","description":"Given triangle 1 with sides of length a, b, and c. Triangle 2 is constructed within triangle 1 by bisecting each side. Triangle 3 is constructed within triangle 2 by bisecting each of triangle 2's sides. And so on. \r\nFind the area of triangle n.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 71.9661px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 359.492px 35.9766px; transform-origin: 359.499px 35.9831px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 41.9792px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 336.497px 20.9896px; text-align: left; transform-origin: 336.497px 20.9896px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven triangle 1 with sides of length a, b, and c. Triangle 2 is constructed within triangle 1 by bisecting each side. Triangle 3 is constructed within triangle 2 by bisecting each of triangle 2's sides. And so on. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9896px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 336.497px 10.4948px; text-align: left; transform-origin: 336.497px 10.4948px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFind the area of triangle n.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function area = your_fcn_name(a,b,c,n)\r\n area = a+b+c+n;\r\nend","test_suite":"%%\r\na=1;b=1;c=sqrt(2);n=1;\r\ny_correct = 0.50;\r\nassert(your_fcn_name(a,b,c,n) - y_correct \u003c y_correct/1000)\r\n\r\n\r\n%%\r\na=100;b=100;c=100;n=2;\r\ny_correct = 1082.53;\r\nassert(your_fcn_name(a,b,c,n) - y_correct \u003c y_correct/1000)\r\n\r\n\r\n%%\r\na=13;b=33;c=44;n=4;\r\ny_correct = 2.0540;\r\nassert(your_fcn_name(a,b,c,n) - y_correct \u003c y_correct/1000)","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":3293343,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":16,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-04-30T18:08:43.000Z","updated_at":"2026-03-11T15:33:11.000Z","published_at":"2024-04-30T18:08:43.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven triangle 1 with sides of length a, b, and c. Triangle 2 is constructed within triangle 1 by bisecting each side. Triangle 3 is constructed within triangle 2 by bisecting each of triangle 2's sides. And so on. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind the area of triangle n.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":2944,"title":"Areas","description":"Given certain dimensions determine the area of that shape. If given only one value assume its the radius. Use round(x) to round each area\r\n\r\nx= [2 2 4 4]\r\n\r\narea = 8 \r\n\r\nx=[3 4 5]\r\n\r\narea = 6","description_html":"\u003cp\u003eGiven certain dimensions determine the area of that shape. If given only one value assume its the radius. Use round(x) to round each area\u003c/p\u003e\u003cp\u003ex= [2 2 4 4]\u003c/p\u003e\u003cp\u003earea = 8\u003c/p\u003e\u003cp\u003ex=[3 4 5]\u003c/p\u003e\u003cp\u003earea = 6\u003c/p\u003e","function_template":"function y = your_fcn_name(x)\r\n y = round(x);\r\nend","test_suite":"%%\r\nx = 5;\r\ny_correct = 79;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n%%\r\nx = [2 2 2 2];\r\ny_correct = 4;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n%%\r\nx = [5 12 13];\r\ny_correct = 30;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n%%\r\nx = [2 6 2 6];\r\ny_correct = 12;\r\nassert(isequal(your_fcn_name(x),y_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":33703,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":83,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2015-02-04T17:37:46.000Z","updated_at":"2026-04-02T10:14:43.000Z","published_at":"2015-02-04T17:37:46.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven certain dimensions determine the area of that shape. If given only one value assume its the radius. Use round(x) to round each area\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ex= [2 2 4 4]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003earea = 8\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ex=[3 4 5]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003earea = 6\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":45337,"title":"Area-03","description":"There are two circles of equal size are inscribed inside a square. They are tangent to each other.\r\n\r\n\u003chttps://serving.photos.photobox.com/4629487514d477b90123a8d594e9bdaa5ddba8e2ac82569375c49cd5551dd3acffb751ed.jpg\u003e\r\n\r\nGiven the side length of the square, find the radius of the circles.","description_html":"\u003cp\u003eThere are two circles of equal size are inscribed inside a square. They are tangent to each other.\u003c/p\u003e\u003cp\u003e\u003ca href = \"https://serving.photos.photobox.com/4629487514d477b90123a8d594e9bdaa5ddba8e2ac82569375c49cd5551dd3acffb751ed.jpg\"\u003ehttps://serving.photos.photobox.com/4629487514d477b90123a8d594e9bdaa5ddba8e2ac82569375c49cd5551dd3acffb751ed.jpg\u003c/a\u003e\u003c/p\u003e\u003cp\u003eGiven the side length of the square, find the radius of the circles.\u003c/p\u003e","function_template":"function y =inscribed_circle_3(a)\r\n y = x;\r\nend","test_suite":"%%\r\na = 1;\r\ny_correct = .2929;\r\nassert(abs(inscribed_circle_3(a)-y_correct)\u003c0.001)\r\n\r\n%%\r\na = 10;\r\ny_correct = 2.9289;\r\nassert(abs(inscribed_circle_3(a)-y_correct)\u003c0.001)\r\n\r\n%%\r\na = 23.6;\r\ny_correct = 6.9123;\r\nassert(abs(inscribed_circle_3(a)-y_correct)\u003c0.001)\r\n\r\n%%\r\na = 0;\r\ny_correct = 0;\r\nassert(abs(inscribed_circle_3(a)-y_correct)\u003c0.001)\r\n\r\n%%\r\na = pi;\r\ny_correct = 0.9202;\r\nassert(abs(inscribed_circle_3(a)-y_correct)\u003c0.001)","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":363598,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":32,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-02-17T06:35:50.000Z","updated_at":"2025-12-07T20:32:03.000Z","published_at":"2020-02-17T06:36:40.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThere are two circles of equal size are inscribed inside a square. They are tangent to each other.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://serving.photos.photobox.com/4629487514d477b90123a8d594e9bdaa5ddba8e2ac82569375c49cd5551dd3acffb751ed.jpg\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026lt;https://serving.photos.photobox.com/4629487514d477b90123a8d594e9bdaa5ddba8e2ac82569375c49cd5551dd3acffb751ed.jpg\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026gt;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven the side length of the square, find the radius of the circles.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":45334,"title":"Area-02","description":"Given the radius of the circle inscribed in a square, find the area of the square that can be fitted perfectly in the corner.\r\n\r\n\u003chttps://serving.photos.photobox.com/951462430971a9cfd5dff5f0f3e94dee75ee1bb89ddb5e3e47e18f79b04d3cd720c92cb2.jpg\u003e","description_html":"\u003cp\u003eGiven the radius of the circle inscribed in a square, find the area of the square that can be fitted perfectly in the corner.\u003c/p\u003e\u003cp\u003e\u003ca href = \"https://serving.photos.photobox.com/951462430971a9cfd5dff5f0f3e94dee75ee1bb89ddb5e3e47e18f79b04d3cd720c92cb2.jpg\"\u003ehttps://serving.photos.photobox.com/951462430971a9cfd5dff5f0f3e94dee75ee1bb89ddb5e3e47e18f79b04d3cd720c92cb2.jpg\u003c/a\u003e\u003c/p\u003e","function_template":"function y = inscribed_circle_2(r)\r\n y = x;\r\nend","test_suite":"%%\r\nr=1;\r\ny_correct = 0.0858;\r\nassert(abs(inscribed_circle_2(r)-y_correct)\u003c0.001)\r\n%%\r\nr=11;\r\ny_correct = 10.3802;\r\nassert(abs(inscribed_circle_2(r)-y_correct)\u003c0.001)\r\n%%\r\nr=45.98;\r\ny_correct = 181.3663;\r\nassert(abs(inscribed_circle_2(r)-y_correct)\u003c0.001)\r\n%%\r\nr=0;\r\ny_correct = 0;\r\nassert(abs(inscribed_circle_2(r)-y_correct)\u003c0.001)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":363598,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":42,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-02-16T18:38:38.000Z","updated_at":"2025-08-03T22:41:51.000Z","published_at":"2020-02-16T18:39:11.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven the radius of the circle inscribed in a square, find the area of the square that can be fitted perfectly in the corner.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://serving.photos.photobox.com/951462430971a9cfd5dff5f0f3e94dee75ee1bb89ddb5e3e47e18f79b04d3cd720c92cb2.jpg\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026lt;https://serving.photos.photobox.com/951462430971a9cfd5dff5f0f3e94dee75ee1bb89ddb5e3e47e18f79b04d3cd720c92cb2.jpg\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026gt;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":50504,"title":"Find the area between curves (P3)","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 541px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 270.5px; transform-origin: 407px 270.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20px; border-block-end-color: rgb(60, 60, 60); border-block-start-color: rgb(60, 60, 60); border-bottom-color: rgb(60, 60, 60); border-inline-end-color: rgb(60, 60, 60); border-inline-start-color: rgb(60, 60, 60); border-left-color: rgb(60, 60, 60); border-right-color: rgb(60, 60, 60); border-top-color: rgb(60, 60, 60); caret-color: rgb(60, 60, 60); color: rgb(60, 60, 60); column-rule-color: rgb(60, 60, 60); font-family: Helvetica, Arial, sans-serif; font-size: 20px; font-weight: 700; line-height: 20px; margin-block-end: 5px; margin-block-start: 3px; margin-bottom: 5px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 3px; outline-color: rgb(60, 60, 60); perspective-origin: 384px 10px; text-align: left; text-decoration: none; text-decoration-color: rgb(60, 60, 60); transform-origin: 384px 10px; white-space: pre-wrap; margin-left: 4px; margin-top: 3px; margin-bottom: 5px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eArea between curves - Problem 3\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFind the area enclosed by the curves \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"94.5\" height=\"19\" style=\"width: 94.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"62.5\" height=\"19\" style=\"width: 62.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e for different \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ea\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eb\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e coefficients\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 426px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 213px; text-align: left; transform-origin: 384px 213px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline\" 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width=\"87.5\" height=\"18\" style=\"width: 87.5px; height: 18px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = AreaCurves(a, b)\r\n \r\nend","test_suite":"%%\r\nfiletext = fileread('AreaCurves.m');\r\nfor ii = [0.4208, 0.5101, 0.2569, 0.1252, 1.1838]\r\n assert(isempty(strfind(filetext, num2str(ii))),'Do NOT use provided answers in your solution')\r\nend\r\nassert(isempty(strfind(filetext, 'if')),'if: Forbidden')\r\nassert(isempty(strfind(filetext, 'switch')),'switch: Forbidden')\r\n%%\r\na = 1; \r\nb = 0.5;\r\n\r\ny_correct = 0.4208;\r\nassert(abs(AreaCurves(a,b)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = 2; \r\nb = 0.5; \r\n\r\ny_correct = 0.5101;\r\nassert(abs(AreaCurves(a,b)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = exp(1); \r\nb = 1; \r\n\r\ny_correct = 0.2569;\r\nassert(abs(AreaCurves(a,b)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = 0.5;\r\nb = 0.4;\r\n\r\ny_correct = 0.1252;\r\nassert(abs(AreaCurves(a,b)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = sqrt(2);\r\nb = 0.1;\r\n\r\ny_correct = 1.1838;\r\nassert(abs(AreaCurves(a,b)-y_correct)\u003c1e-4)\r\n\r\n","published":true,"deleted":false,"likes_count":4,"comments_count":0,"created_by":487522,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":18,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-02-19T18:50:42.000Z","updated_at":"2026-02-05T14:11:12.000Z","published_at":"2021-02-19T18:51:35.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"heading\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eArea between curves - Problem 3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind the area enclosed by the curves \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ef(x) = sin(ax)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eg(x) = bx\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e for different \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e coefficients\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml 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w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eg(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea=1 , 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cow is tied to an outside corner of a rectangular barn of size (a,b) with a rope of length l. What is the maximum area the cow can graze outside the barn?\r\n\r\n\u003chttps://serving.photos.photobox.com/495639807b8e93bb90ab3c212fe921e51fefc77e0b8756d28871096f5482839b5e5d4bb8.jpg\u003e\r\n\r\nNb.the test cases are simpler for this problem. They'll be enhanced in the next case.","description_html":"\u003cp\u003eA cow is tied to an outside corner of a rectangular barn of size (a,b) with a rope of length l. What is the maximum area the cow can graze outside the barn?\u003c/p\u003e\u003cp\u003e\u003ca href = \"https://serving.photos.photobox.com/495639807b8e93bb90ab3c212fe921e51fefc77e0b8756d28871096f5482839b5e5d4bb8.jpg\"\u003ehttps://serving.photos.photobox.com/495639807b8e93bb90ab3c212fe921e51fefc77e0b8756d28871096f5482839b5e5d4bb8.jpg\u003c/a\u003e\u003c/p\u003e\u003cp\u003eNb.the test cases are simpler for this problem. They'll be enhanced in the next case.\u003c/p\u003e","function_template":"function y = grazing_01(a,b,l)\r\n y = x;\r\nend","test_suite":"%%\r\nassert(abs(grazing_01(10,20,5)-58.9049)\u003c0.001)\r\n%%\r\nassert(abs(grazing_01(5,25,2)-9.4248)\u003c0.001)\r\n%%\r\nassert(abs(grazing_01(5,25,8)-157.8650)\u003c0.001)\r\n%%\r\nassert(abs(grazing_01(20,20,20)- 942.4778)\u003c0.001)\r\n%%\r\nassert(abs(grazing_01(10,20,0)-0)\u003c0.001)\r\n%%\r\nassert(abs(grazing_01(12,20,25)-1624.9888)\u003c0.001)\r\n\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":3,"created_by":363598,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":19,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-02-20T10:45:47.000Z","updated_at":"2026-01-29T12:35:16.000Z","published_at":"2020-02-20T11:20:35.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA cow is tied to an outside corner of a rectangular barn of size (a,b) with a rope of length l. What is the maximum area the cow can graze outside the barn?\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://serving.photos.photobox.com/495639807b8e93bb90ab3c212fe921e51fefc77e0b8756d28871096f5482839b5e5d4bb8.jpg\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026lt;https://serving.photos.photobox.com/495639807b8e93bb90ab3c212fe921e51fefc77e0b8756d28871096f5482839b5e5d4bb8.jpg\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026gt;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNb.the test cases are simpler for this problem. They'll be enhanced in the next case.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":61076,"title":"Covering rectangle area of a four-pointed star polygon","description":"Given the four-pointed star polygon formed by the rectangle, with dimensions l1xl2, and four triangles, with height, h, from their bases to the apices, find the rectangle, with dimensions y1xy2, such that has the same area of the given star polygon, and covers the given rectangle (cf. figure below). Given x=[l1 l2 h], return y=[y1 y2].\r\n\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 520.8px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 260.4px; transform-origin: 408px 260.4px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 31.5px; text-align: left; transform-origin: 385px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven the four-pointed star polygon formed by the rectangle, with dimensions \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003el1xl2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and four triangles, with height, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eh,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e from their bases to the apices, find the rectangle, with dimensions \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ey1xy2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, such that has the same area of the given star polygon, and covers the given rectangle (cf. figure below). Given \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ex=[l1 l2 h]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, return \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ey=[y1 y2]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 418.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 209.4px; text-align: left; transform-origin: 385px 209.4px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline\" 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\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = covering(x)\r\n y = x;\r\nend","test_suite":"%%\r\nx = [2 7 4];\r\ny_correct = [5 10];\r\nassert(isequal(covering(x),y_correct))\r\n\r\n%%\r\nx = [7 2 1];\r\ny_correct = [2.5 -2.5] + 1.5*sqrt(13);\r\ntolerance = 1e-12;\r\nassert(all(abs(covering(x)-y_correct)\u003ctolerance))\r\n\r\n%%\r\nx = [5 2 1];\r\ny_correct = [3 -3]/2 + sqrt(77)/2;\r\ntolerance = 1e-12;\r\nassert(all(abs(covering(x)-y_correct)\u003ctolerance))\r\n\r\n%%\r\nfiletext = fileread('covering.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\nx = [7 9 5];\r\ny_correct = [11 13];\r\nassert(isequal(covering(x),y_correct))\r\n\r\n%%\r\nx = [7 9 1];\r\ny_correct = [-1 1] + 4*sqrt(5);\r\ntolerance = 1e-12;\r\nassert(all(abs(covering(x)-y_correct)\u003ctolerance))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":1,"created_by":4993982,"edited_by":4993982,"edited_at":"2025-11-16T14:03:25.000Z","deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-11-15T16:57:30.000Z","updated_at":"2026-03-27T12:50:09.000Z","published_at":"2025-11-16T14:03:25.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven the four-pointed star polygon formed by the rectangle, with dimensions \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003el1xl2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, and four triangles, with height, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eh,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e from their bases to the apices, find the rectangle, with dimensions \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey1xy2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, such that has the same area of the given star polygon, and covers the given rectangle (cf. figure below). Given \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex=[l1 l2 h]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, return \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey=[y1 y2]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"413\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"508\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc 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- 01","description":"Find the area of a five-pointed star inscribed in a circle of radius r.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 21px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 10.5px; transform-origin: 407px 10.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 207.5px 8px; transform-origin: 207.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFind the area of a five-pointed star inscribed in a circle of radius r.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y =yoonir_02(r)","test_suite":"%%\r\nassert(abs(yoonir_02(10)-112.257)\u003c0.001)\r\n\r\n%%\r\nassert(abs(yoonir_02(3)-10.1031)\u003c0.001)\r\n\r\n%%\r\nassert(abs(yoonir_02(pi)-11.0793)\u003c0.001)\r\n\r\n%%\r\nassert(abs(yoonir_02(pi^5)-105126.4832)\u003c0.001)\r\n\r\n%%\r\nassert(abs(yoonir_02(1)-1.1226)\u003c0.001)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":363598,"edited_by":223089,"edited_at":"2023-01-14T09:16:04.000Z","deleted_by":null,"deleted_at":null,"solvers_count":24,"test_suite_updated_at":"2023-01-14T09:16:04.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2020-03-31T00:21:25.000Z","updated_at":"2026-01-03T15:34:12.000Z","published_at":"2020-03-31T00:21:25.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind the area of a five-pointed star inscribed in a circle of radius r.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":2239,"title":"Avalaible area: wall construction","description":"You need to build a wall to enclose a certain area. Calculate the available area after you build the wall. \r\n\r\nAssumptions\r\n\r\n* Wall could consist of multiple layers of material. example: a wall of 2 materials: rock of 1 meter thickness and wood of 0.5 meter thickness. The total thickness of the wall 1.5 meters.\r\n* x and y: the dimensions of the area before the wall is build. example: x=5m,y=4m. Total area 20m^2.\r\n\r\nExample\r\n\r\nArea of dimensions x=5m,y=5m and wall of 3 materials with thicknesses: 0.2m,0.1m,1m . Avalaible area after the wall is build : 5.76m^2\r\n\r\n \u003e\u003e AvailableArea(5,5,0.2,0.1,1) \r\n \u003e\u003e ans=5.76\r\n","description_html":"\u003cp\u003eYou need to build a wall to enclose a certain area. Calculate the available area after you build the wall.\u003c/p\u003e\u003cp\u003eAssumptions\u003c/p\u003e\u003cul\u003e\u003cli\u003eWall could consist of multiple layers of material. example: a wall of 2 materials: rock of 1 meter thickness and wood of 0.5 meter thickness. The total thickness of the wall 1.5 meters.\u003c/li\u003e\u003cli\u003ex and y: the dimensions of the area before the wall is build. example: x=5m,y=4m. Total area 20m^2.\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eExample\u003c/p\u003e\u003cp\u003eArea of dimensions x=5m,y=5m and wall of 3 materials with thicknesses: 0.2m,0.1m,1m . Avalaible area after the wall is build : 5.76m^2\u003c/p\u003e\u003cpre\u003e \u0026gt;\u0026gt; AvailableArea(5,5,0.2,0.1,1) \r\n \u0026gt;\u0026gt; ans=5.76\u003c/pre\u003e","function_template":"function A = AvailableArea(x,y,varargin)\r\n %A=..\r\nend","test_suite":"%%\r\ny_correct = 64;\r\nassert(isequal(AvailableArea(10,10,1),y_correct))\r\n\r\n%%\r\n\r\ny_correct = 3844;\r\nassert(isequal(AvailableArea(70,70,1,2,1),y_correct))\r\n\r\n%%\r\n\r\ny_correct = 49;\r\nassert(isequal(AvailableArea(9,9,1),y_correct))\r\n\r\n%%\r\n\r\ny_correct = 3900;\r\nassert(isequal(AvailableArea(75,70,1,3,1),y_correct))\r\n\r\n\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":24008,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":72,"test_suite_updated_at":"2014-03-10T20:27:07.000Z","rescore_all_solutions":false,"group_id":26,"created_at":"2014-03-08T16:23:45.000Z","updated_at":"2026-02-19T10:38:26.000Z","published_at":"2014-03-08T16:24:08.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou need to build a wall to enclose a certain area. Calculate the available area after you build the wall.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAssumptions\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWall could consist of multiple layers of material. example: a wall of 2 materials: rock of 1 meter thickness and wood of 0.5 meter thickness. The total thickness of the wall 1.5 meters.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ex and y: the dimensions of the area before the wall is build. example: x=5m,y=4m. Total area 20m^2.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eArea of dimensions x=5m,y=5m and wall of 3 materials with thicknesses: 0.2m,0.1m,1m . Avalaible area after the wall is build : 5.76m^2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ \u003e\u003e AvailableArea(5,5,0.2,0.1,1) \\n \u003e\u003e ans=5.76]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":49072,"title":"Area Conversion 2","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 21px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 332px 10.5px; transform-origin: 332px 10.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 309px 10.5px; text-align: left; transform-origin: 309px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eGiven an area in hectares, convert it to acres.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = convert_stuff(x)\r\n y = x*713*pi;\r\nend","test_suite":"%%\r\nx = 121;\r\ny_correct = 299.0031;\r\nassert(isequal(convert_stuff(x),y_correct))\r\n%%\r\nx = 333;\r\ny_correct = 822.8763;\r\nassert(isequal(convert_stuff(x),y_correct))\r\n%%\r\nx = 1.2;\r\ny_correct = 2.9653;\r\nassert(isequal(convert_stuff(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":6,"comments_count":2,"created_by":180632,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":834,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-12-22T21:57:51.000Z","updated_at":"2026-04-13T04:10:57.000Z","published_at":"2020-12-22T21:57:51.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven an area in hectares, convert it to acres.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":43029,"title":"Area of polygon","description":"Given the vertices in vectors X,Y, return the area of the polygon they define.","description_html":"\u003cp\u003eGiven the vertices in vectors X,Y, return the area of the polygon they define.\u003c/p\u003e","function_template":"function A = polygon_area(x,y)\r\n A = x+y;\r\nend","test_suite":"%%\r\nL=linspace(0,2.*pi,9);\r\nx = 1.2*cos(L)';\r\ny = 1.2*sin(L)';\r\na_correct = 4.072935;\r\nassert( abs(polygon_area(x,y)-a_correct) \u003c 1e-04 )\r\n%%\r\nx = (1:10)';\r\ny = [0,ones(1,9)]';\r\na_correct = 4;\r\nassert( isequal(polygon_area(x,y),a_correct) )\r\n%%\r\nx=[0,5,3]';\r\ny=[0,0,9]';\r\na_correct = 22.5;\r\nassert( abs(polygon_area(x,y)-a_correct) \u003c 1e-04 )\r\n%%\r\nx=[0,5,3,11]';\r\ny=[0,0,9,126]';\r\na_correct = 162;\r\nassert( isequal(polygon_area(x,y),a_correct) )","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":85738,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":45,"test_suite_updated_at":"2016-10-05T06:02:53.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2016-10-05T05:00:48.000Z","updated_at":"2025-10-28T03:21:32.000Z","published_at":"2016-10-05T06:02:53.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven the vertices in vectors X,Y, return the area of the polygon they define.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":61088,"title":"Covering a four-pointed star polygon by circles","description":"Given the area, A, of a star polygon formed by the rectangle, with dimensions L×2L, and four triangles, with height h from their bases to the vertices, consider the circles that cover the distances between opposite vertices (cf. figure below).\r\nGiven (A,h), return the 2x2 matrix M = [A1/π a1; A2/π a2], where\r\nin the first row (i=1), A1 stands for the area of the circle that covers the minimum distance (cf. left figure), and a1 stands for the logical 1 if A1 is smaller than or reaches the area A or a1 stands for the logical 0 if A1 surpasses A;\r\nin the second row (i=2), A2 stands for the area of the circle that covers the maximum distance (cf. right figure), and a2 has the same previous false-true meaning relative to the areas A2 and A. Obviously, that A2 \u003e A holds true, then a2 = 0.\r\ninput: (A, h)\r\noutput: M = [A1/π a1; A2/π 0]\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 748.987px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 408px 374.487px; transform-origin: 408px 374.494px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven the area, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, of a star polygon formed by the rectangle, with dimensions \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eL\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e×\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e2L\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and four triangles, with height \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eh\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e from their bases to the vertices, consider the circles that cover the distances between opposite vertices (cf. figure below).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(A,h)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, return the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ex\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e matrix \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eM = [A1/π a1; A2/π a2]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, where\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 102.188px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 51.0875px; transform-origin: 391px 51.0938px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 40.875px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 20.4375px; text-align: left; transform-origin: 363px 20.4375px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ein the first row \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(i=1)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e stands for the area of the circle that covers the minimum distance (cf. left figure), and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ea1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e stands for the logical \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e if \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is smaller than or reaches the area \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e or \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ea1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e stands for the logical \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e0\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e if \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e surpasses \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 61.3125px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 30.65px; text-align: left; transform-origin: 363px 30.6562px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ein the second row \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(i=2)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e stands for the area of the circle that covers the maximum distance (cf. right figure), and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ea2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e has the same previous false-true meaning relative to the areas \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Obviously, that A2 \u0026gt; A holds true, then \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ea2 = 0\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003einput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(A, h)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eoutput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eM = [A1/π a1; A2/π 0]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 484.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 242.4px; text-align: left; transform-origin: 384px 242.4px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cimg class=\"imageNode\" width=\"601\" height=\"479\" style=\"vertical-align: baseline;width: 601px;height: 479px\" 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\" alt=\"Covering by circles\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function M = covering_by_circles(A,h)\r\n M = x;\r\nend","test_suite":"%%\r\nA = 27;\r\nh = 1;\r\nM_correct = [6.25 1; 16 0];\r\nassert(isequal(covering_by_circles(A,h),M_correct))\r\n\r\n%%\r\nA = 36;\r\nh = 2;\r\nM_correct = [12.25 0; 25 0];\r\nassert(isequal(covering_by_circles(A,h),M_correct))\r\n\r\n%%\r\nA = 56;\r\nh = 2;\r\nM_correct = [16 1; 36 0];\r\nassert(isequal(covering_by_circles(A,h),M_correct))\r\n\r\n%%\r\nfiletext = fileread('covering_by_circles.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\nA = 68;\r\nh = 1.2;\r\nM_correct = [13.69 1; 38.44 0];\r\nassert(all(isapprox(covering_by_circles(A,h),M_correct), 'all'))\r\n\r\n%%\r\nA = 89;\r\nh = 2.6;\r\nM_correct = [26.01 1; 57.76 0];\r\nassert(all(isapprox(covering_by_circles(A,h),M_correct), 'all'))","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":4993982,"edited_by":4993982,"edited_at":"2025-11-30T13:14:56.000Z","deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-11-29T14:26:03.000Z","updated_at":"2026-03-22T14:02:11.000Z","published_at":"2025-11-30T13:14:56.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven the area, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, of a star polygon formed by the rectangle, with dimensions \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eL\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e×\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2L\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, and four triangles, with height \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e from their bases to the vertices, consider the circles that cover the distances between opposite vertices (cf. figure below).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(A,h)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, return the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e matrix \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eM = [A1/π a1; A2/π a2]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, where\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ein the first row \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(i=1)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e stands for the area of the circle that covers the minimum distance (cf. left figure), and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e stands for the logical \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e if \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is smaller than or reaches the area \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e or \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e stands for the logical \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e0\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e if \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e surpasses \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ein the second row \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(i=2)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e stands for the area of the circle that covers the maximum distance (cf. right figure), and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e has the same previous false-true meaning relative to the areas \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. Obviously, that A2 \u0026gt; A holds true, then \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea2 = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003einput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(A, h)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":45271,"title":"Calculate triangle area","description":"Imagine that you want to calculate the areas of some triangles given in matrix form. First the coordinates of the vertices of the triangles are in a matrix called coords where the line number represents the vertex number and the column number is the dimension, in this case it is equal to 2 (x, y). The way the nodes connect are found in the lnods matrix where the line number is the triangle number and the column number is the vertex number that makes up each triangle (v_i, v_j, v_k).","description_html":"\u003cp\u003eImagine that you want to calculate the areas of some triangles given in matrix form. First the coordinates of the vertices of the triangles are in a matrix called coords where the line number represents the vertex number and the column number is the dimension, in this case it is equal to 2 (x, y). The way the nodes connect are found in the lnods matrix where the line number is the triangle number and the column number is the vertex number that makes up each triangle (v_i, v_j, v_k).\u003c/p\u003e","function_template":"function y =areas(coords,lnods)\r\n y = ?;\r\nend","test_suite":"%%\r\ncoords=[0 0;1 0; 1 1; 0 1];\r\nlnods=[ 1 2 4; 2 3 4];\r\ny_correct = [0.500;0.500];\r\nassert(isequal(areas(coords,lnods),y_correct))\r\n%%\r\ncoords=[0 0;1 0; 1 1; 0 1; 0.5 0.5];\r\nlnods=[ 1 2 5; 2 3 5;3 4 5;4 1 5];\r\ny_correct = [0.2500;0.2500;0.2500;0.2500];\r\nassert(isequal(areas(coords,lnods),y_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":396229,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":18,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-01-19T02:12:33.000Z","updated_at":"2026-03-14T18:54:18.000Z","published_at":"2020-01-19T02:17:46.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eImagine that you want to calculate the areas of some triangles given in matrix form. First the coordinates of the vertices of the triangles are in a matrix called coords where the line number represents the vertex number and the column number is the dimension, in this case it is equal to 2 (x, y). The way the nodes connect are found in the lnods matrix where the line number is the triangle number and the column number is the vertex number that makes up each triangle (v_i, v_j, v_k).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":45407,"title":"Yoonir - 02","description":"Find the area of a six-pointed star inscribed in a circle of radius r.","description_html":"\u003cp\u003eFind the area of a six-pointed star inscribed in a circle of radius r.\u003c/p\u003e","function_template":"function y =yoonir_04(r)","test_suite":"%%\r\nassert(abs(yoonir_04(10)-173.2050)\u003c0.001)\r\n\t\r\n%%\r\nassert(abs(yoonir_04(20)-692.8203)\u003c0.001)\r\n\t\r\n%%\r\nassert(abs(yoonir_04(pi)-17.0946)\u003c0.001)\r\n\t\r\n%%\r\nassert(abs(yoonir_04(pi^4)-16434.6178)\u003c0.001)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":5,"created_by":363598,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":19,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-03-31T00:59:00.000Z","updated_at":"2026-01-29T14:02:37.000Z","published_at":"2020-03-31T00:59:00.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind the area of a six-pointed star inscribed in a circle of radius r.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":60999,"title":"Total Area Covered by Overlapping Polygons","description":"Given a variable length set of polygon vertex coordinates, compute the total area covered. For example, take two polygons with the following vertex coordinates:\r\np1=[0.2,0.2; 0.5,0.2; 0.5,0.5; 0.2,0.5];\r\np2=[0.4,0.4; 0.8,0.4; 0.8,0.8; 0.4,0.8];\r\n\r\nThe total area covered is the area of the first polygon plus the area of the second polygon minus the overlap. This comes out to 0.24 units.\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 617.571px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407.997px 308.778px; transform-origin: 407.997px 308.785px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42.017px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 21.0085px; text-align: left; transform-origin: 385px 21.0085px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven a variable length set of polygon vertex coordinates, compute the total area covered. For example, take two polygons with the following vertex coordinates:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0085px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.4972px; text-align: left; transform-origin: 385px 10.5043px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ep1=[0.2,0.2; 0.5,0.2; 0.5,0.5; 0.2,0.5];\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0085px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.4972px; text-align: left; transform-origin: 385px 10.5043px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ep2=[0.4,0.4; 0.8,0.4; 0.8,0.8; 0.4,0.8];\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 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\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42.017px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 21.0085px; text-align: left; transform-origin: 385px 21.0085px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe total area covered is the area of the first polygon plus the area of the second polygon minus the overlap. This comes out to 0.24 units.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0085px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.4972px; text-align: left; transform-origin: 385px 10.5043px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function A = lapgon(P)\r\n A=[];\r\nend","test_suite":"%% Test Case 1\r\nP{1}=[0.2,0.2;0.5,0.2;0.5,0.5;0.2,0.5];\r\nP{2}=[0.4,0.4;0.8,0.4;0.8,0.8;0.4,0.8];\r\n\r\nA=round(lapgon(P),6);\r\nA_correct=0.240000;\r\n\r\nassert(isequal(A,A_correct))\r\n\r\n%% Test Case 2\r\nP{1}=[0.1783,0.2985;0.3849,0.6214;0.8407,0.8054];\r\nP{2}=[0.1112,0.8761;0.8927,0.4062;0.6089,0.0228];\r\n\r\nA=round(lapgon(P),6);\r\nA_correct=0.244813;\r\n\r\nassert(isequal(A,A_correct))\r\n\r\n%% Test Case 3\r\nP{1}=[0.5967,0.2763;0.3286,0.2200;0.7586,0.4690];\r\nP{2}=[0.4809,0.5456;0.5589,0.2875;0.5021,0.3001;0.2000,0.7725];\r\nP{3}=[0.4260,0.0843;0.0140,0.4489;0.5535,0.8630;0.4133,0.3718;0.8033,0.0733];\r\nP{4}=[0.0169,0.7757;0.1636,0.9072;0.7480,0.9785;0.2718,0.4179;0.8687,0.2735;0.0599,0.1064];\r\n\r\nA=round(lapgon(P),6);\r\nA_correct=0.459378;\r\n\r\nassert(isequal(A,A_correct))\r\n\r\n%% Test Case 4\r\ntheta=0:0.01:2*pi;\r\nP{1}(:,1)=0.35*cos(theta)+0.6;\r\nP{1}(:,2)=0.22*sin(theta)+0.5;\r\nP{2}=[0.1083,0.3508;0.7413,0.9426;0.2748,0.0933];\r\n\r\nA=round(lapgon(P),6);\r\nA_correct=0.307282;\r\n\r\nassert(isequal(A,A_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":4910069,"edited_by":4910069,"edited_at":"2025-09-12T18:34:35.000Z","deleted_by":null,"deleted_at":null,"solvers_count":7,"test_suite_updated_at":"2025-09-12T18:34:35.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2025-09-12T17:15:15.000Z","updated_at":"2026-03-19T16:19:38.000Z","published_at":"2025-09-12T18:28:07.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a variable length set of polygon vertex coordinates, compute the total area covered. For example, take two polygons with the following vertex coordinates:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ep1=[0.2,0.2; 0.5,0.2; 0.5,0.5; 0.2,0.5];\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ep2=[0.4,0.4; 0.8,0.4; 0.8,0.8; 0.4,0.8];\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"420\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"560\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe total area covered is the area of the first polygon plus the area of the second polygon minus the overlap. 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VVbquu1yujIyM7OzsuLg4s3cBAP574zJItbW1VqtV13WllM1mS09Pr6+vPzpI8+bNO9ajeSHDAAkbTB8gYQMDJGwwd8C8efNMvLo/xmWQPB5PQkKC7zAiIqKlpeXo0+Q/gwcA8BmXzyEZhqFpPyzXNM3r9Zq4BwBw4sZlkCwWi2EYvkOv1xsePi5v9QAAPuMySNHR0U1NTb5Dt9udlJRk4h4AwIkbl0FKTk5WStntdqVUa2urw+FITU01exQA4ISM178Y++GHHxYVFem63tzcvGLFiiuvvNLsRQCAEzJegwQAOMmMy4fsAAAnH4IEABAh7JFHHjF7Q+B1dnZ+9NFHR44ciYyMFHXFurq6GTNmmLWhra3t448/9ng8MTExpgxwOp2ffvqppmlWqzUYA/zZMKSxsTEsLGzy5MkhHuByuZqbm/f8W0REhMViCeWAoQ3/+Mc/vvnmm5/+9KeBvbQ/G0Z8Bvbs2dPf3x/wr4cxPwnt7e3bt2/v6+uLiooK7KX93zD0/RgWFha8b4ejBfVH0Ik7CYNUXV19zz339Pf3b9iwwePx/OIXvxByxaeffnrt2rVLliwxZcOKFSvWrVt36NChV155pbq6+pprrgnsX94ac8CTTz65bt26w4cPP/PMM99///3FF18cwKv7uWFIW1tbbm7uz3/+85/97GchHlBZWXnfffe9+eab1dXV1dXVF1100dlnnx3KAXa7/Y477jh8+PCbb77597///Ze//OWECRMCOGDMDXV1dcuXL6/+t5dffvnIkSMLFiwI2QClVEVFxcMPP9zf3//8889/+eWXGRkZAby6nxtWr179+OOP9/f3//nPf/Z4PKH5pT5B/REUGIMnl4GBgblz57a2tg4ODu7fv3/OnDn//Oc/Tb+i2+2+//77586de8kll5iyYefOnRdccIHb7R46vOaaa15++eVQDmhpafEN+Oabb2bNmrV///4ADvBnw5D+/v7rrrtuwYIF77zzTugH3HvvvS+++GJgr+v/gIGBgdTU1A8//HDoMCsr68033wzxhuHq6urS09N9X5ahGWAYRmJiYktLy+Dg4IEDBxITE3fu3BnAAf5s+Oyzzy644II9e/YMDg4ePnz4sssu++yzzwK7YYRg/wgKlJPtOaRRf++q6VcsLy+32WwrV640a4PVal2/fr3vkYFzzjlnz549oRxw7rnnvvrqq0MDTjvtNMMwjhw5EsAB/mwYsmbNmssvv3zmzJmBvbqfA3bu3Hnuuee6XK6A/+v7M8But5911lm+P4y//vrrAf/7Ev5/Ax46dOiBBx5YsWJFYB+w8mfA4ODgxIkTlVKnn366pmn9/f0BHODPhra2tksvvXTokXOLxZKUlFRTUxPYDSME+0dQoJxsv3HHz9+7GuIrFhcXa5o29Dd5TdkQExPje96oo6Nj69athYWFoRygaZqu64ZhbN68ubKyctmyZdOmTQvgAH82KKW2bdv24YcfvvLKK0uXLg3s1f0ZYBjG119//dhjj7lcLo/Hc8MNN6xYsSKUA9xud2xsbHFx8WuvvRYWFrZs2bI77rgjgAP82eCzYcOGhISESy+9NMQDNE0rKSm588478LEVYAAABJ1JREFUFy5c6HA4cnNz58yZE+INFotl9+7dvsPe3t7hv5wzGIL9IyhQTrY7pND/3lV/rhjsrzb//617enpuu+22O++8c9asWaEf4HK5+vr6oqOjGxoaPB5PAAf4s6G3t7e4uHjNmjWBva7/A3p6ehYuXPjss886HI6tW7fW1dW99NJLoRzQ1tZWU1Nz/vnnNzY2vvTSS88880zAHz/w8yuhr6+voqLid7/7XWCv7ueA7du3T5o0KSoqymq1fvXVV4cOHQrxhrS0tJ6entWrV2/btu25555ramoK9o+pYP8ICpTxsdJ/of+9qxJ+06ufGz7//PPrr7++oKAgsLdH/g+IiooqKCjYsGHDxIkTn3vuuRBveOKJJxITEzs6Oux2+9BrvQL7n3Mec8D06dPXrVs3ffp0pdS0adMyMzN37NgRygFnn332jBkzcnNzlVLx8fGZmZlvvPFGAAf4s2HIW2+9FRsbO3v27MBe3Z8BW7Zs+eSTTyorKxcvXrx+/Xql1MaNG0O8wWq1btq0qaOjY926dd9+++11110X8BdbjlMnW5BC/3tXJfymV382OByOJUuWPPLII7fffnvoB+zatWvTpk2+wzPPPHPv3r0h3hAVFXXw4MHKysrKysrdu3fb7XaHwxHKAR0dHZs3b/Yd9vf3h4WFhXLA1KlThx9qmhbwPzj7+e1gt9szMzMDe2k/B7jd7pkzZ/o+8zNmzOjs7Azxhu++++7gwYNPPfXUpk2b7rrrrvb29rlz5wZ2w3hl9qsqAswwjEsuueT9998fHBxsaWm58MIL9+3bZ8oVP/3006FX0fi8//77QXqJy5gbvv7667lz527ZsqX/3wYGBkI5oKWlJTEx8auvvhocHNy3b19aWtp7770XwAH+bBjuN7/5TcBfZTfmgC+//DIxMXHoxVd79+5NS0urq6sL5YD+/v6UlJQtW7YMDg7u378/PT39gw8+COAAfzYMSU1NHTon4MYcsHPnzgsvvHDoS/HAgQNZWVmbN28O8YY9e/YkJibu3bt3cHDw448/vvjiiw8cOBDYDaMK3o+gQDnZgjQ4OPjBBx+kpaUVFBQkJSUF/FWt/l/xtttuG/HS6qB+NRx/w6pVq2b+p//93/8N5YDBwcHKyso5c+YsWbJkzpw5zzzzTGCv7ucGn2AEyZ8BL7744ty5cwsKCubOnbtx48bQD/joo48WLFiQm5ublJT0pz/9KeAD/NlgGMbMmTO/+eabYFzdnwF/+ctfkpKShk5YuXKlKRuee+65uXPn5uXlLViwIOB/LDgW+UE6aX+56qFDhyZOnBjKp/JCf0WBG44/wOv1ulyun/zkJ4F9qOr/tCEExvwkHD58OKgLx/wMfP/99z/60Y/4f8FisZj4STAMo6+vb9KkScEbMO6ctEECAIwvJ9uLGgAA4xRBAgCIQJAAACIQJACACAQJACACQQIAiECQAAAiECQAgAgECQAgAkECAIhAkAAAIhAkAIAIBAkAIAJBAgCIQJAAACIQJACACAQJACACQQIAiECQAAAiECQAgAgECQAgAkECAIhAkAAAIhAkAIAIBAkAIML/B/bLq8TsfZ7uAAAAAElFTkSuQmCC\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61081,"title":"Slicing the area of a regular polygon","description":"Given the area, A, of a regular polygon with n sides, each of length s, consider its decomposition in congruent isosceles triangles of base s and heigth h. Find the rectangle, with dimensions L×h, which covers all n triangles in their adjacent positions (n\u003e3, cf. figure below). Complete the problem by determining the area, A_r, of the rectangle.\r\nHint: Consider that we are slicing the polygon into triangular slices and put them into the rectangle.\r\ninput: (A, n)\r\noutput: y = [L h A_r]\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 575.8px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 287.9px; transform-origin: 408px 287.9px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 31.5px; text-align: left; transform-origin: 385px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven the area, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, of a regular polygon with \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e sides, each of length \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003es\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, consider its decomposition in congruent isosceles triangles of base \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003es\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and heigth \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eh\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Find the rectangle, with dimensions \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eL\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e×\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eh\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, which covers all \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e triangles in their adjacent positions (\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u0026gt;3,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e cf. figure below). Complete the problem by determining the area, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA_r\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, of the rectangle.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHint: Consider that we are slicing the polygon into triangular slices and put them into the rectangle.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003einput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(A, n)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eoutput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ey = [L h A_r]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 413.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 206.9px; text-align: left; transform-origin: 385px 206.9px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"501\" height=\"408\" style=\"vertical-align: baseline;width: 501px;height: 408px\" 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\" alt=\"Slicing square (n=4)\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = slicing(A,n)\r\n y = [L h A_r];\r\nend","test_suite":"%%\r\nA = 16;\r\nn = 4;\r\ny_correct = [10 2 20];\r\nassert(isequal(slicing(A,n),y_correct))\r\n\r\n%%\r\nA = 20;\r\nn = 5; \r\ny_correct = [10.22849568767431 2.34638608968871 24];\r\ntolerance = 1e-13;\r\nassert(all(abs(slicing(A,n)-y_correct)\u003ctolerance))\r\n\r\n%%\r\nfiletext = fileread('slicing.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\nA = 20;\r\nn = 6; \r\ny_correct = [7*sqrt(10*3^(-3/2)) sqrt(10*3^(-1/2)) 70/3];\r\ntolerance = 1e-13;\r\nassert(all(abs(slicing(A,n)-y_correct)\u003ctolerance))\r\n\r\n%%\r\nA = 32;\r\nn = 8; \r\ny_correct = [18*sqrt(sqrt(2)-1) 2/sqrt(sqrt(2)-1) 36];\r\ntolerance = 1e-13;\r\nassert(all(abs(slicing(A,n)-y_correct)\u003ctolerance))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":4993982,"edited_by":4993982,"edited_at":"2025-11-19T14:59:52.000Z","deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-11-18T11:18:12.000Z","updated_at":"2026-03-20T13:59:51.000Z","published_at":"2025-11-19T14:59:52.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven the area, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, of a regular polygon with \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e sides, each of length \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003es\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, consider its decomposition in congruent isosceles triangles of base \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003es\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and heigth \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. Find the rectangle, with dimensions \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eL\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e×\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, which covers all \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e triangles in their adjacent positions (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u0026gt;3,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e cf. figure below). Complete the problem by determining the area, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA_r\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, of the rectangle.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHint: Consider that we are slicing the polygon into triangular slices and put them into the rectangle.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003einput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(A, n)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eoutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey = [L h A_r]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"408\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"501\\\"/\u003e\u003cw:attr 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61086,"title":"Covering a four-pointed star polygon by rectangles","description":"Given the area, A, of a star polygon formed by the rectangle, with dimensions L×2L, and four triangles, with height h from their bases to the vertices, find the rectangles that have the same area, A, and cover the distance between opposite vertices (cf. figure below).\r\nGiven (A, L), return the 2x2 matrix M, where \r\nthe first row returns the dimensions, y1×y2, of the rectangle that covers the minimum distance (cf. left figure);\r\nthe second row returns the dimensions, z1×z2, of the rectangle that covers the maximum distance (cf. right figure).\r\ninput: (A, L)\r\noutput: M = [y1 y2; z1 z2]\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 635.675px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 408px 317.837px; transform-origin: 408px 317.837px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven the area, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, of a star polygon formed by the rectangle, with dimensions \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eL\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e×\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e2L\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and four triangles, with height \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eh\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e from their bases to the vertices, find the rectangles that have the same area, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and cover the distance between opposite vertices (cf. figure below).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(A, L)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, return the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ex\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e matrix \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eM\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, where \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 40.875px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 20.4375px; transform-origin: 391px 20.4375px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ethe first row returns the dimensions, y\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e×\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ey2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, of the rectangle that covers the minimum distance (cf. left figure);\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ethe second row returns the dimensions, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ez1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e×z\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, of the rectangle that covers the maximum distance (cf. right figure).\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003einput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(A, L)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eoutput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eM = [y1 y2; z1 z2]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 411.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 205.9px; text-align: left; transform-origin: 384px 205.9px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cimg class=\"imageNode\" width=\"508\" height=\"406\" style=\"vertical-align: baseline;width: 508px;height: 406px\" 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\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function M = covering_polygon(A,L)\r\n M = x;\r\nend","test_suite":"%%\r\nA = 27;\r\nL = 3;\r\nM_correct = [5 5.4; 3.375 8];\r\nassert(all(isapprox(covering_polygon(A,L),M_correct), 'all'))\r\n\r\n%%\r\nA = 36;\r\nL = 3;\r\nM_correct = [7 36/7; 3.6 10];\r\nassert(all(isapprox(covering_polygon(A,L),M_correct), 'all'))\r\n\r\n%%\r\nfiletext = fileread('covering_polygon.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\nA = 48;\r\nL = 4;\r\nM_correct = [20/3 36/5; 4.5 32/3];\r\nassert(all(isapprox(covering_polygon(A,L),M_correct), 'all'))\r\n\r\n%%\r\nA = 56;\r\nL = 4;\r\nM_correct = [8 7; 14/3 12];\r\nassert(all(isapprox(covering_polygon(A,L),M_correct), 'all'))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":4993982,"edited_by":4993982,"edited_at":"2025-11-28T15:21:25.000Z","deleted_by":null,"deleted_at":null,"solvers_count":10,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-11-27T15:06:59.000Z","updated_at":"2026-03-21T13:41:00.000Z","published_at":"2025-11-28T15:21:25.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven the area, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, of a star polygon formed by the rectangle, with dimensions \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eL\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e×\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2L\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, and four triangles, with height \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e from their bases to the vertices, find the rectangles that have the same area, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, and cover the distance between opposite vertices (cf. figure below).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(A, L)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, return the 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\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ez1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e×z\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, of the rectangle that covers the maximum distance (cf. right figure).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003einput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(A, L)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":45349,"title":"Area-07","description":"This is a follow up of the problem \r\n\r\n\u003chttps://www.mathworks.com/matlabcentral/cody/problems/45341-area-06\u003e\r\n\r\nin this case, find the total area of the lobes i.e. the area confined by the arcs drawn.","description_html":"\u003cp\u003eThis is a follow up of the problem\u003c/p\u003e\u003cp\u003e\u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/45341-area-06\"\u003ehttps://www.mathworks.com/matlabcentral/cody/problems/45341-area-06\u003c/a\u003e\u003c/p\u003e\u003cp\u003ein this case, find the total area of the lobes i.e. the area confined by the arcs drawn.\u003c/p\u003e","function_template":"function c= quarter_circle_02(r)\r\n y = x;\r\nend","test_suite":"%%\r\nr = 25;\r\nassert(abs(quarter_circle_02(r)-516.5287)\u003c0.001)\r\n%%\r\nr = 55.67;\r\nassert(abs(quarter_circle_02(r)-2561.2789)\u003c0.001)\r\n%%\r\nr = 42;\r\nassert(abs(quarter_circle_02(r)-1457.8505)\u003c0.001)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":4,"created_by":363598,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":18,"test_suite_updated_at":"2020-02-21T08:43:29.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2020-02-21T08:40:42.000Z","updated_at":"2026-03-11T09:28:14.000Z","published_at":"2020-02-21T08:43:29.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis is a follow up of the problem\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/45341-area-06\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026lt;https://www.mathworks.com/matlabcentral/cody/problems/45341-area-06\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026gt;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ein this case, find the total area of the lobes i.e. the area confined by the arcs drawn.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":50499,"title":"Find the area between curves (P2)","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 612.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 306.25px; transform-origin: 407px 306.25px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20px; border-block-end-color: rgb(60, 60, 60); border-block-start-color: rgb(60, 60, 60); border-bottom-color: rgb(60, 60, 60); border-inline-end-color: rgb(60, 60, 60); border-inline-start-color: rgb(60, 60, 60); border-left-color: rgb(60, 60, 60); border-right-color: rgb(60, 60, 60); border-top-color: rgb(60, 60, 60); caret-color: rgb(60, 60, 60); color: rgb(60, 60, 60); column-rule-color: rgb(60, 60, 60); font-family: Helvetica, Arial, sans-serif; font-size: 20px; font-weight: 700; line-height: 20px; margin-block-end: 5px; margin-block-start: 3px; margin-bottom: 5px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 3px; outline-color: rgb(60, 60, 60); perspective-origin: 384px 10px; text-align: left; text-decoration: none; text-decoration-color: rgb(60, 60, 60); transform-origin: 384px 10px; white-space: pre-wrap; margin-left: 4px; margin-top: 3px; margin-bottom: 5px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e Area between curves - Problem 2\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 32.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 16.25px; text-align: left; transform-origin: 384px 16.25px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e Find the area enclosed by the curves \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"63.5\" height=\"20\" style=\"width: 63.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"68\" height=\"32\" style=\"width: 68px; height: 32px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; 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\" 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src=\"data:image/png;base64,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\" width=\"32.5\" height=\"19\" style=\"width: 32.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"29.5\" height=\"19\" style=\"width: 29.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"76.5\" height=\"18\" style=\"width: 76.5px; height: 18px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = AreaCurves(a, n)\r\n \r\nend","test_suite":"%%\r\nfiletext = fileread('AreaCurves.m');\r\nfor ii = [0.5, 0.6667, 1.3606, 2.7754, 22.3242]\r\n assert(isempty(strfind(filetext, num2str(ii))),'Do NOT use provided answers in your solution')\r\nend\r\n\r\n%%\r\na = 1; \r\nn = 3;\r\n\r\ny_correct = 0.5;\r\nassert(abs(AreaCurves(a,n)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = 1; \r\nn = 5; \r\n\r\ny_correct = 0.6667;\r\nassert(abs(AreaCurves(a,n)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = 2; \r\nn = 2.5; \r\n\r\ny_correct = 1.3606;\r\nassert(abs(AreaCurves(a,n)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = pi;\r\nn = 3.1;\r\n\r\ny_correct = 2.7754;\r\nassert(abs(AreaCurves(a,n)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = exp(3);\r\nn = 12;\r\n\r\ny_correct = 22.3242;\r\nassert(abs(AreaCurves(a,n)-y_correct)\u003c1e-4)\r\n\r\n","published":true,"deleted":false,"likes_count":4,"comments_count":1,"created_by":487522,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":15,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-02-19T15:56:21.000Z","updated_at":"2025-08-25T11:22:08.000Z","published_at":"2021-02-19T15:59:16.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"heading\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e Area between curves - Problem 2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e Find the area enclosed by the curves \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ef(x) = x^{n}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eg(x) = ax^{\\\\frac{1}{n}}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e for different \\\"n\\\" and \\\"a\\\" coefficients\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"420\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"560\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e Plot of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ef(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eg(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea = 1, 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61071,"title":"Generalizing square area to triangle area","description":"Cody Problem 61070 asked for the height, h, of a right triangle that had the same area, A, of a square with side length, c, and the hypothenuse length was correlated to the square side by x = 2. \r\nNow, find the height, h, of the right triangle that has the same area, A, of a square with side length, c, and the hypothenuse length is xc, for an arbitrary number x \u003e 2. Here, the height stands for the smallest cathetus.\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 123px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 61.5px; transform-origin: 408px 61.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/61070-square-area-to-triangle-area\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eCody Problem 61070\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e asked for the height, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eh\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, of a right triangle that had the same area, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, of a square with side length, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ec\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and the hypothenuse length was correlated to the square side by \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ex = 2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eNow, find the height, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eh\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, of the right triangle that has the same area, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, of a square with side length, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ec\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and the hypothenuse length is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003exc\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, for an arbitrary number \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ex \u0026gt; 2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Here, the height stands for the smallest cathetus.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function h = find_height(A,x)\r\n h = x;\r\nend","test_suite":"%%\r\nA = 9;\r\nx = sqrt(5);\r\nh_correct = 3;\r\ntolerance = 1e-12;\r\nassert(abs(find_height(A,x)-h_correct)\u003ctolerance)\r\n\r\n%%\r\nA = 10;\r\nx = 3;\r\nh_correct = sqrt(5*(9-sqrt(65)));\r\ntolerance = 1e-12;\r\nassert(abs(find_height(A,x)-h_correct)\u003ctolerance)\r\n\r\n%%\r\nA = 16;\r\nx = sqrt(5);\r\nh_correct = 4;\r\nassert(isequal(find_height(A,x),h_correct))\r\n\r\n%%\r\nfiletext = fileread('find_height.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\nA = 16;\r\nx = 3; \r\nh_correct = 4*sqrt((9-sqrt(65))/2);\r\ntolerance = 1e-12;\r\nassert(abs(find_height(A,x)-h_correct)\u003ctolerance)\r\n\r\n%%\r\nA = 16;\r\nx = 5; \r\nh_correct = 4*sqrt((25 - sqrt(609))/2);\r\ntolerance = 1e-12;\r\nassert(abs(find_height(A,x)-h_correct)\u003ctolerance)\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":7,"created_by":4993982,"edited_by":4993982,"edited_at":"2025-11-13T10:09:54.000Z","deleted_by":null,"deleted_at":null,"solvers_count":15,"test_suite_updated_at":"2025-11-13T10:09:54.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2025-11-10T14:44:15.000Z","updated_at":"2026-04-08T08:26:51.000Z","published_at":"2025-11-12T17:58:52.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/61070-square-area-to-triangle-area\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eCody Problem 61070\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e asked for the height, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, of a right triangle that had the same area, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, of a square with side length, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ec\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, and the hypothenuse length was correlated to the square side by \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex = 2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNow, find the height, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, of the right triangle that has the same area, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, of a square with side length, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ec\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, and the hypothenuse length is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003exc\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, for an arbitrary number \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex \u0026gt; 2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. Here, the height stands for the smallest cathetus.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":45476,"title":"Inscribed circle in a triangle","description":"A circle of radius r is inscribed in a triangle. \r\n\r\nIn the figure, Ac=x and Bc=y. \r\nvalues of x \u0026 y are given.\r\n\r\nFind the area of the triangle.\r\n\r\n\u003chttps://www.analyzemath.com/Geometry_calculators/inscribed.gif\u003e\r\n\r\n\r\n \r\n","description_html":"\u003cp\u003eA circle of radius r is inscribed in a triangle.\u003c/p\u003e\u003cp\u003eIn the figure, Ac=x and Bc=y. \r\nvalues of x \u0026 y are given.\u003c/p\u003e\u003cp\u003eFind the area of the triangle.\u003c/p\u003e\u003cp\u003e\u003ca href = \"https://www.analyzemath.com/Geometry_calculators/inscribed.gif\"\u003ehttps://www.analyzemath.com/Geometry_calculators/inscribed.gif\u003c/a\u003e\u003c/p\u003e","function_template":"function y = ins_cir_tri(x,y,r)","test_suite":"%%\r\nassert(isequal(ins_cir_tri(20,30,10),600))\r\n\r\n%%\r\nassert(isequal(ins_cir_tri(15,10,5),150))\r\n\r\n%%\r\nassert(abs(ins_cir_tri(25,10,5)-194.4444)\u003c0.001)\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":4,"created_by":363598,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":14,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-04-24T17:06:12.000Z","updated_at":"2020-05-11T00:46:34.000Z","published_at":"2020-04-24T17:06:12.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA circle of radius r is inscribed in a triangle.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn the figure, Ac=x and Bc=y. values of x \u0026amp; y are given.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind the area of the triangle.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.analyzemath.com/Geometry_calculators/inscribed.gif\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026lt;https://www.analyzemath.com/Geometry_calculators/inscribed.gif\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026gt;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":61074,"title":"Height of a four-pointed star polygon","description":"Given the area A, of a rectangle with dimensions l1xl2, where the side lengths are integers and form the smallest possible perimeter, and given the total area A_t of the star polygon formed by the rectangle and four triangles (cf. the figure below), with height, h, from their bases to the apices, find the vector [l1 l2 h] such that l1\u003cl2.\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 490.8px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 245.4px; transform-origin: 408px 245.4px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 31.5px; text-align: left; transform-origin: 385px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven the area \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, of a rectangle with dimensions \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003el1xl2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, where the side lengths are integers and form the smallest possible perimeter, and given the total area \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA_t\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of the star polygon formed by the rectangle and four triangles (cf. the figure below), with height, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eh\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, from their bases to the apices, find the vector \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[l1 l2 h]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e such that \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003el1\u0026lt;l2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 418.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 209.4px; text-align: left; transform-origin: 385px 209.4px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"508\" height=\"413\" style=\"vertical-align: baseline;width: 508px;height: 413px\" 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n2EHAAKKfOQRIvoMOwAQpAhHHuujz7ADACGJZOSxPvoMOwAQkkhGHoujz7ADAGEIe+SxMvoMOwAQtvBGHiujX1FRUVdXx7ADAGFoa2s7dOhQWVlZSM+yMvolJSWXXHKJw+Gw8AwAICmHwzFs2LCSkpKQnmXxpr906dKUlBRrzwAA0omLi0tJSVm6dGmoT7Q4+i6X65prrqH7ABCS5OTkwsJCl8sV6hOtv2Vz/fr1o0aNYuQBgCA5HI5Ro0YtW7YsjOdaH32NkQcAghb2sKMTIvqMPAAQpLCHHZ0Q0dcYeQAgCJEMOzpRoq8x8gBAryIcdnQCRZ+RBwB6EeGwoxMo+hojDwCcQ+TDjk6s6GuMPADQjSHDjk646DPyAEAXhgw7OuGirzHyAIAfo4YdnYjR1xh5AEDTNEOHHZ2g0WfkAQDN0GFHJ2j0NUYeALZn7LCjEzf6GiMPABszfNjRCR19Rh4AtmX4sKMTOvoaIw8AWzJj2NGJHn2NkQeAzZg07OgkiD4jDwBbMWnY0UkQfY2RB4BtmDfs6OSIvsbIA8AGTB12dNJEn5EHgPJMHXZ00kRfY+QBoDSzhx2dTNHXGHkAKCoKw45Osugz8gBQUhSGHZ1k0dcYeQAoJzrDjk6+6GuMPAAUErVhRxda9Pfu3Zudnb1161aTThMkRh4AyojasKMLIfpNTU1LlixpbGw07zTBY+QBoIBoDju6YKPv8Xjuueeejz/+2NTThISRB4DUojzs6AJH/8yZM++//35eXl5dXd3o0aOjcKYgMfIAkFqUhx1d4Ojv27fviSeeiI2NXbVq1Y033hiFMwWPkQeApKI/7OgCRz82NvbOO+/csmXLxIkTo3CgUDHyAJCOJcPOTx864FuMHj1aqFWnC33k+ec//9nQ0GD1WQAgKJYMO7rA0Q+Px+MpKyvr/KHT6TTv01u/fn1ubm5zc3NbW5tJHwIAjGLVsKMz68VZXq/X/4dpaWkmfSAdIw8AKVg47Px0AJPer9PpLCkpMemdd8fIA0AKFg47Oin/GoYecScPAMFZO+zo1Im+xsgDQGCWDzs6paLPy7UACMvyYUenVPQ1Rh4AQhJh2NGpFn2NkQeAYAQZdnShRX/u3Ln19fVTp0416TSGYOQBIBRBhh2dglf6GiMPAGGIM+zo1Iy+xsgDQABCDTs6ZaPPyAPAckINOzplo68x8gCwlGjDjk7l6GuMPAAsIuCwo1M8+ow8ACwh4LCjUzz6GiMPgKgTc9jRqR99jZEHQBQJO+zobBF9Rh4AUSPssKOzRfQ1Rh4AUSHysKOzS/Q1Rh4AJhN82NHZKPqMPABMJfiwo7NR9DVGHgCmEX/Y0dkr+hojDwATSDHs6GwXfUYeAIaTYtjR2S76GiMPAEPJMuzo7Bh9jZEHgEEkGnZ0No0+Iw8AQ0g07OhsGn2NkQdAxOQadnT2jb7GyAMgAtINOzpbR5+RB0DYpBt2dLaOvsbIAyAsMg47OrtHX2PkARAiSYcdHdFn5AEQGkmHHR3R1zRGHgBBk3fY0RH9nzDyAAhI6mFHR/R/wsgDICCphx0d0f8fRh4AvZB92NER/Z9h5AHQIwWGHR3R/xlGHgA9UmDY0RH9rhh5AHShxrCjI/o9YOQB0EmZYUdH9HvAyAOgkzLDjo7o94yRB4Cm1rCjI/rnxMgD2Jxiw46O6J8TIw9gc4oNOzqi3xtGHsC21Bt2dEQ/AEYewIaUHHZ0RD8ARh7AhpQcdnREPzBGHsBWVB12dEQ/KIw8gE0oPOzoiH5QGHkAm1B42NER/WAx8gDKU3vY0RH9EDDyAApTftjREf0QMPIAClN+2NER/dAw8gBKssOwoyP6IWPkARRjk2FHR/RDxsgDKMYmw46O6IeDkQdQhn2GHR3RDxMjD6AAWw07OqIfJkYeQAG2GnZ0RD98jDyA1Ow27OiIfkQYeQBJ2XDY0RH9iDDyAJKy4bCjI/qRYuQBpGPPYUdH9A3AyANIxLbDjo7oG4CRB5CIbYcdHdE3BiMPIAU7Dzs6om8YRh5AcDYfdnRBRd/r9RYXF48aNSozMzMnJ+fPf/5ze3u72SeTDiMPIDibDzu6wNHft29ffn7+hx9+eOWVV+bn53d0dDz11FOLFy+m+90x8gDCYtjRBYh+e3v7q6++euLEiZdeemndunXLly/fsmVLTk7Oxo0b3W53dI4oF0YeQEAMO50CRL++vt7tdrtcruuuu05/JCkpqaSkpE+fPu+//77P5zP9gLJh5AEExLDTKUD0P//888bGxquvvjohIaHzwYyMjLS0tM8++6ypqcnk40mJkQcQCsOOvwDRP3r0qKZpo0aN8n+wT58+F1xwwYkTJ1paWkw8mswYeQBBxMfHM+z4CxD9r776qvuD/fr1Gzx4cEtLy4kTJ8w5lfT0kSc5OdnqgwB2l5iYyLDjL673n+7xFp2YmJjzzgvwp4XH4ykrK+v8odPptNsv+vr163Nzc91tbVYfBLAvd0KCpml2i0/vAkQ/Pj6++4M+n+/s2bO9P9Hr9fr/MC0tLdSTKWDp0qULFy4s83g6Ojqam5utPg5gI0lJSXFxcWlpaSUFBQUFBVYfRyABov9///d/3R88derU0aNHExMTBwwYcK4nOp3OkpKSSE8nOZfLVVlZ6Xa7Fy5ceOjQoaamJr4LApgtMTExKSlp2LBhJSUl5L67ACuNHv26ujr/B0+fPv39998PGDAgMTHRxKOpQk//O++8k5WVlZ6ezi8aYJLExMQhQ4ZkZWWVl5dXVlZS/B4FiP4ll1wyaNAgt9vd2tra+eDBgwcPHTp0+eWX843K4JF+wDzkPngBop+WljZ+/Hi3271161b9pVjNzc3l5eVnz569+eabY2JionJIdZB+wFjkPlQBNv2EhIT7779/9+7dv/3tb9evXz906NCqqqpjx44VFRXxDfGwsfUDkdO3+0suuYTtPjS+INTX1997770jR47MyMi45ppr3njjjdOnT/fy9hs2bJg/f34w7xmffPLJpEmTuOoHgqdf3U+aNGnDhg1W/xcsnwBX+rqMjIzXXnvN7N9Ie+KqHwgeV/eRCyr6MBvpB3pH7o1C9AVC+oHuyL2xiL5wSD+gI/dmIPqCIv2wM3JvHqIvNNIPuyH3ZiP6EiD9sANyHx1EXxqkH6oi99FE9CVD+qESch99RF9KpB+yI/dWIfoSI/2QEbm3FtGXHumHLMi9CIi+Ikg/REbuxUH0lUL6IRpyLxqiryDSDxGQezERfWWRfliF3IuM6CuO9COayL34iL4tkH6YjdzLgujbCOmHGci9XIi+7ZB+GIXcy4jo2xTpRyTIvbyIvq2RfoSK3MuO6IP0IyjkXg1EHz8h/TgXcq8Soo+fIf3wR+7VQ/TRA9IPcq8qoo9zIv32RO7VRvQRAOm3D3JvB0QfQSH9aiP39kH0EQLSrx5ybzdEHyEj/Wog9/ZE9BEm0i8vcm9nRB8RIf1yIfcg+jAA6RcfuYeO6MMwpF9M5B7+iD4MRvrFQe7RHdGHKUi/tcg9zoXow0SkP/rIPXpH9GE60h8d5B7BIPqIEtJvHnKP4BF9RBXpNxa5R6iIPixA+iNH7hEeog/LkP7wkHtEgujDYqQ/eOQekSP6EALp7x25h1GIPgRC+rsj9zAW0YdwSL+O3MMMRB+CsnP6yT3MQ/QhNLuln9zDbEQfErBD+sk9ooPoQxqqpp/cI5qIPiSjUvrJPaKP6ENKsqef3MMqRB8SkzH95B7WIvqQnizpJ/cQAdGHIkROP7mHOIg+lCJa+sk9REP0oSAR0k/uISaiD2VZlX5yD5ERfSgumukn9xDfeSG99d69e7Ozs7du3WrSaQCT6Ol/5513srKy0tPTExMTjX3/iYmJQ4YMycrKKi8vr6yspPgQVghX+k1NTUuWLGlsbDTvNICpzLjq5+oecgk2+h6Pp7i4+L///a+BH9vj8WialpaWZuD7FAqfoJiMSr8CuZf0dzB4fILdBZ53zpw58/777+fl5dXV1Y0ePTr803VTUVFRUVFh4DsUDZ+gyCIZfJQZc6T+HQwGn2B3ga/09+3b98QTTzgcjlWrVn366af79u0L93iAcEK96lfg6h42F/hKPzY29s4779yyZcvEiROjcCAg+oK56lfm6h42F/hKf/To0cauOoCYznXVz9U9VGLWffoej6esrKz3t3G73SZ9dEHwCUqqoKDA7Xbv2LEjOTm5o6PD4XCkpaUVFBQE81UtF1V/BzvxCXZyOp0ul0szKfqpqan6e+9dMG8jNT5BeblcLoU/u07Kf458gp067/D5KfotLS1z5szx/0PD5XKtXr06vNew2OQ/GACQTmivyAUASO2nK/3ExMR169ZZexQAgNm40gcAGyH6AGAjRB8AbCTG5/NZfQYAQJRwpQ8ANkL0AcBGiD4A2Igo0W9pabnrrrvmz59v9UGMsX///qKiohEjRgwfPnzatGmbN29W9XsnW7dudTqde/bssfogRvL5fNXV1TNnzhwxYkRmZubEiROXLFly8uRJq89lmDNnzmzatGnatGnDhw8fMWLEzJkzq6urVf0SbW5uLioquvbaa48dO2b1WQxz4MCBCRMmZHazcuXKgM8VIvpnzpx58803q6qqrD6IMbZu3VpQUFBTUzN58uQZM2YcPXp03rx5a9asUe8/qi+//HLJkiVtbW1WH8RIPp9vzZo1s2bN2rNnz+TJk/Pz88+ePbtq1ap58+Y1NzdbfToDdHR0PPPMMw8++ODRo0dnzJgxffr02traWbNmKfkl6vP5Vq9eXV1dbfVBDObxeBobGwcMGJD2c0lJSYGf7LPaDz/88Oyzz2ZmZmZkZDz88MNWHydSx48fz8vLu/rqq3fv3q0/4vF4pk6dOmHChNraWmvPZqyamppJkyZlZGRcccUVn376qdXHMUxtbe2ECROmTp1aX1+vP/LDDz8sWrQoIyPjD3/4g7VnM8SuXbvGjh1bWFh4/Phx/RH9SzQnJ+frr7+29myGq6ysHDlyZEZGRm5u7rfffmv1cQzz2muvZWZmbtu2LYznWnylv3///ttuu+3111+/7LLLHA6HtYcxhP6Pi91www3jxo3TH0lNTX3wwQe/++67bdu2WXs2o7S2tq5evfr222//8ccfMzIyrD6Owf71r381NDTccccdnZ9aQkLCPffcM2jQoOrq6sj/IXXLffHFFw6Ho6ioKDk5WX8kNTX1+uuv93q9tbW11p7NWA0NDc8///xll112+eWXW30Wg33++ecXXHDBxRdfHMZzrYx+S0vLU089tXfv3tLS0qeffjo+Pt7Cwxhl586d7e3tTqczJiam88FRo0ZdeOGFu3bt+vHHHy08m1E+/vjjF154ITU1de3atVlZWVYfx2BHjx4dNGjQZZdd5v9gv379+vbta9WRjDV79uzq6uq8vLzORzo6Og4dOuRwOAYMGGDhwYzV0dFRVlbW0NDw6KOPBjV6yKOlpcXj8Vx88cWDBw8O4+kWX+mPGTNm06ZN8+bN69Onj7UnMcrRo0eTkpK6/OP0AwYMSEhIaGxsVGP+djgcixYt+stf/jJixAirz2K83/3ud9XV1dnZ2f4P/uc//zl8+HBqamq/fv2sOphJGhoannnmmb///e+TJ08eM2aM1ccxzJYtWzZu3Dhnzhz1/uG/kydPer3epKSk8vLy7OzszMzM7Ozs4O81MOtfzgpGYmLiY489ZuEBDHfq1Kke7xA4//zzhwwZcuTIETWu9HNycnJycqw+RfR4vd6XXnqpX79+t9xyi///wMnu2LFjM2fO/OabbzRNy8/Pf+qppxISEqw+lDG8Xu+LL76Yk5Nz++23nzlzxurjGMzr9TY2Nnq93vr6epfL1bdv36qqqlWrVm3fvn3NmjWpqam9P12Iu3eU4fP5Ojo6evyp887jl1pKDQ0NDz/8cH19/bx58yZMmGD1cYz0/fffZ2dn5+fnX3TRRRs3brz33nsPHz5s9aEM0N7evmLFipMnT86fP1+ZP8b8nThxom/fvoWFhZWVleXl5cuXL//oo48KCwu/+OKLl19++VwJ6mTllb56YmJi4uJ6/iU9e/ZslA+DyH355ZcPPPBAbW1tcXHx3XffrdJlvqZpl1566fLlyzVNa29vX7x48VtvvVVeXv7MM8+c62tYFh9++OHGjRufeOKJSy+91OqzmGLq1Km7d+/2fyQhIeH+2/fxkwAAAzpJREFU+++vqqqqqqo6duzY0KFDe3l6NC4/V65c6f/ygXHjxin2Wp5O/fr1u+iii7o//sMPPxw5cmTgwIHKfDPQDv79738XFRXV19cvXry4pKREjRsNehQfHz937twhQ4ZUV1c3NTVZfZyI6K8d+eUvf3nrrbdafZaoSk5OTk9PP3nyZGNjY+9vKfcf6QIaNmxYc3Pzt99+O3bs2M4HT5w40draeuGFF6pxW6ryfD5fRUXF448/3rdv35dffvkXv/iFYtf43Q0cODA9Pf3IkSM+yV+fdfDgwcOHDx8+fHjTpk1dfsrlcqWnp7/77rs9XpnJpbm52eFwdL8QiYuLi42N7f250Yj+3Llz586dG4UPJILx48fHx8dXVVX5l+Kzzz777rvvrr76aq70pfDhhx8+/vjjF1100SuvvKLSDS2app0+ffrJJ5/ctm3bihUr/O9Q8nq9Bw8eTEtLk/1LdPDgwUVFRf6PtLe3V1ZWtra2Tp069eKLL5b9wqujo+Ohhx7avHnzqlWrpk6d2vm41+s9cOBAMPdxcqVvsJEjRw4fPnzTpk033XTTVVddpWma1+tdsWJFSkrKlClTrD4dAqupqXnyySfT09NXr16t3kvP+vTpM3bs2Hfffbe8vHzFihX6DezNzc0vvvhiY2PjvffeK/ut+mPGjHnuuef8H2lpaZkzZ47X6120aJEC1/hxcXHXX3/95s2b33jjjauuukp/hV1TU9Ozzz57/PjxOXPmDBw4MMB7iMo5bSQlJaW4uLi0tHT27Nm5ubl9+/bdvn37qVOnHnnkESXvaldMR0fHn/70J/0VFXfddVeXnx0/fvzzzz8v+636N9988yeffPLBBx9MmTLF5XJpmrZ9+/aWlpYZM2bMnj3b6tMhsOnTpxcWFr711lvXXnvttddeq/3/38G8vLxZs2YFfDrRN96vfvWrQYMGLV269KOPPjp79uzw4cNLS0unT5+u/C6sgOPHj9fU1GiadurUqVOnTnX52bS0NNknb03TkpKSli1bNmnSpJUrV37wwQeapg0fPvw3v/nNjTfeqPA3q1USHx//9NNPZ2dnv/rqq2H8DvLPJQKAjfCKIQCwkf8Hdwfp4F3vy5sAAAAASUVORK5CYII=\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = star_polygon(A,A_t)\r\n y = A;\r\nend","test_suite":"%%\r\nA = 10;\r\nA_t = 24;\r\ny_correct = [2 5 2];\r\nassert(isequal(star_polygon(A,A_t),y_correct))\r\n\r\n%%\r\nA = 11;\r\nA_t = 23;\r\ny_correct = [1 11 1];\r\nassert(isequal(star_polygon(A,A_t),y_correct))\r\n\r\n%%\r\nA = 72;\r\nA_t = 106;\r\ny_correct = [8 9 2];\r\nassert(isequal(star_polygon(A,A_t),y_correct))\r\n\r\n%%\r\nfiletext = fileread('star_polygon.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\nA = 156;\r\nA_t = 180;\r\ny_correct = [12 13 0.96];\r\nassert(isequal(star_polygon(A,A_t),y_correct))\r\n\r\n%%\r\nA = 168;\r\nA_t = 190;\r\ny_correct = [12 14 11/13];\r\nassert(isequal(star_polygon(A,A_t),y_correct))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":4993982,"edited_by":4993982,"edited_at":"2025-11-14T17:36:31.000Z","deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-11-13T17:02:46.000Z","updated_at":"2026-01-15T09:17:29.000Z","published_at":"2025-11-14T17:36:31.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven the area \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, of a rectangle with dimensions \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003el1xl2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, where the side lengths are integers and form the smallest possible perimeter, and given the total area \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA_t\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e of the star polygon formed by the rectangle and four triangles (cf. the figure below), with height, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, from their bases to the apices, find the vector \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[l1 l2 h]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e such that \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003el1\u0026lt;l2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"413\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"508\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" 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3q1mJgYn89n4tF6xbADQAH6yFNZWRm1j9hb9BMTE9etWxe1o4SEYQeAAqJ/J4+U/4gKww4AZUT5Th75os+wA0Ax0byTR77oM+wAUEw07+SRLPoMOwCUFLWRR6boM+wAUFh0Rh6Zos+wA0Bh0Rl5pIk+ww4A5UVh5JEj+gw7AGzC7JFHjugz7ACwCbNHHgmiz7ADwFZMHXlEjz7DDgAbMm/kET36DDsAbMi8kUfo6DPsALAtk0YecaPPsAPA5swYecSNPsMOAJszY+QRNPoMOwCgmTDyiBh9hh0A6GTsyCNi9Bl2AKCTsSOPcNFn2AGALgwcecSKPsMOAPTIqJFHrOgz7ABAj4waeQSKPsMOAPTCkJFHlOgz7ABAQJGPPKJEn2EHAAKKfOQRIvoMOwAQpAhHHuujz7ADACGJZOSxPvoMOwAQkkhGHoujz7ADAGEIe+SxMvoMOwAQtvBGHiujX1FRUVdXx7ADAGFoa2s7dOhQWVlZSM+yMvolJSWXXHKJw+Gw8AwAICmHwzFs2LCSkpKQnmXxpr906dKUlBRrzwAA0omLi0tJSVm6dGmoT7Q4+i6X65prrqH7ABCS5OTkwsJCl8sV6hOtv2Vz/fr1o0aNYuQBgCA5HI5Ro0YtW7YsjOdaH32NkQcAghb2sKMTIvqMPAAQpLCHHZ0Q0dcYeQAgCJEMOzpRoq8x8gBAryIcdnQCRZ+RBwB6EeGwoxMo+hojDwCcQ+TDjk6s6GuMPADQjSHDjk646DPyAEAXhgw7OuGirzHyAIAfo4YdnYjR1xh5AEDTNEOHHZ2g0WfkAQDN0GFHJ2j0NUYeALZn7LCjEzf6GiMPABszfNjRCR19Rh4AtmX4sKMTOvoaIw8AWzJj2NGJHn2NkQeAzZg07OgkiD4jDwBbMWnY0UkQfY2RB4BtmDfs6OSIvsbIA8AGTB12dNJEn5EHgPJMHXZ00kRfY+QBoDSzhx2dTNHXGHkAKCoKw45Osugz8gBQUhSGHZ1k0dcYeQAoJzrDjk6+6GuMPAAUErVhRxda9Pfu3Zudnb1161aTThMkRh4AyojasKMLIfpNTU1LlixpbGw07zTBY+QBoIBoDju6YKPv8Xjuueeejz/+2NTThISRB4DUojzs6AJH/8yZM++//35eXl5dXd3o0aOjcKYgMfIAkFqUhx1d4Ojv27fviSeeiI2NXbVq1Y033hiFMwWPkQeApKI/7OgCRz82NvbOO+/csmXLxIkTo3CgUDHyAJCOJcPOTx864FuMHj1aqFWnC33k+ec//9nQ0GD1WQAgKJYMO7rA0Q+Px+MpKyvr/KHT6TTv01u/fn1ubm5zc3NbW5tJHwIAjGLVsKMz68VZXq/X/4dpaWkmfSAdIw8AKVg47Px0AJPer9PpLCkpMemdd8fIA0AKFg47Oin/GoYecScPAMFZO+zo1Im+xsgDQGCWDzs6paLPy7UACMvyYUenVPQ1Rh4AQhJh2NGpFn2NkQeAYAQZdnShRX/u3Ln19fVTp0416TSGYOQBIBRBhh2dglf6GiMPAGGIM+zo1Iy+xsgDQABCDTs6ZaPPyAPAckINOzplo68x8gCwlGjDjk7l6GuMPAAsIuCwo1M8+ow8ACwh4LCjUzz6GiMPgKgTc9jRqR99jZEHQBQJO+zobBF9Rh4AUSPssKOzRfQ1Rh4AUSHysKOzS/Q1Rh4AJhN82NHZKPqMPABMJfiwo7NR9DVGHgCmEX/Y0dkr+hojDwATSDHs6GwXfUYeAIaTYtjR2S76GiMPAEPJMuzo7Bh9jZEHgEEkGnZ0No0+Iw8AQ0g07OhsGn2NkQdAxOQadnT2jb7GyAMgAtINOzpbR5+RB0DYpBt2dLaOvsbIAyAsMg47OrtHX2PkARAiSYcdHdFn5AEQGkmHHR3R1zRGHgBBk3fY0RH9nzDyAAhI6mFHR/R/wsgDICCphx0d0f8fRh4AvZB92NER/Z9h5AHQIwWGHR3R/xlGHgA9UmDY0RH9rhh5AHShxrCjI/o9YOQB0EmZYUdH9HvAyAOgkzLDjo7o94yRB4Cm1rCjI/rnxMgD2Jxiw46O6J8TIw9gc4oNOzqi3xtGHsC21Bt2dEQ/AEYewIaUHHZ0RD8ARh7AhpQcdnREPzBGHsBWVB12dEQ/KIw8gE0oPOzoiH5QGHkAm1B42NER/WAx8gDKU3vY0RH9EDDyAApTftjREf0QMPIAClN+2NER/dAw8gBKssOwoyP6IWPkARRjk2FHR/RDxsgDKMYmw46O6IeDkQdQhn2GHR3RDxMjD6AAWw07OqIfJkYeQAG2GnZ0RD98jDyA1Ow27OiIfkQYeQBJ2XDY0RH9iDDyAJKy4bCjI/qRYuQBpGPPYUdH9A3AyANIxLbDjo7oG4CRB5CIbYcdHdE3BiMPIAU7Dzs6om8YRh5AcDYfdnRBRd/r9RYXF48aNSozMzMnJ+fPf/5ze3u72SeTDiMPIDibDzu6wNHft29ffn7+hx9+eOWVV+bn53d0dDz11FOLFy+m+90x8gDCYtjRBYh+e3v7q6++euLEiZdeemndunXLly/fsmVLTk7Oxo0b3W53dI4oF0YeQEAMO50CRL++vt7tdrtcruuuu05/JCkpqaSkpE+fPu+//77P5zP9gLJh5AEExLDTKUD0P//888bGxquvvjohIaHzwYyMjLS0tM8++6ypqcnk40mJkQcQCsOOvwDRP3r0qKZpo0aN8n+wT58+F1xwwYkTJ1paWkw8mswYeQBBxMfHM+z4CxD9r776qvuD/fr1Gzx4cEtLy4kTJ8w5lfT0kSc5OdnqgwB2l5iYyLDjL673n+7xFp2YmJjzzgvwp4XH4ykrK+v8odPptNsv+vr163Nzc91tbVYfBLAvd0KCpml2i0/vAkQ/Pj6++4M+n+/s2bO9P9Hr9fr/MC0tLdSTKWDp0qULFy4s83g6Ojqam5utPg5gI0lJSXFxcWlpaSUFBQUFBVYfRyABov9///d/3R88derU0aNHExMTBwwYcK4nOp3OkpKSSE8nOZfLVVlZ6Xa7Fy5ceOjQoaamJr4LApgtMTExKSlp2LBhJSUl5L67ACuNHv26ujr/B0+fPv39998PGDAgMTHRxKOpQk//O++8k5WVlZ6ezi8aYJLExMQhQ4ZkZWWVl5dXVlZS/B4FiP4ll1wyaNAgt9vd2tra+eDBgwcPHTp0+eWX843K4JF+wDzkPngBop+WljZ+/Hi3271161b9pVjNzc3l5eVnz569+eabY2JionJIdZB+wFjkPlQBNv2EhIT7779/9+7dv/3tb9evXz906NCqqqpjx44VFRXxDfGwsfUDkdO3+0suuYTtPjS+INTX1997770jR47MyMi45ppr3njjjdOnT/fy9hs2bJg/f34w7xmffPLJpEmTuOoHgqdf3U+aNGnDhg1W/xcsnwBX+rqMjIzXXnvN7N9Ie+KqHwgeV/eRCyr6MBvpB3pH7o1C9AVC+oHuyL2xiL5wSD+gI/dmIPqCIv2wM3JvHqIvNNIPuyH3ZiP6EiD9sANyHx1EXxqkH6oi99FE9CVD+qESch99RF9KpB+yI/dWIfoSI/2QEbm3FtGXHumHLMi9CIi+Ikg/REbuxUH0lUL6IRpyLxqiryDSDxGQezERfWWRfliF3IuM6CuO9COayL34iL4tkH6YjdzLgujbCOmHGci9XIi+7ZB+GIXcy4jo2xTpRyTIvbyIvq2RfoSK3MuO6IP0IyjkXg1EHz8h/TgXcq8Soo+fIf3wR+7VQ/TRA9IPcq8qoo9zIv32RO7VRvQRAOm3D3JvB0QfQSH9aiP39kH0EQLSrx5ybzdEHyEj/Wog9/ZE9BEm0i8vcm9nRB8RIf1yIfcg+jAA6RcfuYeO6MMwpF9M5B7+iD4MRvrFQe7RHdGHKUi/tcg9zoXow0SkP/rIPXpH9GE60h8d5B7BIPqIEtJvHnKP4BF9RBXpNxa5R6iIPixA+iNH7hEeog/LkP7wkHtEgujDYqQ/eOQekSP6EALp7x25h1GIPgRC+rsj9zAW0YdwSL+O3MMMRB+CsnP6yT3MQ/QhNLuln9zDbEQfErBD+sk9ooPoQxqqpp/cI5qIPiSjUvrJPaKP6ENKsqef3MMqRB8SkzH95B7WIvqQnizpJ/cQAdGHIkROP7mHOIg+lCJa+sk9REP0oSAR0k/uISaiD2VZlX5yD5ERfSgumukn9xDfeSG99d69e7Ozs7du3WrSaQCT6Ol/5513srKy0tPTExMTjX3/iYmJQ4YMycrKKi8vr6yspPgQVghX+k1NTUuWLGlsbDTvNICpzLjq5+oecgk2+h6Pp7i4+L///a+BH9vj8WialpaWZuD7FAqfoJiMSr8CuZf0dzB4fILdBZ53zpw58/777+fl5dXV1Y0ePTr803VTUVFRUVFh4DsUDZ+gyCIZfJQZc6T+HQwGn2B3ga/09+3b98QTTzgcjlWrVn366af79u0L93iAcEK96lfg6h42F/hKPzY29s4779yyZcvEiROjcCAg+oK56lfm6h42F/hKf/To0cauOoCYznXVz9U9VGLWffoej6esrKz3t3G73SZ9dEHwCUqqoKDA7Xbv2LEjOTm5o6PD4XCkpaUVFBQE81UtF1V/BzvxCXZyOp0ul0szKfqpqan6e+9dMG8jNT5BeblcLoU/u07Kf458gp067/D5KfotLS1z5szx/0PD5XKtXr06vNew2OQ/GACQTmivyAUASO2nK/3ExMR169ZZexQAgNm40gcAGyH6AGAjRB8AbCTG5/NZfQYAQJRwpQ8ANkL0AcBGiD4A2Igo0W9pabnrrrvmz59v9UGMsX///qKiohEjRgwfPnzatGmbN29W9XsnW7dudTqde/bssfogRvL5fNXV1TNnzhwxYkRmZubEiROXLFly8uRJq89lmDNnzmzatGnatGnDhw8fMWLEzJkzq6urVf0SbW5uLioquvbaa48dO2b1WQxz4MCBCRMmZHazcuXKgM8VIvpnzpx58803q6qqrD6IM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the area of ​​the square.","description":"Four circles are inscribed in the square ABCD. The perimeter of each circle is *aπ*.\r\n\r\n\u003c\u003chttp://imgfz.com/i/UzgCJut.png\u003e\u003e\r\n\r\nGiven *a*, obtain the area of ​​the square.\r\n","description_html":"\u003cp\u003eFour circles are inscribed in the square ABCD. The perimeter of each circle is \u003cb\u003eaπ\u003c/b\u003e.\u003c/p\u003e\u003cimg src = \"http://imgfz.com/i/UzgCJut.png\"\u003e\u003cp\u003eGiven \u003cb\u003ea\u003c/b\u003e, obtain the area of ​​the square.\u003c/p\u003e","function_template":"function y = squartArea(a)\r\n y = a;\r\nend","test_suite":"%%\r\na = 0;\r\ny = 0;\r\nassert(isequal(squartArea(a),y))\r\n%%\r\na = 8;\r\ny = 256;\r\nassert(isequal(squartArea(a),y))\r\n%%\r\na = 1;\r\ny = 4;\r\nassert(isequal(squartArea(a),y))\r\n%%\r\na = 10;\r\ny = 400;\r\nassert(isequal(squartArea(a),y))\r\n%%\r\na = 50;\r\ny = 10000;\r\nassert(isequal(squartArea(a),y))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":446926,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":95,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-05-18T03:09:51.000Z","updated_at":"2026-02-05T12:03:10.000Z","published_at":"2020-05-18T03:09:51.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/media/image1.JPEG\"}],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFour circles are inscribed in the square ABCD. The perimeter of each circle is\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eaπ\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, obtain the area of the square.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray 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: Square","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 20.8px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 10.4px; transform-origin: 407px 10.4px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.4px; text-align: left; transform-origin: 384px 10.4px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eDetermine the ratio of the area of a circle to the area of a square, Given the side of the square = radius of the circle.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = area_ratio(x)\r\n y =\r\nend","test_suite":"%%\r\nx = 6.76;\r\ny_correct = pi;\r\nassert(isequal(area_ratio(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":564784,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":113,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-12-05T15:46:44.000Z","updated_at":"2026-02-14T16:21:13.000Z","published_at":"2020-12-05T15:46:44.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDetermine the ratio of the area of a circle to the area of a square, Given the side of the square = radius of the circle.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":49657,"title":"Determine the area of square if length of the diagonal is given","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 21px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 10.5px; transform-origin: 407px 10.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eWe have to find the area of square if the length of the diagonal of a square is given.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = your_fcn_name(x)\r\n y = x;\r\nend","test_suite":"%%\r\nx = 4;\r\ny_correct = 8;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":822117,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":72,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-12-29T15:05:52.000Z","updated_at":"2026-02-06T15:13:38.000Z","published_at":"2020-12-29T15:05:52.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWe have to find the area of square if the length of the diagonal of a square is given.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":50447,"title":"Calculate Triangle Area, A, B and Gamma is given.","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 359px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 179.5px; transform-origin: 407px 179.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eCalculate Triangle Area:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e A\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eB \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eand\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e Gamma\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e [degree] is given as follows:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 209px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 104.5px; text-align: left; transform-origin: 384px 104.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cimg 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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eRound the answer to four decimal places\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = AreaTriangle(A, B, Gamma)\r\n\r\nend","test_suite":"%% \r\nA = 4; B = 6; Gamma = 56.45; % [degree]\r\ny_correct = 10.0008\r\nassert(isequal(AreaTriangle(A, B, Gamma),y_correct))\r\n\r\n%%\r\nA = 5.7; B = 8.9; Gamma = 132; % [degree]\r\n\r\ny_correct = 18.8499\r\nassert(isequal(AreaTriangle(A, B, Gamma),y_correct))\r\n\r\n%%\r\nA = 48.3; B = 643; Gamma = 8; % [degree]\r\n\r\ny_correct = 2161.1425\r\nassert(isequal(AreaTriangle(A, B, Gamma),y_correct))\r\n\r\n%%\r\nA = pi; B = 2*pi; Gamma = 43; % [degree]\r\n\r\ny_correct = 6.7311\r\nassert(isequal(AreaTriangle(A, B, Gamma),y_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":487522,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":31,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-02-18T16:05:19.000Z","updated_at":"2026-03-21T09:29:10.000Z","published_at":"2021-02-18T16:05:19.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate Triangle Area:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e A\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eB \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eand\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e Gamma\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e [degree] is given as follows:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e 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12.5;\r\nassert(abs(square_area(x)-y_correct)\u003c1e-4)","published":true,"deleted":false,"likes_count":4,"comments_count":4,"created_by":134267,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":247,"test_suite_updated_at":"2017-05-31T18:18:43.000Z","rescore_all_solutions":true,"group_id":1,"created_at":"2017-05-16T16:59:29.000Z","updated_at":"2026-02-25T17:47:50.000Z","published_at":"2017-05-16T17:01:02.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind the area of a square whose diagonal length is given as x.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":46948,"title":"area","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 20.8px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 10.4px; transform-origin: 407px 10.4px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.4px; text-align: left; transform-origin: 384px 10.4px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003efind the area of a cube of side \"x\"\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = your_fcn_name(x)\r\n y = x;\r\nend","test_suite":"%%\r\nx = 1;\r\ny_correct = 6;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 2;\r\ny_correct = 24;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":430136,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":215,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-10-19T15:10:51.000Z","updated_at":"2026-02-11T18:22:05.000Z","published_at":"2020-10-19T15:10:51.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003efind the area of a cube of side \\\"x\\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":44391,"title":"For a rectangle, if x is the length and 2x is width. Then find out x from the area of the rectangle?","description":"For a rectangle, if x is the length and 2x is the width. Then find out x from the area of the rectangle?\r\n\r\nif the area is equal to 200 then the length of the rectangle is 10.","description_html":"\u003cp\u003eFor a rectangle, if x is the length and 2x is the width. Then find out x from the area of the rectangle?\u003c/p\u003e\u003cp\u003eif the area is equal to 200 then the length of the rectangle is 10.\u003c/p\u003e","function_template":"function y = length_of_rect(A)\r\n y = A;\r\nend","test_suite":"%%\r\nA = 200;\r\ny_correct = 10;\r\nassert(isequal(length_of_rect(A),y_correct))\r\n\r\n%%\r\nA = 32;\r\ny_correct = 4;\r\nassert(isequal(length_of_rect(A),y_correct))\r\n\r\n%%\r\nA = 18;\r\ny_correct = 3;\r\nassert(isequal(length_of_rect(A),y_correct))\r\n\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":93545,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":109,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2017-10-26T09:21:07.000Z","updated_at":"2026-02-06T18:21:25.000Z","published_at":"2017-10-26T09:21:07.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor a rectangle, if x is the length and 2x is the width. Then find out x from the area of the rectangle?\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eif the area is equal to 200 then the length of the rectangle is 10.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":44505,"title":"Calculating Ring Area","description":"In two-dimensional space, a ring can be constructed by using two concentric circles. Determine the area of a ring which has r1 as the inner radius and r2 as the outer radius.","description_html":"\u003cp\u003eIn two-dimensional space, a ring can be constructed by using two concentric circles. Determine the area of a ring which has r1 as the inner radius and r2 as the outer radius.\u003c/p\u003e","function_template":"function area = RingArea(r1,r2)\r\n area = r1+r2;\r\nend","test_suite":"%%\r\nr1 = 4;\r\nr2 = 5;\r\ny_correct = 28.27433;\r\nassert(abs(RingArea(r1,r2)-y_correct)\u003c1e-5)\r\n%%\r\nr1 = 7.5;\r\nr2 = 8.25;\r\ny_correct = 37.11006;\r\nassert(abs(RingArea(r1,r2)-y_correct)\u003c1e-5)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":180632,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":107,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2018-01-24T18:16:13.000Z","updated_at":"2026-02-06T12:07:01.000Z","published_at":"2018-01-24T18:16:13.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn two-dimensional space, a ring can be constructed by using two concentric circles. Determine the area of a ring which has r1 as the inner radius and r2 as the outer radius.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":2378,"title":"Area of a triangle","description":"A triangle is given with base *'b'* ,vertical hight *'h'* . then find it's area.","description_html":"\u003cp\u003eA triangle is given with base \u003cb\u003e'b'\u003c/b\u003e ,vertical hight \u003cb\u003e'h'\u003c/b\u003e . then find it's area.\u003c/p\u003e","function_template":"function A = trg_area(b,h)\r\n A=f(b,h);\r\nend","test_suite":"%%\r\nb = 1;\r\nh=5\r\ny_correct = 2.5;\r\nassert(isequal(trg_area(b,h),y_correct))\r\n\r\n%%\r\nb = 1;\r\nh=10\r\ny_correct = 5;\r\nassert(isequal(trg_area(b,h),y_correct))","published":true,"deleted":false,"likes_count":4,"comments_count":0,"created_by":22553,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":984,"test_suite_updated_at":"2014-07-07T12:31:13.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2014-06-18T17:40:40.000Z","updated_at":"2026-04-14T21:14:43.000Z","published_at":"2014-06-18T17:40:40.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA triangle is given with base\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e'b'\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e ,vertical hight\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e'h'\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e . then find it's area.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":51173,"title":"Squares inside a square! ","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 99.7778px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.5px 49.8889px; transform-origin: 406.5px 49.8889px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 40.8889px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 20.4444px; text-align: left; transform-origin: 383.5px 20.4444px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eIf you have a square has a side (x) that is divided into four squares. Two of those squares carries smaller squares inside them. Each side carries 5 squares. Find the area of one of these small squares. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.4444px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 10.2222px; text-align: left; transform-origin: 383.5px 10.2222px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.4444px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 10.2222px; text-align: left; transform-origin: 383.5px 10.2222px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = squares_inside_square(x)\r\n y = ;\r\nend","test_suite":"%%\r\nx = 500;\r\ny_correct = 2500;\r\nassert(isequal(squares_inside_square(x),y_correct))\r\n\r\n%%\r\nx = 100;\r\ny_correct = 100;\r\nassert(isequal(squares_inside_square(x),y_correct))\r\n\r\n%%\r\nx = 50;\r\ny_correct = 25;\r\nassert(isequal(squares_inside_square(x),y_correct))\r\n\r\n%%\r\nx = 30;\r\ny_correct = 9;\r\nassert(isequal(squares_inside_square(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":4,"created_by":995198,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":70,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-03-24T11:45:55.000Z","updated_at":"2025-12-25T11:51:40.000Z","published_at":"2021-03-24T11:45:55.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf you have a square has a side (x) that is divided into four squares. Two of those squares carries smaller squares inside them. Each side carries 5 squares. Find the area of one of these small squares. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":45195,"title":"Calculate the area of a circle","description":"Given a circle of diameter x calculate its area","description_html":"\u003cp\u003eGiven a circle of diameter x calculate its area\u003c/p\u003e","function_template":"function y = areaOfCircle(x)\r\n y = x;\r\nend","test_suite":"%%\r\nx = 1;\r\ny_correct = pi * 0.25;\r\nassert(isequal(areaOfCircle(x),y_correct))\r\n%%\r\nx = 15;\r\ny_correct = pi * 56.25;\r\nassert(isequal(areaOfCircle(x),y_correct))\r\n%%\r\nx = 20;\r\ny_correct = pi * 100;\r\nassert(isequal(areaOfCircle(x),y_correct))\r\n%%\r\nx = 100;\r\ny_correct = pi * 2500;\r\nassert(isequal(areaOfCircle(x),y_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":348097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":144,"test_suite_updated_at":"2019-11-05T16:44:06.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2019-11-05T16:37:48.000Z","updated_at":"2026-02-12T19:03:56.000Z","published_at":"2019-11-05T16:44:06.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a circle of diameter x calculate its area\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":60750,"title":"Area of a rectangle","description":"FInd the area of a rectangle with a length L and width W. Round to the nearest integer.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 21px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 10.5px; transform-origin: 407px 10.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFInd the area of a rectangle with a length L and width W. Round to the nearest integer.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function A = your_fcn_name(L,W)\r\n A = ;\r\nend","test_suite":"%%\r\nL = 1;\r\nW = 1;\r\nA_correct = 1;\r\nassert(isequal(your_fcn_name(L,W),A_correct))\r\n%%\r\nL = 3;\r\nW = 6;\r\nA_correct = 18;\r\nassert(isequal(your_fcn_name(L,W),A_correct))\r\n%%\r\nL = 4.5;\r\nW = 5;\r\nA_correct = 23;\r\nassert(isequal(your_fcn_name(L,W),A_correct))\r\n%%\r\nL = 482.2;\r\nW = 572.34;\r\nA_correct = 275982;\r\nassert(isequal(your_fcn_name(L,W),A_correct))\r\n%%\r\nL = 3542113582974;\r\nW = 0;\r\nA_correct = 0;\r\nassert(isequal(your_fcn_name(L,W),A_correct))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":4700639,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":31,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-10-18T20:19:06.000Z","updated_at":"2026-02-09T16:28:46.000Z","published_at":"2024-10-18T20:19:06.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFInd the area of a rectangle with a length L and width W. Round to the nearest integer.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":45333,"title":"Area-01","description":"Given the radius of the circle inscribed in a square, find the area that is not bounded by the circle but inside the square.\r\n\r\n","description_html":"\u003cp\u003eGiven the radius of the circle inscribed in a square, find the area that is not bounded by the circle but inside the square.\u003c/p\u003e","function_template":"function y = inscribed_circle(r)\r\n y = x;\r\nend","test_suite":"%%\r\nr = 1;\r\ny_correct = 0.8584;\r\nassert(abs(inscribed_circle(r)-y_correct)\u003c0.01)\r\n%%\r\nr = 5;\r\ny_correct = 21.4602;\r\nassert(abs(inscribed_circle(r)-y_correct)\u003c0.01)\r\n%%\r\nr = 0;\r\ny_correct = 0;\r\nassert(isequal(inscribed_circle(r),y_correct))\r\n%%\r\nr = 12.1;\r\ny_correct = 125.6794;\r\nassert(abs(inscribed_circle(r)-y_correct)\u003c0.01)\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":363598,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":67,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-02-16T18:24:27.000Z","updated_at":"2026-02-09T14:23:49.000Z","published_at":"2020-02-16T18:24:41.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven the radius of the circle inscribed in a square, find the area that is not bounded by the circle but inside the square.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":2402,"title":"Area of a Square ","description":"Inside a square is a circle with radius r.\r\n\r\nWhat is the area of the square?\r\n\r\n","description_html":"\u003cp\u003eInside a square is a circle with radius r.\u003c/p\u003e\u003cp\u003eWhat is the area of the square?\u003c/p\u003e","function_template":"function A = area_sqr(r)\r\n A= ;\r\nend","test_suite":"%%\r\nr = 2;\r\ny_correct = 16;\r\nassert(isequal(area_sqr(r),y_correct))\r\n\r\n%%\r\nr = 3;\r\ny_correct = 36;\r\nassert(isequal(area_sqr(r),y_correct))\r\n\r\n%%\r\nr = 25;\r\ny_correct = 2500;\r\nassert(isequal(area_sqr(r),y_correct))","published":true,"deleted":false,"likes_count":10,"comments_count":1,"created_by":22553,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":857,"test_suite_updated_at":"2014-07-02T18:36:38.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2014-07-02T18:34:11.000Z","updated_at":"2026-04-06T22:48:48.000Z","published_at":"2014-07-02T18:36:38.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eInside a square is a circle with radius r.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWhat is the area of the square?\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":44308,"title":"Component area","description":"Find the area of the component below, all measurements are in mm\r\n\r\n\u003c\u003chttps://image.ibb.co/hocruF/Component.png\u003e\u003e","description_html":"\u003cp\u003eFind the area of the component below, all measurements are in mm\u003c/p\u003e\u003cimg src = \"https://image.ibb.co/hocruF/Component.png\"\u003e","function_template":"function A = your_fcn_name(h,w,r)\r\n A = h,w,r;\r\nend","test_suite":"%%\r\nh = 50;\r\nw = 20;\r\nr = 12;\r\nA_correct = 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column-rule-color: rgb(60, 60, 60); font-family: Helvetica, Arial, sans-serif; font-size: 20px; font-weight: 700; line-height: 20px; margin-block-end: 5px; margin-block-start: 3px; margin-bottom: 5px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 3px; outline-color: rgb(60, 60, 60); perspective-origin: 384px 10px; text-align: left; text-decoration: none; text-decoration-color: rgb(60, 60, 60); transform-origin: 384px 10px; white-space: pre-wrap; margin-left: 4px; margin-top: 3px; margin-bottom: 5px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eArea between curves - Problem 1\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 24.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 12.25px; text-align: left; transform-origin: 384px 12.25px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFind the area between the curves \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAALIAAAAwCAYAAAC18iC7AAAJr0lEQVR4Xu2cB4x1RRXHf9gbIiJgQdFIlWAEsXdUlIhSxIZdUcGu2I0dgqigRlEwGqmxgoI1oAhEsAQMqEjT2Fts2CtofubMl7vvu3d35r67b+9730yy2c2+uXPPnPnPmXP+58zbiNqqBhZAAxstwBzqFKoGqECuIFgIDVQgL8Qy1klUIFcMLIQGKpAXYhnrJCqQKwbGqoEbAk8F9gfuDnwL+ChwPPD3SaErkMe6jBu2XIL4bcBmwMnAdsBzgO2BVwFHAv9pqqgCecMGzFhn/2BgX+CVwF9DyB2Bj8TfjwMur0Ae6/JVudSAxvUlwJeAbzdUcj3grfHZfYHzKpArYMaugRsB/wCumRD0dcCTw29ugrwmRMa+olW+dRpIFvn2wDOBP1SLXNExjxq4FXACcFwEgEvmUIO9eVzSDU9mcfpE4F7AKxoB4DpNVCAvFiiKuNc5mrqMxSHAa4Fft8m91kD2/fcAfg78dADF3ha4DfAN4L8DjDdPQxRzr3MyuS2Bw4I7vrRL5rUE8nWC5P59ZGyGAN61gAOA6wInTpLmc7JwfcUs5l77vmiGz90YeAtwGnDOcu8dAsiOcUfgAcAtgO8CZ7f5MQ1BBPGLgF8MCOI0vPI8HrjBBgTmXtzrDAHZ51WC+OXAucBXGiesc90P+B6wzkJPC2SPM32X+wRRfQfg83EM6M/8s2MGAk1Su5m56TPZrmeUy+Pos8BZQw484rGKudcRz0VDJ652nwCxIm8BbBKGMGX9puKRrw28NAAsMN05ZmSOAj4JHAj8sUVZ2wLvjN3W6fMMoGTz8kcALwZ+NMB48zjEstzrGk1I3NwvUtB7Ax8Mo+N6vR24abgSbwQ27pDx0cCpzc+msci7BWA1+88PV+LmwKOAr03mwuOlTuINUb1kUcjVq6jMdNzeDHjTKr9rFacx1dDLcq9TjTz9w5sCHwJcH09vQf1FwP+bnv5zySv6AjkB0pThk9oI6g4hdgI+ABw8kUcvkbmk752B9wPPBi4peXAB+q7Iva7xHJVPo+bPlyPw/0FfmfoCWV/YSiQtsPWiS/Leywij67EL8LzSHddzgh5NRwMXhTszBDPSU5SZP7Yi9zqlRBqxN2eOcWy4nZN1xJ7eMhLPBY6ZhjLtC2SjxlPiKLCI47cZE9JB1x+yQPrwjP5DdXk1sOsyPvtQ7xnTOFnc65QCu1F8T067CvhOi3t3zwDye4NmyxmrtU8fIDfL6d4X0aWVSis1j3mDwJcBp6/UecDP3fWHAo8FLhtw3LEOlc29tkzgdsBTgt7y5LTmV4PlqSZVOmRTTuMk6471iac6pXOBLJ0l02CVfldbCdQPjWsqjwQuzNCIE71bTPRhwObA04DPxLO6DfKMKuBM4AXAb1rGvWs847UZ+81LM+i5N/AY4IFR1mi9QdLdLeNolzEyaHoNYEIom3ttKEIcmAcQWB7xnwvGwLGML8yUPr3J206pRN93EPCzmOOegMXyWm6TWf6/qOUCuTmox8EZMdE9CsDhTpeuW6+6v0PireL//w5aRhfGbJ3AtU5V98QNZorb7KDj/6RlLGmdjwUtaPVUSRM4J5U80NF3vULwjDGlKV1YXTID5AfFnPVNTTx53UefUwPx9fAzn1XCvTZk8LR0nhauG/ukWCKxHg8BPhGGbEn5ZMY8ml00Kgb8fwOc37vC+vtugS1H/OFZAVnAeAFQy6A1+H7mZFwACW7BUXpMeRJoKXyngNaqu2ubSu8SY5vIHhpUmO4saWsJ5CSnDJFy6+trKQ2M5MabaVv7yB69p4R7jRd48umjauEn450msyAdphsgw9C3yVbJDwtWrb8GSECncoIXRgxVPH6pRW4qdbmkR5sgAtkMoOD4XaGkyT3QQhgBG1yqkCUXEDvGTBcYvRpTCuRCMVete4ruDZgujuSTgfMQLEzSrXW+rtEkt9/czJ6oupija6VATsyDlJtJBn9ylTkNkG8dXLW+ogkYLYcVczltEYCcAmWtl+6R8cCfciaf0SedsBld/w9ibzH/K6fzLPuUAjkd0+5i3Qp9z9w2jWthAZA+ocdqqTKTj6yss6T9cvWS08/Az+P3ERFnDGkVEx/8+jk+sYprLe4f5XRXFiZCXKzSYK+5wG44I2hrJ0xj5nLXjpGAbB7f70iYx3Z94B1RCtCVXOgzL1kOkxqmiN3kba5Fn3Fn/kypRU5Bl7yfdb9tdFfXJErpt+Y4qa5ja6B0E+mXfzXoJQubStoYgj3ltQ5BiyzlaIlsn4C5a97JIidGqKjGoUSZq9m3BMh9EyFJ/mQZPcJKEiJmj94dNN8zgncsqe+Q7tOalzAsSeYxANkMmtbyU/H7JoC865LvdZgCJMk4/RLYB/hmx1hixc81JNacj6qVALnpp8n5ecSVtFT3cEWU7eUEidaletnQMkzpJv1kFZ+OQflkSwLNQLXd5Uosi2xHqtArkXmt+0qNye3KEFn0pNV8eHCu6l/9yC+bsOgb/MnryhG7YdSx+p3UpTjxvW4ga8jX++61tVZUCZB3AD4O7NzzmHaufh+BAct630sQilAe61GlgCyafgJgAiYpL1mP5Ce7CCZl9PPaivhNHLj4AsHs19ibPqvMkCl/E0EWl7tZrfG2JT5ZEPuZLoesjDxwjmFom7/+t5cQHM/mZQQ5XktxpTc1YGZUrQE24bKaNeS916cEyPq4ZvTOD//4xz3eatWcZLhWtu0Iuwvw6aiq03KbqZNETxbCb2X0cy2s1uMvsQCtN2sB77HpA7oQ81Bc7yY3ySOIfxiWtnn9PRVr6ce6mX8ViZJ1NyV6rImPmP73tDOIbmty166D4B5lKwFyuv0xTdTs+8zeeNu57SqU/rAKNQHgV4jqT7tYqZmStn5VBsSF9O+u29daGi2L/txQyYPVXkTjCAt0LNjxt0xLM/gScP7PU0iDoK7Mjg3R1NdeUSVogKwr6IVPTzM3V2kSawiZssfIBXKzaKgk0GoTJAVv0kkXZEta3lGqUN65q5iofMT6xGg1kAvklFkT0PqtHnvTNHe8xT/epC6h8HLfOavNkitP7bfKGsgFssD7QlQrDXH/LUXBd4pApeu2dZ/pu9ksqjGSb14j7zNWfWZONNAGZJMOFpDIHFiDKr8oeA2cDAbkEYdovts6Y+sIrNoagtIRxLoSBpL6d30j+SHmV8eYoQbagJyqoWQMdCO8NWBCQjdg2W976Sm35YOCuO2rA0qHlG4zaMktKCodv/YfqQbagCzJLs8rZ2jBtqS8QPYCZ21VA6PUQK6PPErhq1BVA0kDFcgVCwuhgQrkhVjGOokK5IqBhdDA/wAhzwlPY6BW9AAAAABJRU5ErkJggg==\" width=\"89\" height=\"24\" style=\"width: 89px; height: 24px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAALMAAAAmCAYAAACPv6oDAAAJWUlEQVR4Xu2bB8wtRRXHfyhRBIQgAooiYDQECRhCVIoNKyoqoYmAghERBAQ0FiyAIjZAVKpSlKrGBgSCigaUjlKEEDASCEUFOxZQUTC/lzMv85a9d2e/u3t53/12ki8v7+7u7MyZ/5z5n/85uwxDGywwIxZYZkbmMUxjsAADmAcQzIwFBjDPzFIOExnAPGBgZiwwTTA/CXgJ8DPgXxNa8HHAlsD1wJ8n7Gt4fEYsMC0wrwZ8DDgRuKUj2z0DeD/wJeDOjvocupnHFpgGmNcADgW+3CGQk8nt+0MDoOcxApuH7on+eOAfTbf2DWYH8jngKuAbwCNNA5rD9S2AnYAPA/+cw/PDI0uXBZ4L7AZsDGwArA28Dzi6aZh9g1mQvTzoQF9Ac9d+EHggvH8fG6bJjsP17i2wI/At4O/A64DLm17RJ5ifDpwEfD6CvqaxTHJ9XeCE2DQ3T9LR8OxSY4G3A6cBlwC7AL9tGlmfYH4n8DJgn9hdTWOZ5Lre+TDgv8AngP9N0tnwbLEF9gO2Bo4Hzi1+qvnGJwCfBQ4MeiGF/E/TY32BeWXgZODHwFeaBtHR9VcHoN8K3NFRn0M34y3wceCTwK7AWR0aa83oT4pa3HdfYN4E+G4EZgZ/02jPAb4Zxj1vGi8c3kFfYDaovxC4F9geuLHE1n2B+d2AnGfnKWrA6TSQM0s1hkCwBAGT3dMXmKUXXwC+A+wB3F8yzBIwPys87GuA20L+ej5wTvw9GJw4cZrEX5VYSgeyCrA5sEOoH2YIJf3XxiSeFh5XdeQU4COA781b4llPnRJPL7Fv23tWAN4cdvg14P/1Sm5U5/4DWOQNR8UEZkbXAl4PvAnQw3lKyW3/AosKyzYLPqrstRfw7baDzO7vA8xPBo4D3hZz/TSwHnAA8FrgKcBPgC+GsLDYaY0Ds4bRgMcAVwLvBW4Pg7hzjsom9eJMOlk+khga3PuqoKuzncD/ayzaVyNV/ZmYjOD0XfYjL5a27An8raYjjfvSOBH+0GKRVg2OprEmacYHpXPO3+M6mJ436Pl5JJkcv7/nthbo4yjUE4FnR+TvmqjtCw4d0UURkNufjmercArHTjDhPsAscJXkdJgJvG5GcaG8q6Aglzbrq8NbLNmNA7OGOyMyL4LamorU7OTMEbJJAsZ1DV6kzobJqx8EXAC8J3akkfJPC4zuc2+Jv18V3J9ueSzBrNOQjqkIaG8181yTT7a+oiVty4MoTzJPUtP/HwXua2Gbcbf2AWZPFNfb+WoPQe2YUw2OyRTBrgNMDm/RSTUKzLmr/zqwb8XAcmLrLH5ZA5wEDHeMclnbliZzU/TvJlIZKeHALvwH5gDmtmPs6n7tr/qiLZ2ntMygJ2+JP2qD/SM5VPL+XN7SMeiNLSsoCqZKXhDOqks1I3dm0iwdonPON1/ueJY4CUeBOSkDqhLVVGJuJKU3vUp+pE8K5o2C+LvzTg++V0cp6uw938DsXFVgnhlR+48qk1ouKJYnVFFKt/J8cjr+LDUrdQrVE7gQ2yNvy2nouL5MtLnmrwoaoZLxi8oDFq2dHfcUeeYczFWdz2ybXOxFcSQadeYBySQ0w3EbDHq8vGEOC+ixJz2SFhmsLs3NuhXrDQTcqE1rXYILt2FpSrcy4U0BN4hFOm/MAupSuySKU3r/qPtKwZwkOZmBp3pdAix3dktgc5RnNoo2MNg9It6U+Fg2Cnp8kbzGhajyr7kEgLkRDGKODGrTNqASzBrERfjTpCvQ8/MvDB6rN9oO+F7N+8bFJiXDMxjU87+gTfKhpOO4p2vOnCiVZcIqW3WlCem0uToo2uIE2bgA0KhSGcxdLWf+TRjkU0HA5V91hfFzkeZy+6XA091ZnJcHkqfz/W24pe+edgCo3Q1qdAqPWpQwxupR22IMoQcvSulmhtQpHB5Bnz8vcSS3AOy4W7sEcx6nWS5sIPzvystzGqJU531F0pwGl0pYVH9NdHw3cClwT0NApkeR57VNmqwfRv9+/Ltii+M10RMDTxeuTZs2mPOFk1JV61e0vVKoWqpNPbhNWUAKLNXujWd0PGrUard/bGOYhnu7BHMuydWdVLlNalnBKM+cR9l6ZTldm5YCm3eVlO5Fx1IbdVazPh4vLrJaaFpIKY5arJ6sLiBM71STVFRfmtvIiDwGbYGWMqM0wYSROrGB0Lj55/PVKfjRgn/GP9XUsEGUSRMVlIcnMFSXYE4qlipGXQpbm1hFp9rzjroPPUaBOQ/CFPEl4h75pTXJiXMrr3lE1slq6qtmtsz2PRTHoYY1oLR5BLugeiT1UemHIJDL1/XnaSDHN43+uwkWaBqP5p4595gpeaJcd35saG1ooGMsYKAtB67OX4VJm1v7q438lMxkl6dUtWhHvVnbGlhWlYK2c+8KzLkkV6eQuTm/FmltKeStdQMdBWY7VwqyFjlvGthU48U1fKba/7axCJaCmkqtNtUKVRGBLInX4+YJA5+3WMkFcsHdkYK7bkOlzXPDPCnQ1+5qyma1bNZiqwV7Ennt4KBXJqYMhkzrOzdBaplr3gSy4NR2Jop0CMY16cseubPrKG0xLyBV9FoXX/50BeaVwhYmvHIw6/BeGV8rqco4j5EfMNeBOeXv5by6dY8pPYVfVqdm0b0Bybgvo/XuLpJGq6t1lSO5Mczo+O8Rlbpnj0J/84h1V5rSHvU+lQFPDwFioDofmiDzJDGCd65So1MzR6EnNgA32WF9gvSrCmTn6XoZ+bvQ0i/5sd43pw/WY3hCqjSN66ut3boCs+/VBp6qUil5vs5rnfgC39PorqbBVcGsgXXj6pN7Z7KbO+R5kV3zhTa5aVNeX56jZ7bPOu/cNL6S66oYUhPT3U56aNOzQF/F+XOaQRXM8k694TahYFQ7FeweZ6YwSzTgRFfsp5pcmdOAKw+lQFXvrupSlXK6eMfQxzyxQA7mlDr1eJO7jCrU8fplLXRLPaeaoJxYrl1SY1FqPtPtcmtVELn10BawBXIwp4hSKW7c17DSBrnSEuV3DTYU0B5JFrn8sCNAC2TlHLOFA5AXMIjT1Ks0IwUdSh8K+XkwJW8W5IeEJzSx0cbL+ryEXiJfF8i0WQ43nhqsfQ3Uoo3lZvjeOjUjfVnyiogolYaMgv3dIn0j5d/PsE2Gqc1TC4yrzZinUxqGvVAtMIB5oa78DM57APMMLupCndIA5oW68jM47/8Dvp08RZxbCC0AAAAASUVORK5CYII=\" width=\"89.5\" height=\"19\" style=\"width: 89.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e over the interval [0 2] for different \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ea\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eb\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e coefficients:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; 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0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = AreaCurves(a, b)\r\n \r\nend","test_suite":"%%\r\nfiletext = fileread('AreaCurves.m');\r\nfor ii = [3.5773, 6.1773, 5.5773, 11.2970]\r\n assert(isempty(strfind(filetext, num2str(ii))), ... \r\n 'Do NOT use provided answers in your solution')\r\nend\r\n%%\r\na = 1; \r\nb = 1;\r\n\r\ny_correct = 3.5773;\r\nassert(abs(AreaCurves(a,b)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = 3; \r\nb = 0.3; \r\n\r\ny_correct = 6.1773;\r\nassert(abs(AreaCurves(a,b)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = -1;\r\nb = 4;\r\n\r\ny_correct = 5.5773;\r\nassert(abs(AreaCurves(a,b)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = pi;\r\nb = exp(1);\r\n\r\ny_correct = 11.2970;\r\nassert(abs(AreaCurves(a,b)-y_correct)\u003c1e-4)\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":487522,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":25,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-02-19T12:36:27.000Z","updated_at":"2026-01-23T10:01:56.000Z","published_at":"2021-02-19T12:40:47.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"heading\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eArea between curves - Problem 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind the area between the curves \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ef(x) = x^2\\\\, \\\\mathrm{e}^{- x^2}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":48000,"title":"Lateral Area of a Right Rectangular Pyramid","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 42px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 21px; transform-origin: 407px 21px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eGiven the length (l) and width (w) of the rectangular base along with the height (h) of a pyramid, determine the lateral area of a right rectangular pyramid.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = area(l,w,h)\r\n y = l^2+w^2+h^2;\r\nend","test_suite":"%%\r\nl = 1; w=1; h=1;\r\ny_correct = 2.2361;\r\nassert(isequal(area(l,w,h),y_correct))\r\n%%\r\nl = 2; w=2; h=12;\r\ny_correct = 48.1664;\r\nassert(isequal(area(l,w,h),y_correct))\r\n%%\r\nl = 12; w=3; h=1;\r\ny_correct = 39.8816;\r\nassert(isequal(area(l,w,h),y_correct))\r\n\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":180632,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":36,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-12-17T03:05:41.000Z","updated_at":"2026-02-17T08:25:19.000Z","published_at":"2020-12-17T03:05:41.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven the length (l) and width (w) of the rectangular base along with the height (h) of a pyramid, determine the lateral area of a right rectangular pyramid.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61157,"title":"Scaling vertically parabola by evaluating its area over an interval","description":"Let p be a quadratic polynomial, with its axis of symmetry being the y-axis. Considering the vertical shift of its vertex to the origin, find the positive constant, k, that scales the shifted parabola such that its area over the interval [-a; a] (a\u003e0) will be equal to the area under the original parabola (see figure below).\r\ninput: (p, a)\r\noutput: k\r\n\r\n\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 447.8px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 408px 223.9px; transform-origin: 408px 223.9px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eLet \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ep\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e be a quadratic polynomial, with its axis of symmetry being the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ey\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e-axis. Considering the vertical shift of its vertex to the origin, find the positive constant, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ek\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, that scales the shifted parabola such that its area over the interval \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[-a; a] (a\u0026gt;0)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e will be equal to the area under the original parabola (see figure below).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003einput: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(p, a)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eoutput: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ek\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 255.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 127.9px; text-align: left; transform-origin: 384px 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bPr06Xl5eewsukPPP/98u3bt3n333UWLFt13330zZsy4detWWu05sxdeeIEQ8sknnyxatKh58+YxMTFff/31xo0bc3JySktLmc1dnTp1SkxM/PDDDz/++OOOHTsuXbp04sSJIizJg/diH2alVrsWrRSy6puzdu1aQsjs2bNrfYROZzeNltPg62WxWK5evdqpUyepByKUq1evBgYGsjtLyEH9v1RQu40bN27YsGHbtm3sVWHxzZs379ixYzt37mzbtm1Dn2symWbMmFFUVOTa0yny/HUym82lpaUdOnSQeiBCuXz5cocOHdh7B+TOYCB/L/EQQkhaWh1Z7jp+qdxtRwGOugIQxvXr14cPH56SkmK7ajcajXq9PigoqHXr1qIN49SpUzExMTt27LDdU1hYePz48eDgYGqLM4B8sVPcDTnMiuI+lyQ27EQ3jroC4ElQUNBDDz300UcfXb16Va1W//nnn59++mleXt7ChQvFnJyFhoaqVKq33nrr7NmzDz/88I0bN1JTU4uLixctWmTr0Akgd+wUdyM6YLphhJ42rSZC63QkKQkdQAEaz8fHZ+HChQEBAV999dWuXbuaNGny4IMPfvzxxwMHDhRzGEqlMiUlZdWqVbt3705PT2/atGmfPn02b958//33izkMANc14jArihtGaG5FN6bRAHxQKpULFixYsGCBtMNo06bNihUrVqxYwcurNegMbAAeNOIwK4q7rUMz2CGZ3fUUAABAWo04zIrinhGavbGMOeoKAABAco07zIrinhFao7Fbe2avyQMAAEilcYdZUdwzQhP71AH2XIF3q6ys3Lp164gRI7p37x4WFtanT59XXnnl/PnztgdkZmaGhYVt3LixtleYN29eTEzM9evXCSFWq3Xbtm29e/cOCwt77rnnbt261cjhbdy4kcdjMxrDZDJNnjzZ9p0C8K9xh1lR3LBSjIGjrgAIIYQYjcZXXnklOzu7Y8eOcXFxTZs2PXPmzIEDBw4ePPj+++8PHz68oS+Yl5f33nvvhYaGxsfHd+rU6Z577tmxY0d1dfXkyZOFGD+A52j0YVYUt43QOOoKgBBCiF6v//HHH+fOnfviiy/ajs04c+ZMfHz82rVrH374Ye5RylwpKSm2/y4uLjYajTNnzmSi+6lTp955550XX3xRoPEDeA5eU9zEjbPcxH6TGRLd4K2OHDmiVCpjYmJs4ZkQ0rNnzwkTJly5cqWoqMi1l0XPaoCGMRjsIhEf24DdOUKjAygAIV26dDGbzQbOjoZ58+adPHkyMjLSdo/ZbN68eXO/fv3CwsKio6P37NlTXV1te3BMTIzBYJg8efKMGTMIITNmzIiIiEhNTY2LizMaje+++65tLbmqqmrr1q3R0dFhYWE9evSYNWsW+zrAarUeOXJkxIgRXbt2DQ8Pf/PNN+teyTaZTCtXrmSWvYcNG3bw4MFJkyZNnjzZZDIxy8aJiYmpqak9evQIDw/fs2cPIeT8+fMJCQl9+vQJCwvr3r37iBEjDhw4wDQrvX79ekxMTGJi4t69e6OiosLCwqKiorZu3Wo75Ipx7ty5SZMmde/enTt+ABdRnT5dOsyK4rZZbgY6gIJLXNug19DmdeK8y+OPP56WljZ37lzm6MlHHnmkXbt2Ds+z2rBhQ/v27V9++WVfX9///ve/c+bMUSgUzJHJDF9f31deeSUiIuKjjz564YUX+vTp06VLl9dee+2DDz4YNmzYsGHDQkJCqqqqkpKStm/fHh4ePmvWrJKSEp1Op9FodDodc6r0N998M2fOnHbt2i1dupQQkpqaeu3atdrOUzGZTC+99NKRI0dGjx49aNCgn376adasWVar9eGHH7Y9JjMz8+TJk0uXLi0uLg4PD8/Ly4uPj7/33nsTEhK6dOmSl5e3c+fOOXPmBAYGRkVF2Z6SnZ09atSoiIiIjIyM5OTk8+fPJ/99WG9hYWFCQsLIkSOnTJly+PDhjIyMK1eu6HQ65jhqABdRnT75WHh18wiNDqDgEvapM85r6FFqLryLRkNqP2XRsfvvv3/79u2vvfba4cOHDx06RAhp3rx5bGxsfHw8dfTkgw8+mJqaypzG+NBDD02dOpUJY7YH+Pr6RkVFmUwm5gHMMZF37tzZsGHD/fffP3ToUEJIdnZ2RkbG+PHj33nnHSYTHh0dnZCQ8O67765ataqysnLLli2dOnWyBewhQ4ZoNJraaqezsrJ+/vnn+fPnJyQkKBSKuLi4iIgIrf3+SbPZ/MYbb8T8PSNZs2ZN06ZNN23a9MADDxBCRo4cGRUVNWPGjNzcXFuEvn379ooVK5h19JEjRy5evHjPnj1jx45lnkIIeeedd8aNG0cI+ec//+nn57dr1y6DwSDt+V3g3vjr9Mnmzlluwkl0s/+BACTl2gS6oeGZERoaunPnzpycnJSUlBEjRhBC9u3bN2HChCVLlrCzu4MHD2bCMyEkODi4a9euV65cYeKx87755psmTZqwD1eOiIhQq9W//PLLlStX8vPzL1y4EBcXx4Rn5o3i4uIcvpTFYvn222+Dg4NHjRrFXEkoFIrhw4d3796d/bD27dv37NnTdvPVV189fPiwLdYSQoKCgqg5elRUlPrvGYyvr+/EiRMtFktubi5zT8eOHW2xXKFQDBgwwGg0FhcXN+jfAcAOf50+2dx8Dk0I0WhqVqDT05HoBoE0NDvj2jS9Mdq0aTNu3Lhx48ZZrdazZ88uXLjws88+GzBggG2WTB2ve889Db5Av3XrVlFRUfPmzS9dusSeFldXVxuNxtLS0pKSEpPJ1KNHD/azqJs2ZrP5jz/+6NChAzu97O/vHxQUxH5Yhw4duOdOVlRUnD59+rfffjt69GhOTo7RaGR/tXXr1v7+/rabrVq1UiqVZ86cYW7ec8897H8K1MQBD6gqbp64f4SOiamJ0EwHUCS6QQAFBVKPwBGmZuqRRx5Zvny57U6FQtGzZ8+33nqLm8duJKvVarFYbt68uXjxYu5XS0pK+HojNupKorCwMDEx8dixY4SQpk2bdu3atW/fvj/88EO9r4NIDEIRJsVNhI7QFRUVGzZs+OKLL27evNm8efORI0fOmjXLlv7ih0ZDtNqalKJW62KiELyJCOFWnIjeunXr5s2bHz9+vKSkhNr37Ofn16xZM37DklKp7NKly+XLl3fs2NGxY0fuA06dOhUQEJCbm8usYTMuXrzo8NX8/PyCgoJ+/fVXo9FoO/v5zp07ZWVlrVq1cviUysrKZcuW5efnb9q0adCgQc2aNWPe9KeffmI/rKys7Pbt28xXCSHFxcXl5eXdunVr+HcM4AS+t0HbCLgOfeXKlWnTpn300UctWrSYOHFiWFjYzp07NRoN/xsb0AEUGkilavD/RHgLF94lKCho9OjR58+fX758eUVFhe3+ysrK1NTU8vLyxx57rMEvaq9JkyY+Pj4Wi4W5+cgjjxQXF+/bt8/6d+Gc0Wh87rnnBg8eXFBQoFKpunXrduDAgcLCQuarpaWl3377rcNX9vHxefLJJ4uKivbu3Wt7tcOHD1+6dKm2wRiNxnPnznXt2jUqKooJwNXV1dnZ2dRC8rFjx06fPs38d1VV1VdffdWiRYvo6OhG/UMAOERNoHntnSXUHNpqtW7ZsuXkyZPz58+fMWNGkyZNrFbr5s2bV65cuWXLliT+kgCEoAMoeLUpU6bk5eXt3r3766+/7tevX6dOnW7evHnkyJE///zzmWeeYc9lXdO6dWulUvn111+HhIQMGDBg2LBhP//888qVKw8fPjx27NiKiort27efO3duwYIFKpVKoVAsWbIkISHh6aefZvZV173bKjY2duDAge+99965c+eY3VaZmZm1PZgQEhQUFBkZuW/fvtdee23o0KEVFRUZGRlnz55VKBTspWij0ajRaJ5//vkuXbqkp6efPHlywYIF999/f+N7jAPQeD3MiiLUHPrixYv79u0bNGiQRqNhWh0xOy87d+584cIF9sU+D9Rqu5CME6PBmwQEBKxdu3b9+vUPPvjgsWPHtm/fnp2d/eCDD27evFmr1TY+y92mTZuEhITCwsK5c+cePXrU19d3yZIlS5cu/f333xMTE998801CyAcffPCvf/2LqceOjIz85JNPOnXq9NZbby1fvrx3797MxmiHlErlunXrnn322YMHDyYmJp45c2bVqlXsym2Kj49PcnLypEmTfvrpp7lz577//vt9+vT55ptvBgwYUFBQYAvS/fv3X7Ro0WeffZaYmHjr1i328AB4JsA2aBuFtaF7PJ1z4MCBl156afXq1WPGjHH+WWvXriWEzJ49u8Hvp9OR+Piam8J8U41ksViuXr3aqVMnqQcilKtXrwYGBtYxAZKE679UIIXr168/9dRT/fr1Y7cKb+jTg4ODN23aZFvb5pE8f53MZnNpaWmHDh2kHohQLl++3KFDB2ozgiwYDHbbNtLSXNhPVMcvlVBz6EuXLjFFJQcOHBg6dCjT/2/hwoVCdddDB1AAN7R58+Zhw4ZduHDBds/Ro0evXbuGqi5wD9Q2aL63+woVoZkuwRs3bnz11VebN2/+1FNPtW3b9vPPPxekUozB/qfJzhbkLQCAVwMHDrx58+b06dPT09P379+v1WoXL14cGho6evRoqYcG4ARhtkHbCJg0MJlM2dnZa9asYXrvVVdXb9q0KSUlhekOWFu+Iicnh7onIiKC3f2/Nj4PPaS0TZ11OlNioiUkpDHj553FYikvL/fg3r8VFRUKhUJuWW6z2Sy3IYFNr169Pvzww5SUlOXLl9+5c6dly5ZPPfXUq6++2qJFC6mHViuz2VxWVib1KOyYzeaKigp2kxYPU15e7u/vL7cst09hoZI1hzYlJlqc+MXIzc09ceIE+56cnBxbkzv6LRo3wnpMmjRp2LBhzH83adJk8uTJBw8eZLoDdu7cmd/3skydSlatqtkYrdeTqVP5fYtGslqtqFUBoPTr12/Hjh18vVrbtm2zkULzOAqFUCVTjeGzbVvNDZXKIsB2PqEiNFNB2r17d3ZMatmyZdeuXfPz88vLy2t7YlRUlOtVGGq1bQVaOWsWefllF19HGBaLxWw219aKwQNUVla2atVKbhNWuY0H3J2fn5/c/orNZrPVapXbqHhkNBoDAwPlNocmR4/W/Lda7eS/v1qtVjtd7y3UOjRT6GE2m9l3Wq3Wv/76S6B3JISzEQ0HaQAAgBD0euG2QdsIFaF79+7t5+f3008/VVZW2u68cePG6dOng4KCWrduLci7qtV2a/XYGA0AAEIQrNMnm1ARumfPnpGRkTk5Ofv372fWD6qrq7/44osLFy7Exsa2b99eoPe1a1mOPVfgHSorK7du3TpixIju3buHhYX16dPnlVdeOX/+PC8vvnHjxoiIiFOnTknydB6ZTKbJkyfHxMTUdlg1gLMMBrv4ItiZikJFaKVSuXjx4rZt2y5YsGDMmDELFy4cOnToe++917Nnz+nTpwtYMIWN0eBljEbjv//97+Tk5IqKiri4uEmTJqlUqgMHDowePfrAgQNSjw7AE1HHv8fECPQ+Ai689+rV67PPPlu3bt2333576tSp++6774UXXnjxxRcF30ehVtcsD2Rn48Ro8Gx6vf7HH3+cO3fuiy++yHTYJYScOXMmPj5+7dq1Dz/8MHXmFQA0FrvTJ9V2mlcCnm1FCAkODl6xYsXx48fz8/OPHTu2YMECMbY5slfsdTr6YgfAsxw5ckSpVMbExNjCMyGkZ8+eEyZMuHLlilANggC8lmCnQXMJG6GlQU2aUdENHq1Lly5ms9nAuRKdN2/eyZMnbd1+Kisr09PTo6Ojw8LCevToMX36dNtCdXV19f79+0eOHNmjR4+wsLDw8PCEhISCWg64rqqq2rp1q+11Zs2axb4IsFqtR44cGTFiBNPo980336z7OCmTybRy5crevXuHhYUNGzbs4MGDkyZNmjx5sslkYpaNExMTU1NTe/ToER4evmfPHkLI+fPnExIS+vTpExYW1r179xEjRhw4cIApdrl+/XpMTExiYuLevXujoqLCwsKioqK2bt1aVVXFftNz585NmjSpe/fu3PED1I/q9CnkUYoy217GF42mZgVaq0WiG2jsJJV7iYmhPhEef/zxtLS0uXPn7ty5c8yYMY888ki7du2oUo+qqqo333xzx44d0dHR8+bNKyws1Ol0U6ZMSUtL5mdwtwAAIABJREFU69WrV2pq6nvvvde/f3+tVtusWbPMzMxvv/326tWrH3/8cWBgIPU6SUlJ27dvDw8PnzVrVklJiU6n02g0Op0uODiYEPLNN9/MmTOnXbt2zHlWdR89aTKZXnrppSNHjowePZo5enLWrFlWq/Xhhx+2PSYzM/PkyZNLly4tLi4ODw/Py8uLj4+/9957ExISunTpkpeXt3Pnzjlz5gQGBtq6MmVmZmZnZ48aNSoiIiIjIyM5Ofn8+fPJycnMVwsLCxMSEkaOHDllypTDhw9nZGRcuXJFp9N5cLM/4Bm7ilvgk449NEKzT4xmMhI4MRrY/v68dj/JydQv8/333799+/bXXnvt8OHDhw4dIoQ0b948NjY2Pj4+MjKSCdVHjhzJyMj497//PXfuXOaeRx999OWXX87KygoODs7Ozh40aNB//vMfpm1kXFycVqvdtWtXYWEhFaGZ1xk/fvw777zDdCWKjo5OSEhgWvlWVlZu2bKlU6dOtoA9ZMgQjUZTW+10VlbWzz//PH/+/ISEBIVCERcXFxERobW/eDKbzW+88UbM35U4a9asadq06aZNmx544AFCyMiRI6OiombMmJGbm2uL0Ldv316xYgXTbHjkyJGLFy/es2fP2LFjmacQQt55551x48YRQv75z3/6+fnt2rXLYDCEh4c34qcCXkOUbdA2npjlJtgYDd4lNDR0586dOTk5KSkpI0aMIITs27dvwoQJS5YsYRK8er2+ZcuWo0ePts2t+/Tpc/jw4VmzZgUGBm7btu2///2vrauzQqGobT/kN99806RJk4kTJ9qOnY6IiFCr1Uwr3/z8/AsXLsTFxTHhmRASHBwcFxfn8KUsFsu3334bHBw8atQoZlQKhWL48OHdu3dnP6x9+/bs46JfffXVw4cP22ItISQoKIiao0dFRdl6Nvn6+k6cONFiseTm5jL3dOzY0RbLFQrFgAEDjEZjcXFx7f+6ACyibIO28dA5NCEkKanmxGidjqSlSToaAMG1adNm3Lhx48aNs1qtZ8+eXbhw4WeffTZgwIBRo0YZjUZ/f/+WLVvW9tzq6upr166dOXMmPz//0KFDx48fv+ce+vL91q1bRUVFzZs3v3TpEntaXF1dbTQaS0tLS0pKTCZTjx492M+ibtqYzeY//vijQ4cO7PSyv79/UFAQ+2EdOnS49957qedWVFScPn36t99+O3r0aE5OjtFoZH+1devW7DMkWrVqpVQqz5w5w9y855572M0jbZcaAPUTaxu0jedGaI2mJkITQnQ6rEZDDff9ZejShX2LKZt65JFHli9fbrtToVD07Nnzrbfemjp1KrMiW8frWa3W77//fuHChX/88QchpGXLluHh4Q57jFitVovFcvPmzcWLF3Nfp6SkxPVvqnbUhUJhYWFiYuKxY8cIIU2bNu3atWvfvn1/+OGHel8HkRh4wK7HVKmE2wZt47kRmmBjNNTOU3IqrVu3bt68+fHjx0tKSqh9z35+fs2aNWMiU0BAQGVlZXl5edu2bZmvlpeXP//886GhofHx8a+//nq3bt2WL1/euXNnZsvWxo0buRFaqVR26dLl8uXLO3bs6NixI3cwp06dCggIyM3NHTJkiO3OixcvOhy5n59fUFDQr7/+ajQalUolc+edO3fKyspqO4GgsrJy2bJl+fn5mzZtGjRoULNmzZg3/emnn9gPKysru337NvNVQkhxcXF5eTlzUgBAo7CLJIRPcROPXYdmYGM0eLqgoKDRo0efP39++fLlFRUVtvsrKytTU1PLy8sfe+wxQoharS4vL8/MzLQd4ffjjz/m5eX17t376tWrJSUl0dHRoaGhTHguLS3V6/Vms5l7Bt0jjzxSXFy8b98+2+sYjcbnnntu8ODBBQUFKpWqW7duBw4cKCwsZL5aWlr67bffOhy5j4/Pk08+WVRUtHfvXturHT58+NKlS7V9s0aj8dy5c127do2KimICcHV1dXZ2NrWQfOzYsdOnTzP/XVVV9dVXX7Vo0SJagJMBwbuIuA3axqPn0FSiW6/HNBo8z5QpU/Ly8nbv3v3111/369evU6dON2/ePHLkyJ9//vnMM88w09lHHnlk/PjxKSkpOTk5Y8eOPXHixBdffNGzZ8/hw4ebzebg4ODNmzdXVFRERETk5eXt2rWrtLS0qqqKOpuOEDJs2LCff/555cqVhw8fHjt2bEVFxfbt28+dO7dgwQKVSqVQKJYsWZKQkPD000/PmDGD1LfbKjY2duDAge+99965c+eY3VaZmZl1nBYaFBQUGRm5b9++1157bejQoRUVFRkZGWfPnlUoFOylaKPRqNFonn/++S5duqSnp588eXLBggX3339/3TuzAeohbo0Yw6MjNLHfGB0fjwgNnicgIGDt2rUjR47cvHnzsWPHDh8+3LRp04iIiBdeeMHWaMzX13fJkiUPPPDA5s2b586d27x589GjR8+bN4/ZTLVhwwatVpuWlvbXX3917tx5zpw5YWFh06dPz8vLY+er2a+j0+kSExPvueee7t27f/DBB8OGDWPqsSMjIz/55JOlS5e+9dZbTZo0eeKJJ2bMmPHuu+86HLlSqVy3bt2aNWt27ty5e/fuBx54YNWqVVu2bKntO/Xx8UlOTlYqlXv27Pnmm29atmwZFxe3Zs2a119/vaCgwBak+/fvP2bMmDVr1pSUlHTt2pU9PADXsSfQYm3fVdjyS3Kwdu1aQsjs2bN5e0W9nsTG1tzMypJwY7TFYrl69WqnTp2kGoDQrl69GhgYWMccSBL8/1KBYK5fv/7UU0/169cvJSXF5acHBwdv2rTJtrbNL3n+OpnN5tLS0g4dOkg9EKFcvny5Q4cO7CJ8sQkZSur4pfLodWiCjdEA8rV58+Zhw4ZduHDBds/Ro0evXbuGqi6QHSlS3MTzIzTBidEAMjVw4MCbN29Onz49PT19//79Wq128eLFoaGho0ePlnpoACyib4O28YIIjROjAWSpV69eH374Yfv27ZcvXz5r1qzdu3c/9dRTn3/+ucOtXACSoY7KELjTJ5unV4oxsDEaQJb69eu3Y8cOvl6tbdu22dnZfL0awF1Uipu9ciowL5hDE2yMBgAAl0ixDdrGO+bQGg3RamsCs1brMS2lwBk5OTlSDwE8RE5Oju3gDfAKEtWIMbxjDk3st69hKdqbDBgwgJePVIvFYjKZGv86slVWVib1EARkNpu5DVhcEBUVNWDAgMa/DrgHqkZM9M263jGHJoQkJdn9Q+PEaK8RFRXFS4Q2mUyVlZVU72tPUlBQEBoaKvUohFJSUuLv7y/QJmnwWAaD3aqoiDViDK+ZQ1PZCWyMBgCAurGPylCrxZ/XeU2EJqgXAwAAp1E1YqJPoIl3RWhqkxX7nx4AAICN2gYtxTZdb4rQxD5Is9MXAAAAbOzFUInqlrwsQrPTFFQGAwAAgKHXS57iJl4XoXGQBgAA1EvSbdA2XhahCQ7SAACAOkl3VAbF+yI0DtIAAIA6SHdUBsX7IjSxD9JIdAMAAJt0R2VQvDJCx8TU/Ldej43RAABwl6RHZVC8MkJrNHbXRNh2BQAADHnUiDG8MkITHKQBAAAcBgNJTq65KfXxDd4aoanTJxGkAQCAWvSUrkaM4a0RmthfHGVnSzYMAACQCamPyqB4cYTGQRoAAGAjpxoxhhdHaNSLAQCAjZxqxBheHKEJ6sUAAIAQwukjJoPwTLw9QlNJDARpAADvZDDYrXVKXSPG8O4ITeUxUC8GAOCdZFYjxvDuCE1QLwYA4PWoGjF5TKAJIjR9kAbadAMAeBuqRky6w6woXh+hiX2QZneTAQAAj0dNoOWR32YgQnMSGuwfFQAAeDa5prgJIjQhnKIAJLoBALyHLGvEGIjQhBDUiwEAeCUZT6AJIvRdqBcDAPBCcq0RYyBC/w31YgAAXkXGNWIMASP0H3/8MWLEiDCOefPmCfemrkO9GACAV5F3ipsQ4iPcS1+7dq24uLh58+aBgYHs+6mbcsEUCNh+WunpMryeAgAA3rBrxORxVAZFwAhdXFxcVla2ePHif/3rX8K9C5+mTauJ0DodSUqyO/wKAAA8hvzOmuQSMMt97tw5QkhYWJhwb8Ez1IsBAHgJedeIMYSK0Far9fz58/fdd19ISIhAbyEI1IsBAHg8WZ41ySVUhL5169aVK1cCAgK+/PLL6OjosLCw8PDwhQsXFhUVCfSO/KAqBXAeJQCA55HlWZNcQkXoP/744/LlywUFBdu2bfvHP/4xceLEtm3bfv755+PGjTtx4oRAb8oDqqEMzqMEAPA8Mu4jxiZUpVh5eXmTJk0effTRDz74gCnerq6u3rRpU0pKysqVKzdt2qRUKh0+MTMzZM0aMnNmjp/fUeaeiIiIyMhIgcbJ5TN+vJJVL2ZKTLTwlKi3WCzl5eUBAQG8vJoMVVRUKBQKPz8/qQciCJPJdPv2bV9fX6kHIpSKioqysjKpRyGU8vLy27dvWywWqQciCLPZXFFR4e/vL/VAhFJeXu7v7+/jw0/A8iksVLJqxEzjx1tE/M3Pzc21TVMtlpD//Gd8ZGStVwhCzaHDw8N//PHHjz/+2La3qkmTJlOnTo2MjMzLy7t06VJtT9y3b7zBIOUSsGXqVHYJt89bb/H1ylarVaFQ8PVqID6r1Sr1EMBF+NNzawqFgse/Pp9t22puqFSWqVP5euWG2rhxgMFAdu+eXdsDBNxtxRUQEBAaGnr8+PGSkpK6H2k2R0VEREmWeFCrbSvQfjt2+G3fzsurWiwWs9ncqlUrXl5NhiorK1u1auWpc2gfHx/mG5R6IEIpLS314O+uqqrK39+/ttSduzObzVar1YN/fEajMTAwkJ85tMFAduyoualWi/zvplar1Wo1IUSnIxcv1vNgAXdbMVlB7v0KhaJJkyb1Pj0+XoAxOYnaGId6MQAAzyCPGjGDwW4pvDZCReiUlJTevXunpaWx7ywpKcnLy3NyC5bBIF2QpprLoF4MAMAzyKNGLD3dqTMUhYrQsbGxSqUyIyOjoKCAuaeysnL16tXnz58fOnRoaGhobU/088ux/bdOJ117bJxHCQDgYeTRR4yqtWJHPYpQEbpv374vv/xyfn7+8OHDZ8yYMW/evNjY2B07dvTv33/27Nl1LCfMnHmUfdOZPIAgNBq7lp+SjQMAAHgij0bc7PSwSkWGDTta2yOFitAKhSIhISE1NTU8PDwrK+vLL7/08fFZtGjRli1b2rRpU8cTVSq7iwu9XrppNPuHh6VoAAC3Jo8+YlRuWKOpayACVoopFIqYmJidO3deuHAhPz//0KFDCQkJztRSUidWxMYKN8Y62S+iI0gDALgxdmBUqSSpEaMKxFSqehLtAkboxqCCo2QlY+xrGxykAQDgvqijMqSYQ2u1dkVNVKTjkmmEpirsJCsZY19kSZlwBwCARqA+wKWoEeNm2eu9SJBphCaciwtpSrWoejFMowEA3JHUE2hq/7BKVf8Emsg5QnNLxqRZCGZfamHbFQCA26Fmr1IcBU3N4anZX23kG6EJIUlJdhc68fFSxEfqZ4lENwCAe6FqxERPcXMn0E4OQdYRmnAWC6QpGWMHaSmbkQIAQMOxU9wSFYixOZPfZsg9QqvVdvFRmmotqigf02gAAHdBhQ3RN1lRS7R1b4CmyD1CEznsvKJK7lAvBgDgLiTtI+ZagZiNG0RoYh+knTwShGdo0w0A4HakbsRNnZDR0Pd3jwhNpQWSk0XPNFP1YmjTDQAgf9QmK3GruKkTMqhFW2e4R4Qmctgezf6nRQdQAACZ40ZIcblWv83mNhFa+u3R1L8ugjQAgJxRuVZxa8SoVpiuHUXtNhGacE7UEHt7NFVigHoxAAA5ozZZiTiHbmSBmI07RWgiea4bbboBANyCpDViLm+AprhZhJb4RA206QYAcAvSbbJqzAZoiptFaEJIVpbdTbG3R6NNNwCAzEnXiNvlBp8OuV+EJpzt0aIGaeonjWk0AIDcSNeIm7sB2pkTMmrjlhGaShpIkOu2YdeXAwCA5AwGqRpxN34DNMUtIzSRtmSMKtnHtisAAPmgasTE2mTFb36b4a4Rmrs9WrwgjTbdAACyxQ4GIm6y4p4A3fh3dtcITTinRycni1i2hW1XAAAyJNEmKyEm0MStIzSR8PRobLsCAJAhiTZZ8dKfhMu9I7SUp0ejTTcAgKxItMmKqlaeOpW3CwP3jtCEkLQ0u9lsbKxYuW606QYAkBVqk5UoNWLc/Pabb/L24m4foQmnrlvUXLcE7woAAI5QZ002Ziey0/hq8OmQJ0RoqlhPvFw3dYGGejEAAKlQH/2i1IjpdLw1+HTIEyI0kaoVKLZdAQDIhOg1YgYD/Z68XxV4SIQmUrUCZU+jxe5tBgAAhBBpNllptXw2+HTIcyK0NK1Ase0KAEBy1GRW+Cpu6gCrxjf4dMhzIjSRqmSM2naF064AAMQk+iYrbv02vwViNh4Voal/JmqRQChUOgXTaAAAMYm+yYo6wIrKpfLIoyI04eS6k5PFynWz3xIAAMRBTcXUaqE3WXEPsBJu1dvTIjSRJNeN064AACRhMNjNZwWeQAvUf7s2HhihqWOvxMh1Y9sVAIAkxD3JKj2d/wOs6uCBEZo4OvZK8Fw3TrsCABCZuF1KqPy20BNo4qkRmoif68a2KwAAkYnYpUS0+m02j43QEuS62VdT2HYFACAocbuUiJzfZnhshCbi57qpTXhi7PQCAPBW1DkZQm6DFj+/zfDkCE04F1WCB00cGg0AIALunich30r8/DbDwyO0Wm33Q9TrBQ7SODQaAEAEVEZUyE1WkuS3GR4eoYnIuW6Vijz5ZM1NJLoBAITATnEPHixczJQqv83w/AhNODNbYeu6J02q+W+qkAEAABqP2mT1xhsCvY+E+W2GV0RoKtctbF03lQHBNBoAgF9ibbKSML/N8IoITUTOdaN7CQCAQMTaZCVtfpvhLRGaiNnDBN1LAAAEIspR0JLntxleFKG5PUwEDNLoXgIAwDuxjoKWPL/NEClCV1VVzZ8/PyIi4tSpU+K8o0NUrlunEywDje4lAAC8o7qUCJN31uulz28zRIrQe/fu/fLLL8V5r7qJmuu2wcZoAIBGEqVLiUzy2wwxIvT58+dXrlxptVpFeK96iZfrRvcSAAAeidKlJD3dbllSqvw2Q/AIXVlZmZKSEhgY2L9/f6Hfy0ki5bqpPQBIdAMAuMxgsEtxC3MUNJXfVqsly28zBI/Q27ZtO3To0Lx580JCQoR+L+eJlOtm/2zRvQQAwGXCb7KSVX6bIWyEzs3N3bRp07hx49QSpgkcof7pDQYSGyvA29hf5fm8/bYA7wEA4AWE71Ki1drlt5OS7LbNSkLACG00GlevXt2mTZvZs2f7+PgI90auoVYXhOosYt+9xO/oUQHeAwDAk/kdPepz6FDNbQHmtjqdXbGQWi3oaZbOEipwWq3Wzz777Jdffvnoo4/atGnj/BMzM0PWrCEzZ+b4+d0NZhEREZGRkUIMctcuEhjYynYzNpacOmUKCbHw+R5jxiiXLPEpLGRu+W/fXjZkCJ+vLycVFRUKhcLPz0/qgQjCZDLdvn3b19dX6oEIpaKioqysTOpRCKW8vPz27dsWC69/3bJhNpsrKir8/f2lHohQAlatsv23JSTEFBlJeP1dLSz0iY9X2m6GhFjef98k0F9Dbm7uiRMn2Pfk5ORERUU5fLBQc+jc3Nz169dPmjQpOjq6QU/ct288VVEvqAMHzOybCQn8X7JYXn/d9t/KjAx0L3FfMtmPAC5QKBRSDwFcZTD45eTYbrE/Ufny4ot284rXX7dInt9mCDKHLi0tXbZsWVhY2KxZs1z7wzCboyIiokRYvB42jKjVNfntnBy/tWv9eC5BmDmTvPii7VartWulLz8QRmVlZatWrTx1Du3j48N8g1IPRCilpaUe/N1VVVX5+/srlcr6H+qGzGaz1Wr12B/f2rU1/61S+c2cye9HjE5H2Bl0jYbMnOlHiFCfY2q12vnCLEHm0IWFhfn5+SdOnHjooYfC/vbll18ajca4uDgnO4sJe0YkS1aWXTmAIIdqUN1LMI0GAHAG1eaT73mbDOu32QSZQwcGBo4fP95stksg5+TkFBUVxcbGduzYMTAwsN4XYf7hxPnHSkuzq+XWavn+NUhLs/slS0+XeJMdAIBbELLNJ7djlazCMxEoQoeEhCxdupS6c968eTdv3nzppZfCw8PreK6fX47ZfHfNXKcj06aJ0c9FrSbffUeeeOLuTb2eaLV8x1CNpiZIJycjQgMA1IPb5pPX9WHqeIwlS6RsH+aQ7M62mjnTbj+SaJ24hgwR+ABpNAEFAGgQIdt8co/HWLaMx5fnh+wiNNU3W6htyo4I22iM2mIv2jI7AIA7ErLNp4TLzzodcb5+WrwInZKScuLEibpT3Ayqk4sg3b4cEbrRGL1JANNoAIDaCNnmk2ofJtrxGAbD3cSwQuFUnJbdHJoh3hmR9oRtNKZWm9nb0tmXhwAAwMZa4zRHRVka2FqjDtz2YaLVBVFXBvXGF5lGaCqfIdTxU45QFwexsXzujTKOH19zQ8wMPgCAG7H/eCydPZuvF5Ywv83dOFbvxF2mEZpwIqVoJWMqFcnKsruHxxm8+emn7TL4mEYDAHDZn5NhefRRXl6Vu71KtOMxXLsykG+E5paMibZuS13aMJuveMPOp4iZHAAAcAuCrUBT26s0GvGOx6ByphqNU1cG8o3QhJCkJLr8WbRmXFlZgm2+on4ymEYDALBRk02eoih3e5WY+W3qe3LyqkPWEZpwLp7E3KMk4FujCSgAgEPUBJqn8Cxtd08qC+v8W8s9QlOHdFIrxEK/NfuCi8/NV1TwF22NHQBA5uxXoPlKcUu1vYpwlmgb9NZyj9Dk78sNq5WIf/QflWbncy0c02gAAIow52RIuL2qkXN3N4jQhEgQm224O7P5WZCWqlQdAEC2BJhAS5vfTk+3m3819BtyjwgtIQE3X1HTaAAAb8adQDd6I5TD06vE2V5FHB380dBVdUTo+nEXpPkJ0liNBgCwYecnVSpezsn44Qe67EzM06tcq99mQ4R2CrUgzc82ZmoXAfsqAADAq9g6VjP4OCdDpyP/+lfNTZHz21SYcO0bQoR2liDdQKmLROS6AcA76fV2H6mNnkBzl5/F3ArE1+I3IrSzBFmQpi6rcCQlAHghvg+alLC7J4N6L5fn7ojQDSBIN1BqaQLTaADwNlRLzEaXcEvY3dPGtkO4MYvfiNANw383UCrsowkoAHgbXifQEnb35LJaG/XuiNANRl3e8bAgzV5xwZGUAOBVeJ1AS7v7mXd3I3RlZeX58+erqqqkHY1bUKsdtDFpFCoJgm1XAOA9qC4ljZhAM+FZqu6eQrgboY1GY0JCQt++fefPn3/8+PHq6mpphyVz1E+dhwVpTKMBwAtRH3eNm/Byl59F6+4pkLsR2s/Pr3fv3lVVVRkZGePHj+/Tp8+yZcsKCgqsEvbbbCCRZ55ZWXbVeo1dkKaOpMQ0GgC8AX8TaFktP/PlboRu0aLFunXrTp06lZ6e/vjjj9+5c0en0w0ePHjgwIGrVq0qLCyUeahWKEhystjHT/C8Q5p9sYdpNAB4PP5WoD1s+dnGrlLM19d30KBBW7ZsYUL1yJEjy8rK1q9f/9hjjw0ZMmTz5s0lJSVSDbQ2CgVRKO7+t8jbidVqXndIYxoNAF6FmkC7uiOKu/xMdYF0X45ruZlQzcyqMzIynnnmmcrKyuXLl0dFRQ0dOvSLL74wmUwiD7Q27J+p+DNPnndIYxoNAF6Cvwm0HHY/C6Se3VbXr18/duzY8ePHmdmz1Wq9ePHia6+9NnDgwM2bN8uh9ps6qISfZpwNwecOaWoajb3RAOCpeJpA63QeuPxs4yBCW63WwsLCVatWRUdHDxo0aMWKFefOnXvwwQdTUlJOnDhx4sSJd999t0WLFitWrFi/fr34I+biee9Tw3F3SLsepNmvxc8BHQAAMmMw8DKB9tTlZ5uaCG21WgsKClauXDlw4MDHHnts/fr1V65cCQ0NXbRo0S+//PLVV1+NGzcuICAgICBgwoQJq1evbt68+cGDByUcug031Sx+rptakHY9141pNAB4PCquujSB5jbfdvfdz1w+zP+VlJRMmzbt7NmzzM2OHTtOnjw5Li4uODjY4dNCQ0MDAwNv374t0jDrk5VVUy9GCImPJwUFog6AuUqwXRno9WTKFPLJJy69VlJSze+dTkemTfO0XzoA8GY8TaAPHpR497PBIPhpHHfn0Far9datW/fdd9/06dN//PHHn3766d///ndt4ZkQUlVV9cwzz7z99tvCjq4h2MkN7rWVCKgF6U8/dXUqT11OYhoNAJ6EjxVonY688ILdy4if39Zq7TYTCeFuhA4ICPjkk09ycnIWL14cEhKiqO89g4ODZ86cGRUVJeDQGojKb0iyhsvdIe3iGNiVDzqd2MVvAAACMRjsTvBzKUEo7dnPDL2+5vsQLkjfjdD+/v4hISFNmjQR6n1EIXnJmEpFZ9ddHAOVrMHeaADwDNQEuuEzX4OBxMba3SPy2c/E0SWCQNMojzrbivpxGwwShDaVym4CzP1lcham0QDgYagJdMPz2w7PxhB/93N6Oj0GgS4RPCpCE06um4fzmxuOamfjYhsTTKMBwMNQE+iGV3ZRzUkkWX42GOwmUGq1gBVqnhahiQxy3dwxuHihgGk0AHiMRq9Ac8/GEH/5mZvfFrSA3AMjNDfPLEmum/rVcaVqDNNoAPAYjVuBplYMmRcQefmZOOowKuhmWA+M0ISTZ2YHbNGo1fT7vv22T4NfBdNoAPAAjZtAFxb6yKE5CZXfFnoCTTw1QhP7PLNUJ2dyF6QnTmzT4JdgwzQaANxR4ybQGRkBhw7VzHDEb05CJOow6rERmsl1W62ShWcG1cYkJ8evwUEW02gAcGtf6u5MAAAgAElEQVSNm0BrtWTVKqXtplTNt0XObzM8NkKTRp1mxqfGVo1hGg0Abq0RE2g5VIcRKfLbDE+O0DLBQ9UYptEA4KYaMYGWSXWYhCdoIUKLgVs11rA9YJhGA4CbcnUCLZ+jqyTJbzMQoUVCVY01uNcYptEA4HYaMYHWaiU+uoohVX6bgQgtnu++s0RFmW03G9ZrDNNoAHA7rk6gtVq7yB4SYtm82cLnwJzGTqqLX6SGCC2q1atL2TcbVjVGTaPFb2cKAOA8V7tw63T0tPXzz0v4G1aD2fYEiZ9mR4QWVUiIxfWqMWoajXOjAUDOXGqP6bAsKyREmgk0m9UqQZodEVpsajW9RbsBVWOYRgOAWzAY7D6gnJt7cgt0CgqkqQ6TCURoabhYNYZpNAC4hYbvT3J4sqSXEzBCW63W//3vf0899VT37t27du06dOjQ/fv3V1dXC/eOboTqNabXOz2TxjQaAGSOmkA7F2nlcLKk3AgYodPS0qZMmXLq1KnY2NixY8dWVFTMmjVryZIlVVVVwr2pG6G23ut0dkUVtUpKsnsairoBQG4avgLNrQ6TpHeY3AgVoS9fvpyWlta5c+cDBw5s2rQpJSXlu+++i46O3rdv38mTJwV6U9dIcoA0cXSFGB/v3JSY/euu12MaDQAyQn0oORGeHVaHid87TIaEitC//fZbVVXViBEjQkNDmXsCAgLGjRtnMpmOHTsm0Js2lEJBFAopU8VqtUsNQTUaTKMBQKaoPdD1pbi5hThS9Q6TIaEidHR0dE5OTmJiIvvOixcvEkLat28v0Js2iEJR899STaOJyw1BMY0GABlq4ASaCc/s6rDkZLkceiQHItVyG43GDRs2pKen9+7d+9FHHxXnTevGzjA3uAcnr5KSyIgRDRwMptEAIEMNmUBzi7cTExGe7QgeoU0m0+TJkyMiIt57771//OMfqampbdq0EfpNnUElUqSdiO7fTw+m/iCNaTQAyEoDJ9Dc4u2UFCGG5cZ8hH6DO3fudO7cuXPnzseOHWM2X61du7ZXr161PT4nJ4e6JyIiIjIyUoix7dpFAgNb2W7GxpJTp0zCNa+xWCzl5eUBAQEOv/r++6RPn5rB6PXkjTcs8+aZan25MWOUS5b4FBbevanVlgnzr+S8iooKhULh5+cn7TAEYjKZbt++7evrK/VAhFJRUVFWVib1KIRSXl5++/Zti0X61lRCMJvNFRUV/v7+Eo7Bp7DQb8kSW0SxhISYxowhtf9GpaQo3367JgCFhFh27TLV9vDy8nJ/f38fH8EDlghyc3NPnDjBvicnJycqKsrhgwWfQwcFBa1YsWLFihWZmZkLFy40GAzvvPOOyVR74BHXgQNm9s2EBAF/A6xWq4K9+m1PpaIH8/bbPnVPjC2vv15zQ6/32batkSOEulmpbnDgPur40wN+6PU+hw7Zbtl9OnFs2+bDDs8qFdmwwVxH8bZCofDSvz6riMrKysaMGdO3b99ff/3V4QPWrFmzZs0aMYdktVrVaishNf9LThbqjaqqqn7//fe6H5OVZTcYQqxZWXU+gT16lYq/wbriypUrlZWV0o5BOEaj8fr161KPQkD5+flSD0FA169fNxqNUo9CKJWVlVeuXJFyBAUFzn8WFRTYfcSpVNa0tHpe/vfff6+qquJxvGxpaVZxIyGtjsAnatfPFi1ahIaGWiwWWXUWy8qyK7pq2HlTfHNY2l3XYdDslR7qJBkAAHFQK9C1NwNzuLdKwu6etq3YzOZbuREqQq9bt65Pnz67d+9m33njxo3Tp08rlcqWLVsK9L6uoX6dpK2MTkpqSNdutdru0RLuGwMA72Qw2H1oUh9K9g+k9lZpNFIWb1OdUgiRXcWtUBE6MjKysrJy/fr1RUVFzD1VVVUbN248f/78Y4891rFjR4He1zVqNfnuu5qber3EQToriwweXHOzniBN/YJj5xUAiEmvt4u6tYRc7t6qwYMl7rxNFZMvWSK7TilCReioqKjnnnsuPz9/2LBhL7zwwrx58wYNGpSWlhYRETFr1iwZluQNGWL3s5E2100Iycx0ev8VdcVKZckBAIRDzUNrn0Bz91ZlZgo6snro9XQn8GXLJBtMbYSK0L6+vgsWLNiwYUNYWNgPP/zw5Zdf+vj4LFq06OOPP5bbBNqG2yVbWtR46prZUxetkg8dALwE1aKklgm0ViuvgzEcdgKXIQErxZo0aTJ06NCvvvrqwoUL+fn5hw4dSkhIUCqVwr1jI1E/JGkbjRFHv8S1zuzVartaC52uzuoyAAA+UNWptUyguedWSX4whlZLL4fLLb/NELWWW/64jcak1YCjNbAaDQAioybQ06ZxH6LXOziLUtpwSB31q1bLt9UoIjSNPY2WwxZ5tZpOvzgO0lQLXAlP7AIAb+DEBFpue6uI++S3GYjQNCa3bLXKIjwzNBoHm6QdxF/qFy09XcAxAYCX406N7XHDs+TnVnG3VyUlyfogakRoB2S4IJGURMaOrbnJ/T27ix3JMY0GAIFQLUqo0/YcbX1+803pk8lUPbnkE/p6IUK7jS+/dKKTCXVBiNVoABBCnSXc3K3PKhV54w2RhlYb7vYqOee3GYjQ7iQry4lN0jiVEgAEReXnHIVnautzQYE4I6uVey0/2yBCu5m0tPqCNJVuwt5oAOCRwWBX40LVqDrqTCLt1meGu2yvoiBCuxnupR+VuiEEx2kAgGDqPCSDu/WZOppIKu6yvYqCCO1+uNekWq19FKauDzGNBgBe1HlIhlbrIJMsh/BMWFtn3SW/zUCEdkvcTibx8fZBGg1MAIB36em1HZLhsHGYrDLJzB5a+Vw0OAMR2l2p1XTxhV11Bvc4DfQBBYDGMBjsgjDrQ0anc7DPWFbh2Uaeo6oNIrQb46Zr7NqNyerUawBwd7XssKL6ehJCkpPlvs/YXSBCuzduu7GaII0+oADAl1p6fMqwcZgnQYR2nbQnX9kkJdGXqzVBGtNoAOCFox6fBgMJDbV7FMIzvxChXaRQ1Hlgs7i4FRk1a9LsII0GJgDgAuqjIymJqFQOT8VAeOYXIrQrFIq7/1Hrgc2io9qN1TTQQQMTAGgMaoeVSkU0Gm7bbY3GnXYxuQtE6AajQjL1ayqhrCwyZEjNzZoEFBqYAIDLOBNobnh2r03GbgQRusG4BzbLZ1763Xf0TDo0FA1MAMBVnH7WBrWGG54lb7vtqRChXUGFPPksSBPOmvTdIE2tDiFIA4Az7D/aDElp3EOr5NB221MhQruIajYrnwVpbisfg4HEau0bmOh0cknNA4Bs2S+KGdSa+HQ191QMN2rR5XYQoV3H7RYik6jHDdJ6PYk1yDU1DwDyxPqUMBBVvCFJtuGZu+/LMyBCu85hc2yZcHAElkGlJcms29h5BQC1s/+I0BO13qCy3ZRbeGZy77ZdNh4DEbpRqO7XslqQ5pZvJJMkA1HV3JbPWAFAblifDwaiiic1l/yyCs/E/kRqDwvSiNCNRW1Els+CNCFEpao5c42hJaySMb0eO68AwAH7JsHszw3m0l8+4Zl7ppYnQYTmAVUobXd8hQywZ9I6otETdc1t+eTlAUAm7FuUGIhKRzTMf8utcpuzF8zTtmUjQvOAuyAtq/wxle62m0YTBGkAsKfVsqtebfltuSW3qfBMOPtgPQAiND+4C9JTpkg2GC72la+eqO2m0TjzCgBs7HdY2bJuzPRUPuGZEHLwoN1Hl0d2BUeE5g21IP3pp/IKfOyJPrvogxCZTfkBQEL2O6yYlBt3A6fkdDrywgs1Nz0vv81AhOYT+1fEapXXLzRhBWkDwc4rAOCwz6jpidpAVDIMz9zlZ1mtjvMIEZpPthVfqoJaPtTquyOkd15hNRrAy3EKxOJJGhP85BaeqVMvk5LklX7nESI0z7gbnOTGdr1pVzJGHTAHAN5Gr6cKxGS49mxrTmKj0RCNRqrhCA4R2hsxM2l651VyslzalgKAyOwTx3qiNqjUcps9E/vmJMRzl59tEKG9FJOQp3Ze6WMxjQbwOgYDMcTaFYilq5JktbGKodfTzUk8dfnZBhHae6lUJK1AbetFQAhRG3TxoXrJBgQAojMYiDZWrzLoa+5RqZOy1HILz9Tyswwz8EJAhPZqKhVRF9gliZIM8aGhqOwG8AoGA4mPNUwzsJJnKpUqK02GkY8akuc1J3EIEdrbqVR2u8RUxKAxaOPjEaQBPBwzK1UZ9Gqir7k3KUmG4Zlhtd6tw/XI5iQOIUIDfTmaRJKJwYAgDeDB7iaNDYY0Yr+zWPaF0Varh1eHsSFCAyGEPv0jjcQzf8AI0gCex2AgoaHEYCB0ePae0OcmEKGBEEKIWs2+dlaTu4kvBGkAD6PTkdBQQlh/5ndRpwuADCBCw9/sKyNtF9exsThFGsBDaLV3tz2rCCe/jQm0/CBCAwsr160ihmRyt8IzPh4NxwDcnlZbs59YQ9JVxFDzNS+pvHI3iNCSUSjkF/Y4JWO2v+HkZLTuBnBj7PCsIoYk9tk59otcIB+I0BJQKIhCQQghycnyW+XllIzZ/lunoxvWA4D8MU332d246Pw2JtByhQgtNioky64US61m/ylTtSR6PYI0gDsxGEh6ul141hAdCsTcBSK02NRq+vAr2WWP7c9yyyJ2MVmvv1sICgAyx+yZtOtlTQxJhLW6hgIxeUOElgb7mpV73Kn07P9os1R2FxHMZkp5Tf0BwB7zwcI+r06lImkqLQrE3IiwEfr8+fPTp0/v0aNHWFhYnz59Fi5cWFRUJOg7ugvqWDe9XmYzafvEl9qgy0rWs7+OfiYAcmbrSWKjUpGsNIPaoKu5CwVisidghD5w4MDo0aOzs7P79u07ceLEoKCgzz//XKPRIEgzqINZdDqZbTu2n0ar9dqCAnq5CkEaQIa0WnopignPKq18N0DrdHfrZ4FNqAhdUlKybt26gICA7du3f/rppytWrDh48OD8+fPz8/Pfffddi8Ui0Pu6Ee4fiLxaYVPj0+tV6dq0NARpAFnT6ewWnsnf5yirDHq7v1WNRj5nNxoMd5OICNIUoSJ0Xl7euXPnRo4c2bdvX+aeJk2aPP300w888EBubu4ff/wh0Pu6F7WaPoFcXgGPOuAtOVlFDFR+nhASGyu/dXQA78PsqqLWyzQaUlBAVMRg9wU57bCiCnHk2ChCOkJF6CtXrrRo0SIyMlLBuihq2rRpixYtBHpHN2W/uYkQuZV2U3/G8fGEkKwseszYhQUgLWYaSv1hJif/nQiLl2l+m1vOlpwsn4sH6QkVoadMmXL8+PExY8aw7zx37tzp06eDg4Pvvfdegd7XHSUlkREjam7Kq7SbqiXR302UJSXRf+N6Penfv82hQz5ijg4ACCGFhT4TJ7Zhp99UKlao0+nsUnOy2QDNXFWww3NiIsKzHfF2WxmNxrVr1966dWvChAlKpVK093UL+/fTpd0yCtJUSdvfI9No6BR9YaHPE0/4yChLD+AF9HrSvbtPYWHNxTFzyvPdUMfkvtlfk80EOj2dUFcVKSmSDUaeRJrxmEympKSkQ4cOTZo0adSoUXU8Micnh7onIiIiMjJSyNGJxGKxlJeXBwQEOPzq+++TPn1a2W7q9eSNNyzz5pnEGl2d3n+/1dixtluWZ581rVtHCImMJMePk1GjlOxPh9hYcuCAOSrKLME4hWQymW7fvu3r6yv1QIRSUVFRVlYm9SiEUl5efvv2bc+rUd2+3e/FF/3Y94SEWHbtMqlUhPlhKpcs8WHNUk3r1lnk8VNOSVG+/XbN5wYz7NqGVl5e7u/v7+PjCSm63NzcEydOsO/JycmJiopy+GAx5tClpaUvvfTS7t27x4wZs3jxYg/+jKub1WpV1F6qqFKRAwfsoppcwjMhRK0mrAjts22b7dKXGTaVMxs+3G/6dE/4W6JYqW5w4D7q+NNzUwYDeestHyo8M3+PtpyXz6FDPtu22b5qmTXLEh0t4hhrtW2bDzs8q1RkwwYzO1VHUSgUXvrXZxXY+fPnn3zyybCwsLfffvvOnTt1P3jNmjVr1qwRekhSqaqq+v333+t+TFaWlRCr8D8WlzAjY/6nUlFfVKvtvk6IVa2WZJRCMRqN169fl3oUAsrPz5d6CAK6fv260WiUehS8KSiwqlT0X1xycp0PUqmsBQWSjJZSUEB/lqSl1fOU33//vaqqSozBSaGOwCfsHPrQoUOTJ082GAxvvPHGggULvHb27DymtFumF4vs5SuDgSo6z8oiiYl2k36mgzeWpQH4xa1/JoQsWGCma6y0WrsH2ffblwq3ElajQWezWgkYoXNzc+fMmXPnzp0PP/wwPj6+SZMmwr2XJ5FvKSO1PZoqECUkMdFIJeqZv0Z59UoDcGdMvzCqneeCBebZs0vtHqfX2/3hyaPBJ/faoqaiDRwRKkIXFRXNnz+fEJKamvr4448L9C4gNm4XNHtqNSkooK/U4+PJrl3CjgvA4xkMZN8+x/3CqDvpFJc86re5e6sGD5bDuGRNqHKenTt3Xrp0qWnTpq+++ipVo9GxY8d169a1adNGoLcGATF/6rY/fmYjh/01MPORQXUwHTfOQQM1AHCSw8y2SkUKCgghxEztnEhPpyeqMshvc/dWZWZKNhh3Icgc2mQy/e9//yOE3Llzp6ioqNDe1atXrTJdaAUncFqBcpeaHV7XY1kawDUOw3Ny8t3w7ODR7L89tVomeWS7Y6pVuF53iiBzaKVS+emnnwrxyiALaWl2R+fExzv8qEhKIjExdlUhtvPk5fGJAeAGtFoHme1al2+5+W3Z/LFZrXcPxmAycTKY1bsB8XqKgedgOgraUE2LWBwuSycny6ljGoBcMX9YDheeaw27VCqZynhJzWq9e80gp0HJGiI0uIT6I3OU62YwHyjUHyQy3gB1syWc2Bxe8to9h0oly2YCbVNQIIeicreBCA2uqq+u28bhsjTzAYRj5gC4HG6pSk6uc+2W2mgsj/ptaCREaHAVJ9cdMGtWHQ9PSnLw+YKMNwBbbZntpKR65sP+O3bQ9dtIJbs/RGg3Jn1ss891KzMyfA4dquPhTI6OGjYy3gAMh5ltJgVVd2bYLyen1dq1ds+RX34bXIAI7a4UCnkcUmmfSfNJSKj74SoV+eEHZLwB7DBTZyqzTf7eUlVP2TO3fhs7mTwFIrRbsvWAkT5IU8tdnH7dDtWR8aY+oQA8HvNHw506p6U5NxOm+m/Loz8J8AIR2v1QMUyv5/T8E1l9/bodYjLe3Brv2FhkvMGLMFNn6nfemcz2Xdz+28hvexBEaPfDTWJptVKfTuF0XTdbHTXe0mfvAQRWW1GYU5lt20vIr/828AgR2i1xe1zHx0sapLm5bqdjbFKSg88jlI+BZ6utKMzZzDZDludLAo8Qod0VkyVmow6rEJtGU8WOynq986NhDgBA+Rh4g7qLwhqwQ0qnY1+VW594QsJWIDhhViCI0G6Mm9OSdhG37N137W43sO6rtvIxTKbBY9Q2dW5ws3r7/LYlJOTGO+/wMkIX6PUkPr6mfBV4hAjt3jQa+q9dwiBtCQ42Hzhgd5dzC9I2DsvHMJkGD1Db1LmePtu1vZb9X5bl9dctwcGNH6QL2CtaCNK8Q4R2e0lJdHJLypm0Wm0XYPX6hoZWxyfSYzIN7qyOqbOzRWFs3OMxJMpvGwx2p9wRgitpniFCe4K0NHreKeWaNHVQRu2HatSBKR/DZBrcHZ9TZ9srUsdjSFS/za0HrfVMTHAVIrSHoMKic41DBEP9mbo0FEymwd0x+/t5mzoTGR2PwQyEapSCrV68Q4T2HFlZZMiQmpvcBJR41Gr6AGlXrxfqmExLeQkCUCdm6sytlXR96szgtg+T4ngMbnjGTmyBIEJ7lO++o2fSkqEOkHau0ZhDzIca9+9fpyOhoUh6g+zodHxPnW2vy97VJNHxGA7DM7XzE/iCCO1p2GvSVquUI+F3K5hG43gyzSS90c0b5MCW3eF56kzkcjwGMwoqPOOcDuEgQnsaJt2kVksdnomjS+vGTXhrW5lm8vmYTIOEbBVh3A7bjZ06E0frRFlZ4rcPY0bB/gaZP0n0MRMOIrQHktFVrUrVyM1XXA5XpsnfFWTobQTic5jWJoRoNI2eOjO426sQnr0DIjQIjI/NVxTmo4H76cB8iDzxBJLeIBKDgQwe7DitnZxM0tL4CGA6neTbqxCepYIIDcLjLkjzEUKZBmTciUtmJpLeIDhbWvuHH+zut6W1+aniYt6G/epS1EwjPEsFERqEx/1Y4W+nVN1Jb8Rp4J0tNnOvDnmoCKPeiZqeS7S9ir1qxpSXIDyLAxEaREF9svCxIG1jS3pTUOkNvHPYhITwVRFG4S4/S9eyi6k8lVGNi3dAhAaxUHkxPhak2Zjy9doqvdGGDBqJ2UnlsAkJn2ltG71e8uVnitWK5LbYEKFBRMIsSLMxSW+HcdrhxytAvZhks8OLPN6qtR2+pY0MwjMD4VlkiNAgIrWazpEJ0LqTabXkcHFar8fiNDSAbcmZu4vP1uqO/6DFXX6mOvSB10CEBnE1+nhKJ9XxAZqcTBQKxGmoS93lYGlpji8B+SGbwyVBcojQ3k6hoI+QE5wAO6Rrw/QK5X7IEsRpqEXdsZlZchYwYspg9zPIByK0V1MoCPm7PFVU1MJd41p2O/NuiNPgjHpjs7DF1HJdfgapIEIDIeIHaVEWpNlsi9Off+7gq7Y4jToy78TMmxUKx7F5/fr/3979h0VRJ34A/6wsCrmrmGAl68Mu6IlmxXWiPMV9WQpLL+uQ7PFHKdBJj3WRmV56We3S6Rld5VOkZfqIZKdmovd4GfnABRRdJJVAglkJq8cqiYCwoCAL+/3jg+M6M7ssy87OzO779fT0wDjLfGBg3/P5LcxwMG4hWH+EIs1+BulAQvsvVhrRUVTew+qQNpnIo48KfU2tljzyiLP6NB1Hhpz2H87btOlQ7aee8soYZu7ez+LNfgaJQEL7L+7WU3TqsPewOqR37/ZOczNTn3aS05iX5Q/oHCon2SzIUG1eWVnsvZ/Rvg1IaD/nKKS9t7gH621IyFFjLExOFxby/CttUcDULN9jMvVvRaVQ8M+h2rfPu9lM+BYn8dbCXXgMlTgktL/jrrLL3cdG2MuzNrIWeNQY9/pJSQ7r08y6ochpH0AbtBMT+X+96Viw4mLyyCPeXZeD1f3sxWWv6ZXpcFGQJiQ09D+yszqFvRfShLDjUeBRY1zO271pTqvVqjfeUKPOIUcmE3njDfVtt6mMRp5ao/04bW+vmcUavE2I16Y+03imPw2EtGQhoYGQq91erJD2Xm2WtWQSd1CrVzA5bbPxv1NnZweh6VtGmAZtnY5kZwdxT6AtOILPoXIiK0uUvTFoZ5b9w4pXB6CAy5DQ0I9bkybebHJmXVuwtcYGRLO5vt5hT6R90zeq1NLEjNB21BTErAsmJpFGh+3cyc5j7ngUkAgkNFyHN6S5A2oEId6oMV50PbIBu6hRpZYOpqeZd4Q2sRukLey6YK7grh3mldFhWVnsZnXEs5QhoYGtuJgsWHDdkfR0r4QQ903Ku6PGeDFN3+vWWTUaK/cEGtUKBaJaTExrtqPnOo3Gum6dlQ7SFn8VEN61w4TvA8/KYj+40MdQkCwkNPDYu5ddw/BSR51eL/qoMV5aLVm7tuv771ud1L3sW7+91Org32g3c3o6USictWanpZHcXPL9961r13ZJYvNEkdYO48az0YhJ11KnFLsAIFH0mZ7+SbPmQwnLYCAnT5I9e/o/pW9n3poeOiBa2zEY+jvKuf3QNKcJIVlZJC2NRESI3Zrqc0wmUlJCSksHeAxi6qU0lZuavFG2gXF3lhR+dJjJRPLyeOIZS5ZJH+rQ4JDBQHJzvRvP1O7d7FFjYgztdoLWzJz0UpOrUU1XrUpMRAP4UDE1Zjr+y1E82/c06/Venz01INbOksKPDkM8yxoSGpwRrf7H6i0Ub2i3c7SX2mYjRqPDdkpa52P6qnfuxAjwQbCfMeU8mPX6/uHZkuhp5sVqaBZ+dBhtgWJdE/EsI2jlBkmidQv7SSFGI0lIkOpbLzEYiMHQX18pKXE4vo0ZIUSresRrHfyy4mI7NqXXk9RUOXQl8A7eFrKOb78mCXNNg0EOPyu4yksJffz48fT09I0bNyYlJXnniiB79C3Mvn2bdkhLNaTJ1XdAF6Oavl0bjUhrQuxSmX4wIPpDS02VXjs2LzEGb3MnPQv8SACe542Ebm1tzc7Obm5u9sK1wKfQbaRlFdIUK6ppU60jrLTW60lCQv8HPozW7QabyvSHI7NaoEiDt222a8t5Ip5lSvCEbmhoyMzMrKqqEvpC4Jv0epKWdl2+pafLaAonjWpCSG5ufxo5GllG0Sxnvl2mei2byqJjbkQypdWSxYvJrFnyfGThtjV7sR+YhjTiWb4ETOje3t7Dhw+/8sor3d3dU6dOra2tFe5a4Mtyc4nFQvLz+z+V2Pwr1+n1RK93tWJN2VevydVKpFYr5R75fkweEzLoSCbEV9oSxJhbxSLCXAzwHAETura29qWXXgoKCtq6dWt1dTUSGty3f/9164vR+VcyDGnKvmI9YI+1PW6o0/m+9L+EhGtHvIamj8nU/wENY+bTQZHR84dLuDvEeWvlbfAZAiZ0QEDA0qVLMzIyRo0aVV1dLdyFQDrKypRCjQXMzb3u/U7mIc1geqzJ1amrhLMbpxOOspCGNBPeVEQE0euvnc8K8oYGJWsXQvuvTD8+ffpaJBPigSVZfaSuzIs79Vn+v67gZQIm9NSpU6dOnSrc1wepGT/+FsK394ZncOdf0UnSPjQAmqlb05Zwk6m/SurGGqL2OeqyCYO+zOD5ciTb4536jK5gGCTJzYcuLy9nHbnjjjtiYmJEKYxnWa3WtrY2tVotdkEEMWZMCP0gMZEUFHTFxXV5/hohIeTgwZB5864dMRqt4eEd8+d7/locHR0d3d3dgYGBXrgWISQkhPmGc3sAABypSURBVMTEEPqLv2lTf9bSqP7mm6Dycp7djiVIo7FqNNbwcGt8vJUbyRcveq8kbW1t3d3dVivP3icep3r9deWGDcynVo2mKyfHGhIi3Dfc1dXV3t4eHBws0NcXXVtbW3BwsFIpucByQ2VlJWvodHl5eVxcHO/JvvANy4XNZlOwmhF9xbx5IfafzpkT9PDD1u3bBXg31Ou7CgqC5sxhDigzMkhoqHeqYzbxRt3Q2tfVWlkXIV0NDUpCSHl5kNmsJISUlLjZ++vB4tEW9bvvthJCNBqrIE9p7vLan57yww/t45lotV05Odb4eO9c3VcpFAoR//pEJLmEjouLW7FihdilEITVau3q6goJCRn4VLmhk5btO93y81XNzcL0u82ezZokHTJvnhcmSSuVysuXL0vn9tGCTJvW/ynT2M8ausXqOR5s6zfTLstkMP1/QgIxmfo/5fzglVf/L6GKfk9PT3BwsEqlEvYyO3eSzMzrjqSlqebOFfaihHR1ddlsNun8cnqcxWIZM2aMb9Sh9Xq93uU3K1/4hkEKiovJ6tUdb7xx7R2wpITodMIskkyXYLZfpEkmK5l4gX2UDkp9fb2OtQwVDApr4TAi1NRn5tkIfB52zgCPWbXKUlBwXcMmnbosyGbJaWnslaVYtXgAbzKZ2MtsChPPWVns64APQ0KDJ+n1pL6e/YCfnk4OHhTgYrm5CGmQBG48C7AyiclEPvmkfyyCjw5oATYkNHgYnVfCam9OSRFmi2duGzprjQgAofEuu+3plUnoRR588NoRhLQ/QEKD59GQZi27QbulPZ+erMcB7kJOAMLhLrstWDyzxve5vqwNyJeXEnr58uV1dXXYetKvGAzssdz0jSYry9NXQkiDKHh3YPZ0PNOOZ9ZFvLj7BogJdWgQEG+3tNEoQIs3Qhq8jDeePbrrmsnEXpqMXG2gQjz7CSQ0CIu3W1qQedIIafAar8RzYiI7nnkfecGHIaFBcKxuaQGXBmINHENIgxB449mjT52OWrax9Ya/QUKDl9BuaWFX7qO9gAhpEI6jePZQxdZRyzazARr4FSQ0eI83lvxCSINwhI9nbss2vQJr5j/4CSQ0+ByENAhB4HgmhN2yTQgxGtHx7NeQ0OCLENLgWcLHM7l+iAb9FUbLtp9DQoOP4g1pLAsKbqCLegoczxQNabRsA4WEBt/FO9MLIQ2DsnMne81tOrFKsKZntGwDAwkNvg4hDW7buZO9oSSdkiwktGwDAwkNkuaZJUJ5Q1qQTTHBh2RlseM5LQ1TksGbkNAgXQoFMRo9tN8Gt1svPZ39/gvA4M5KNho9vuY2gHNIaJAoZnM9j+23wd1PeudOYTbFBDnjXTQEW1WAGJDQIA+eqUzn5vJsiomQBgadlYd4BmlAQoNE1dez+449U5nmbopJd64G4M7HG/JGj6wVSAAGBQkNEsXab4Phgcq0Xs+zc7VnurtBtnjXJBnacti0gYbprwEYLCQ0SJrB4LAyPaRhXtw5M1jPxJ/xbiY1hEVDaF82k/gIaXAPEhqkjr5VckfR0pUk3G/0putOcGdheWaCF8gH72ZSQ1gyjA5A5Db/AAwWEhrkIS2NvzJNG73d7O3jrgxKCDEaMXbMXzja69HdNb2Y1h3WL6RWiw5pcAcSGmTDUc807UR2s+rL25hJx47hPdW38e71SJfcdOuL0ZZyVj8JHWqGVTzBPUhokBnenmkyxLUSc3PZzejolvZtdBAXq+PZ3WHbjpq16RJkmKgFbkNCg/zQeq99R6H9tn1u4i7o6LGlUkBKWIO4KHeHbZtM5N57+Zu16RJkqDrDUCChQa7ocGxPjsehXxHd0j7MUcfz4IdtM83an3/O/mK0WRtVZxg6JDTIm8HgiQo0g75ZJydfd5B2S6PFW+5oowhrxxT6WDbIqi7NZu7TIf31QTaDpyChATgOHmS/+5pMqgcfVOfni1MeGDJ1fr7qttt4Op7d2quKm8EYEQZCQEID8OEuDkpI0JNPosVbfkwmkpUV9OST1x2kE+08UdtFszYIBwkN4ABvtzRavOWFjtnm7XjmzgcYDNq3gtHaICgkNPidQYzO5p2C7YFFR0F4vGO2CfFgYzRd6g7N2iAcJDT4HaORKBSDyWm+Fu/+RUdRmZYm3tVIPNeyTQ2tEg4wMCQ0+BdmD4PB5bRe33XiRFdc3HUHMWFagphZUNdXnbsWLOgqKHB7JwwAUSChwa+5ntNWjcZy6BDPDh4e2A4TPMRR1dlotOTkWDUacUoF4C4kNPgRk4ns28dznMnpgZfidrSDByrT4nJQdXZxhjJ9NYDUIKHBj2i15JFHHK5ERivDA+e0o+0wUZkWi6MB27m5Aw4KY5KdPqUBSAoSGvwOXYPZeU5zhwCzOalMD/xi8BCTiaSn8/zAXVvIMz2df2kwAIlAQoOfYnK6sJDnX+m05wE2tXS0HSZ9MZpNBcVUflmreA60uJfJ1L8VlULBfikhRKcToKgA7kJCg1/TaklSksP6tMnkQgXL0XaYtDLODQEYOkfbPTrtdWYmSKen8/RFDGENUAChIKEBBmj3dun1vD3TtA0WndMexCwXw23WdtzrbDKRN95Q33abymjk6X+wX7YTy4+ApCChAfoxOW2zubXzNO2Z5oY8Oqc9wtHjDhOwnF5npkFbpyPZ2UHcL6nVEpsNS2qDdCGhAa5Ds7m+3q0FHZmQ5zZ6M53TyOnBctTlTAjR6500a+t0/A3axK7KDSBlSGgAfrRK7A7a6F1czJPwtHN661bktEtMJrJ1q8OtmGm/sePHKG77h1bbv9cFX5UbQHKUYhcAwEfRrbGysnjSZflyQggxGklqKno++dF6M+84Oxqzg2yY1misqalk2TIlft4gI6hDA3jYdcliMBCbbYCZ1xhHZo/pb+bG8+C3YrbZSFoayc0l33/funZtF+IZ5AV1aABPYtalysoiaWkkIoKkpRFiMJDUVJKXxz95uqTEvXqhTzGZSEkJyctz2G/s7s+HDrFvahpS6QBEgTo0gCDoXGpaG0xMJFl5Tmd00bP9cygZMxDM6TxlU6oBc8vB3yChAYRFK4d02WddonZnhMFUPFBO+8MUajoXysnCm1otMRpNxfU7IwyJ6Vqa4AB+Ba3cAB5DE5a2Wzs6IT2dEKLVag1pRgMxZhmIkf+8xMT+pt2EBJ65W7JGW7Md14hNRFuiTSvVG3YaCe+PB8BPCFuHNpvNmZmZ0dHRkZGR8fHxH3zwQU9Pj6BXBBARnQ5NJ/MYjc6ClWa5kRgUxEZyc/mn/tCT6IobWVmyr1UzrdmJiY7iuYTo00mujtSnm/jbtLH9FPgVARO6trY2JSXls88+u/POO1NSUqxWq9FoNBgMfhvSjY2NR44cEbsUAjpy5EhjY6PYpRDKoG4fK6oHmHpLRxs7WXSUFdXC7MnxwQcfeP6LMk3ZCkV/azZfL7uJaLOIMZEUJ5LinSTN0RejbQruqaqqqqysdPPFkof3Fl8lVEL39PS8++67bW1tb7/99u7du19//fXCwsL4+PgDBw6Ul5cLdFHpE+RNUDJ8+6+oqqqqqqpqsK+iUZ2bS2w2/n2w2KfabCQ312Htu7/qbSQKBZk40bMV67y8PM98Idrxzqy3mZ7uvEE7kRTrSL2RGEqInvccrZa88EL/4w537XMXHTly5Ndff3XzxZLn8wnt2++cTgjVD11XV1deXh4XF6e/+l6jVqtXrFiRnp5+6NCh+Ph4BZqrwM/o9USvJwYDMZlIXl5/9ZJn3e+0NJKW1n/Szp0Oh3afOnUt8GntUsT1T2gqnz7trBPenlZL0tJ0xlQT0Tr6d72eJCT0fwDgn4RK6BMnTjQ3N0+fPj04OJg5qNPpNBpNTU1Na2vrjTfeKNClASSO1pYJcVojpCcxee4kqold3Zq+kIk1gTKblqSkhJSW9mezi+g3dbV4JiP7H/V6otX64Ng4APcIldC0tTM6Otr+4PDhw0NCQk6fPt3R0YGEBnDJ9VFdYizRkxJn55tM11LTvpJN/0tIIKdPk4iIa8l99QON1XrdQwD9Osw5tNZPyKDb1el16bMCJ3hRVwZwQqiEPn36NPfgyJEjb7755pqamra2NoGuC+CztFpiMCQaDVpi0hKTnpQmkIHSmsHEreMu4S8IITqdB8pJrqY+zV7Hg7sGsbMngF8SKqF5B2wrFIphwwYYm+bb48gaGhreeustsUshFLPZnJ+f/80334hdEEHQ30zRb19ICGnsmmnq0pcQPSFupbUwTETbGNRonjixYeLEa9XhtjYi9k+Mor+WDQ0NYhdEEA0NDWazWfRfTuE0NDTk5+eLXQqh0DFbvP8kVEIHBgZyD9pstr6+PievmjlzpkDlkYgVK1aIXQQBPfzww2IXQUCO/oS8zGgkhHxDCOsxKKSKJFeRZDFKJA++/cup0Wg0Go3YpRCQb79zxsXFOco+oRI6IiKCe7Czs7OxsVGlUo0ePZr3VXFxcRJ5HwQAABCXUPOhaUL/8ssv9gevXLly8eLF0aNHq1Qqga4LAADgG4RK6IkTJ4aGhpaXl1++fJk5eOrUKZPJdOutt44ZM0ag6wIAAPgGoRJao9HExMSUl5cXFRXZbDZCiMViycnJ6evre+ihh7BcCQAAgHMKm2AzHiorKzMyMi5evBgbGzt+/PiysrLz588vXLgwKyuLdxwZAAAAMARMaEJIfX39hg0bysrKrly5Mn78+CeeeGLRokWIZwAAgAEJm9AAAADgHmH3hwYAAAD3IKEBAACkCAkNAAAgRZJL6Pb29uzs7NjY2MjIyOjo6AULFhw9elSmneVWq/XFF19cvHhxR0eH8zN//vnnGTNmRHK899573imqx3V0dKSmpq5evVrsggxab28v3cKc/gYuW7asvr7e+Uvkfvt++umnhQsXTpo0KSoq6r777isoKJDdX5zZbM7MzIyOjo6MjIyPj//ggw94twaw989//pN7y+64444ffvjBO2X2rKKiopkzZ8q08Izjx4/HxsYWFRUNeKYP3D6bzXb06NFHHnlk0qRJkZGRd911V3Z2dnt7u/05Qq366R6z2ZyWlnbq1CmdTnfvvfeeOXOmoqJi6dKlmzZtmjNnjtilGxybzVZQULB///4777xzwJMbGhqam5tHjx6tVqvtj7M+lYve3t5du3aVlZXNmzdP7LIMjtVqXb9+/a5du8LCwlJSUs6ePVtaWlpVVbVt27aYmBhHr5L17SsqKlq5cmVPT09iYuKIESNKS0uffvrpNWvWZGRkyGXdgtra2vT09JaWFmZip9Fo/PHHH51P7Dx+/LhCoQgLCxs+fDhzUK1WK5XSeld0RX19fXZ2dldXl9gFGZLW1tbs7Ozm5mZXTpb77bPZbNu2bcvOzg4MDExMTBw1alRZWdnWrVtramo2b9587a3DJhl9fX1ZWVmRkZFbtmyxWq304Lfffjt9+vT4+PgzZ86IW7xBsVqtO3bsmDx5sk6nW7RokcVicX7+9u3bIyMjP//8c+8UT1CXLl1av359ZGSkTqdbtWqV2MUZnPLy8ttuu23JkiXt7e30yKeffjp58uSMjIxLly45epV8b19LS0tycvL06dOPHTtGjzQ0NCQlJc2YMePkyZPils1FV65cefrppydPnvzpp5/SI+3t7UuWLJk8efIXX3zh6FUdHR1Lliy55557zp8/762SCqWysvL3v/+9Tqe7/fbbq6urxS6Om/73v/8lJyfrdDqdTldYWOj8ZB+4fSdPnpwxY0ZSUlJdXR09cunSpbVr1+p0uk2bNjGnSaiV+8KFC6WlpZMmTZo/f35AQAA9+Lvf/W7u3Llms/nkyZPiFs91tMFt/fr1Op3OxVrUiRMnQkJCbrrpJqHLJrSffvpp8eLFO3bsmDJlSlBQkNjFGRybzVZQUNDd3f2nP/2JuXGzZs26//77v/nmG9Yi8/bke/uqq6tra2sfeOCBO+64gx4JDw9/5plnLly48Pnnn4tbNhfV1dXRzfv0V7e8VKvVK1asGD58+KFDh2wOmus7OztPnz4dHh5+ww03eK+snnb58uX333//scce6+7u1nlqb2+vo/1KycnJv/zyy9SpU115iQ/cvi+//LKpqWnJkiXMjQsODn788cdDQ0OPHj3KdIxKK6GHDRs2adIk1qrdY8eOFatI7tm0adORI0dSUlK2bNkSEhIy4PkdHR0NDQ033XTTzTff7IXiCaejo8NoNB4/fnzlypVyXDmuvb29qqpq3LhxkyZNYg4qlcoZM2ZYLJbq6mreV8n69lVUVPT09MycOdO+QTs6Onrs2LHffvttd3e3iGVz0YkTJ5qbm6dPnx4cHMwc1Ol0Go2mpqamtbWV91Xnzp1rbW2NiooaOXKkt0rqeV999dWrr74aHh7+4Ycf/va3vxW7OG6qra196aWXAgICtm7dOnfuXFde4gO3r7GxMTQ0dMqUKfYHR44cOWLECPsjEkroKVOmFBYW5uTk2HckWCyW4uJitVotowqKRqPZtWvXa6+95uJvT3t7u9lsVqvVOTk5dIhcbGwsd8iALEybNu3w4cNPP/20feeQXHR3d7e0tEyYMGHUqFH2x+nv3rlz53hfJevb19jYqFarWVsLjx49Ojg4uLm5WRb9mo2NjYSQ6Oho+4PDhw8PCQlpa2tzNEjz7NmzHR0dfX19y5Yti46OpkPkDh8+3Nvb641Ce0hQUNDatWsPHjxo/0wpOwEBAUuXLi0sLLzrrrtcfIkP3L5169YdPXo0NjbW/uB333139uzZ8PBwJjsk3alus9n27NlTWVn5hz/8gfUXKGXPPvvsoM43m83Nzc1ms7muri4uLm7EiBF0yEBpaem2bdvCw8MFKqfHqVSqF154QexSuO/ChQu8b+hhYWEqlYomAZd8b19nZ+f58+e5x2+44YZbbrnl3LlzsqhDnz59mntw5MiRN998c01NTVtbG++rampqCCEffvhhVFRUcnJyS0vLF1988cwzzyxatMhgMMil+Sc+Pj4+Pl7sUgzV1KlTXWzcZvjG7WMxm81vv/32yJEj58+fz7RpSTehbTZbfn7+m2++GRkZuXbtWpn+0F3R1tY2YsSIP/7xjy+//DJtqbt8+fIrr7zy0UcfvfPOO3/729/kMjpR7np7e61WK/f4sGHDnIxqlu/ts9lsvN8vIWTYMAm1rjnHO6tKoVA4+RZ6e3vb29tVKtWGDRvmzp1Lb259ff0TTzzx8ccf33333bKbOeJXfPL2NTU1rVq1qq6ubs2aNTNmzGCOS/TvsLe3d9u2bX/961/Dw8O3bNki5YrI0CUlJR07dmzjxo1MR1pwcPBTTz0VHh5ONwQTt3j+IyAggDdN+/r6HA04InK+fQqFwtHTQ19fn5cL4zbeZ3ebzebkWwgICHjllVeqq6sffPBB5tlLp9M988wzVquVDiQWqrgwZL53++rr61NTUysqKjIzM9PT0+3rA+Ik9HvvvedkmnlHR8fatWuzs7OnTZu2a9cuaXaxFBUVsSbLuzLL3nVjxoyZMGFCe3u7i7MDvcn57ZMF3tsXGhqqUqm4Jzc1NXV0dAxqIJiUbx9j5MiR48aN4x6/dOnSuXPnbrzxRtagFWmKiIjgHuzs7GxsbFSpVKNHj3b9S2m1Wtqd0dnZ6bkCgpfI9Pb997//XbhwYV1dncFgWLFiBeuJU3J16KampmXLluXn58+ePXvHjh3jx48Xu0TeYLFYeBvrlEolM/EMhEb7X81m86VLl+yP//rrr4SQW265xdEL5Xv7tFqtxWKh3yCjra3t8uXLY8eOlcV8OZrQrLlwV65cuXjx4ujRo3kfuQghvb29bW1tvJUtpVIpl6Va/JZv3D6bzbZ///7HH3+8q6vrnXfeWbJkCbfk4vSQLV++fPny5dzjFotl1apVFRUVy5Yt+8tf/iLlvmc603zoX8dqtT777LMFBQVbt25NSkpijpvN5p9//lmac3gc3T4ZcXT7pkyZcuzYsRMnTjCVS6vV+vXXX6vV6ttvv517vhxvn72YmJjAwMCysrJ7772XeXeoqam5cOHC9OnTZVGHnjhxYmhoaHl5eWpqKtPRcOrUKZPJ9MADD7CmblJnzpxZtGjR8OHDd+/ebf/gdezYMYvFIus5PP7AZ27fZ5999uKLL44bN27Lli3Tpk3jPUdCdeienp6NGzd+9dVXq1evXrNmjZTj2YOUSuX9999PCMnLy2Pmbra2tq5fv76lpWXevHk33nijqAX0L/fcc49Codi+fTtzLwoLC+mKxxMnTuSeL/fbN3ny5KioqMOHD3///ff0iNls3rx5c1hY2D333CNu2Vyk0WhiYmLKy8uLiopopcpiseTk5PT19T300EO81anx48dPnz79zJkz//rXv5j5Od99911OTs7YsWMffvhhr34DMEi+cfsqKytffvnlCRMm5OXlOYpnIqmx3NXV1Z988gkhJC8vb8+ePax//fvf/+4D8wqo1atXHzhw4Pnnn6c10dmzZy9YsGDv3r0JCQkJCQmEkNLS0o6OjuTk5EWLFoldWP8SFxeXkpKyd+/eOXPmxMfHnz17tqKiIiQk5KmnnmLqZ750+8LCwjIzM1euXPnoo4/+3//9H12Xu7Ozc82aNdIc/8FFx+UdO3bsueee27NnD12X+/z58wsXLoyLi6Pn/PDDD4899lhISMjHH388btw4pVL5/PPP19bW/uMf/9i/f39sbCzdAiAgIGD9+vW33nqruN8RsPje7bNarbm5uXTJgdTUVNa/xsTEbNy4kbYESCihKyoq6GxU3uGvslg8wT2BgYFZWVmxsbHvvvvup59+SgiJiop68skn586d6ycNCdJB70V0dPT7779/4MCB4cOHJyQkrFu3zsmSinK/fXPmzAkNDX3ttdeKi4v7+vqioqJWrlw5e/ZsuXTmEUJiYmL27du3YcOGsrKy8vLy8ePHG43GRYsWOfn5h4eHf/TRR++9997Bgwf37dtHb3RmZiaz+ilImdxvX0tLS2VlJSGks7OTO65No9EwXewK2Q1MBwAA8AcS6ocGAAAABhIaAABAipDQAAAAUoSEBgAAkCIkNAAAgBQhoQEAAKQICQ0AACBFSGgAAAApQkIDAABIERIaAABAipDQAAAAUoSEBgAAkCIkNAAAgBQhoQEAAKQICQ3gpywWy8KFCyMjI1988UWr1cocP3DgQFRU1KxZs8xms4jFAwAkNICfUqvVa9asUavV+/fv//rrr+nBhoaGzZs3BwYGPvfcc+Hh4eKWEMDPIaEB/FdMTMzSpUuvXLmyefNmi8XS09Pz1ltv1dfXp6SkJCUliV06AH+nFLsAACAahULx+OOPl5WVVVRUHDp0aNSoUYcOHYqKivrzn/8cGBgodukA/J3CZrOJXQYAENOXX36ZkZGhUqmGDRvW3t6+adOmOXPmiF0oAEArN4Dfi4+PX7x4cUtLy4ULF+bPnz9r1iyxSwQAhCChAUChUMTGxgYGBioUioiICKUSnV8AkoCEBvB3TU1NOTk5Vqs1ICBg+/btP/30k9glAgBCkNAAfs5ms7377rs//vjjvHnz0tLSmpqaXn/99cuXL4tdLgBAQgP4t6NHj+7fvz8sLOyJJ57IyMiIjo7+z3/+U1BQIHa5AAAJDeDHWltbX3311c7OzmXLlv3mN78JCwvLzMxUKpVvvvlmfX292KUD8HdIaAA/ZbPZ9u7dW1VVFRsbu3DhQnowKSnpvvvuO3v27JYtW3p6esQtIYCfQ0ID+KmqqqodO3aoVKqVK1eq1Wp6MDAwMDMzMyws7N///ndRUZG4JQTwc1ixBAAAQIpQhwYAAJCi/wdrcstogQANuwAAAABJRU5ErkJggg==\" alt=\"Scale parabola\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function k = scale_parabola(p, a)\r\n k = x;\r\nend","test_suite":"%%\r\np = [1 0 1];\r\na = 2;\r\nk_correct = 7/4;\r\nassert(isapprox(scale_parabola(p,a),k_correct))\r\n\r\n%%\r\np = [1 0 -1];\r\na = 2;\r\nk_correct = 0.25;\r\nassert(isapprox(scale_parabola(p,a),k_correct))\r\n\r\n%%\r\np = [5 0 0];\r\na = 0.5;\r\nk_correct = 1;\r\nassert(isequal(scale_parabola(p,a),k_correct))\r\n\r\n%%\r\nfiletext = fileread('scale_parabola.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\np = [-3 0 1];\r\na = 1;\r\nk_correct = 0;\r\nassert(isequal(scale_parabola(p,a),k_correct))\r\n\r\n%%\r\np = [-3 0 2];\r\na = 1;\r\nk_correct = -1;\r\nassert(isequal(scale_parabola(p,a),k_correct))\r\n\r\n%%\r\np = [-3 0 2];\r\na = 3;\r\nk_correct = 7/9;\r\nassert(isapprox(scale_parabola(p,a),k_correct))\r\n\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":2,"created_by":4993982,"edited_by":4993982,"edited_at":"2026-01-16T14:57:57.000Z","deleted_by":null,"deleted_at":null,"solvers_count":12,"test_suite_updated_at":"2026-01-16T14:57:57.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2026-01-10T14:36:03.000Z","updated_at":"2026-03-29T13:27:42.000Z","published_at":"2026-01-15T14:52:59.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eLet \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e be a quadratic polynomial, with its axis of symmetry being the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e-axis. Considering the vertical shift of its vertex to the origin, find the positive constant, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, that scales the shifted parabola such that its area over the interval \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[-a; a] (a\u0026gt;0)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e will be equal to the area under the original parabola (see figure below).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003einput: 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":50462,"title":"Calculate quadrilateral Area: sides and diagonals given","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 352px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 176px; transform-origin: 407px 176px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eCalculate quadrilateral Area: sides (a,b, c, d) and diagonals (e, f) are given\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 232px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 116px; text-align: left; transform-origin: 384px 116px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"269\" height=\"226\" style=\"vertical-align: baseline;width: 269px;height: 226px\" 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\" 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9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e Round the answer to four decimal places.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eHint: use Bretschneider's formula\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = AreaQuadrilateral(a,b,c,d,e,f)\r\n\r\nend","test_suite":"%%\r\na = 4; b = 4; c = 4; d = 4; \r\ne = 4*sqrt(2); f = 4*sqrt(2);\r\n\r\ny_correct = 16;\r\nassert(isequal(AreaQuadrilateral(a,b,c,d,e,f),y_correct))\r\n\r\n%%\r\na = 3; b = 3; c = 3; d = 3; \r\ne = 3*sqrt(3); f = 3;\r\n\r\ny_correct = 7.7942;\r\nassert(isequal(AreaQuadrilateral(a,b,c,d,e,f),y_correct))\r\n\r\n%%\r\na = 5; b = 5; c = 8; d = 8;\r\ne = 4+sqrt(55); f = 6;\r\n\r\ny_correct = 34.2486;\r\nassert(isequal(AreaQuadrilateral(a,b,c,d,e,f),y_correct))\r\n\r\n%%\r\na = 97.7; b = 76.6; c = 110; d = 66.5; \r\ne = 151.7; f = 91.6;\r\n\r\ny_correct = 6341.4175;\r\nassert(isequal(AreaQuadrilateral(a,b,c,d,e,f),y_correct))\r\n\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":487522,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":20,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-02-18T20:12:44.000Z","updated_at":"2026-03-04T22:07:29.000Z","published_at":"2021-02-18T20:25:42.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate quadrilateral Area: sides (a,b, c, d) and diagonals (e, f) are given\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"226\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"269\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e Round the answer to four decimal places.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHint: use Bretschneider's 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a Polyshape_01 (ps) Return its Perimeter, Area, and Centroid.","description":"Return the perimeter (P) of a polyshape object, which is the sum of the lengths of its boundaries.\r\nReturn the total area (A) of a polyshape object, which is the sum of the areas of the solid regions that make up the polyshape.\r\nReturn the x-coordinate (Cx) and the y-coordinate (Cy) of the centroid of a polyshape. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 104.667px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407.5px 52.3333px; transform-origin: 407.5px 52.3333px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21.6667px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 10.8333px; text-align: left; transform-origin: 384.5px 10.8333px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eReturn the perimeter (P) of a polyshape object, which is the sum of the lengths of its boundaries.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 43.3333px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 21.6667px; text-align: left; transform-origin: 384.5px 21.6667px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eReturn the total area (A) of a polyshape object, which is the sum of the areas of the solid regions that make up the polyshape.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.6667px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 10.8333px; text-align: left; transform-origin: 384.5px 10.8333px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eReturn the x-coordinate (Cx) and the y-coordinate (Cy) of the centroid of a polyshape. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"%%\r\nfunction [P, A, Cx, Cy] = PolyShape_01(ps)\r\n % Return the perimeter (P) of a polyshape object, which is the sum\r\n % of the lengths of its boundaries.\r\n \r\n % Return the total area (A) of a polyshape object, which is the sum\r\n % of the areas of the solid regions that make up the polyshape.\r\n \r\n % Return the x-coordinate (Cx) and the y-coordinate (Cy) of the\r\n % centroid of a polyshape. \r\n end","test_suite":"%% Test 1\r\n ps = nsidedpoly(13,'Center',[17, 47],'SideLength', 101);\r\n [P, A, Cx, Cy] = PolyShape_01(ps);\r\n assert(isequal(round(P,4),1313))\r\n assert(isequal(round(A,4),134508.0227))\r\n assert(isequal(round(Cx,4),17))\r\n assert(isequal(round(Cy,4),47))\r\n\r\n \r\n%% Test 2\r\n ps = nsidedpoly(13,'Center',[17, 47],'SideLength', 101);\r\n ps = translate(ps,[237,-1723]);\r\n [P, A, Cx, Cy] = PolyShape_01(ps);\r\n assert(isequal(round(P,4),1313))\r\n assert(isequal(round(A,4),134508.0227))\r\n assert(isequal(round(Cx,4),254))\r\n assert(isequal(round(Cy,4),-1676))\r\n\r\n \r\n%% Test 3\r\n ps = nsidedpoly(13,'Center',[17, 47],'SideLength', 101);\r\n ps = translate(ps,[237,-1723]);\r\n ps = scale(ps,0.135);\r\n [P, A, Cx, Cy] = PolyShape_01(ps);\r\n assert(isequal(round(P,4),177.255))\r\n assert(isequal(round(A,4),2451.4087))\r\n assert(isequal(round(Cx,4),34.29 ))\r\n assert(isequal(round(Cy,4),-226.26))\r\n\r\n \r\n%% Test 4\r\n ps = nsidedpoly(13,'Center',[17, 47],'SideLength', 101);\r\n ps = translate(ps,[237,-1723]);\r\n ps = scale(ps,0.135);\r\n ps = subtract(ps,nsidedpoly(17,'Center',[43, -220],'SideLength', 1.7));\r\n [P, A, Cx, Cy] = PolyShape_01(ps);\r\n assert(isequal(round(P,4),206.155))\r\n assert(isequal(round(A,4),2385.7031))\r\n assert(isequal(round(Cx,4),34.0501))\r\n assert(isequal(round(Cy,4),-226.4324))\r\n\r\n \r\n%% Test 5\r\n ps = nsidedpoly(13,'Center',[17, 47],'SideLength', 101);\r\n ps = translate(ps,[237,-1723]);\r\n ps = scale(ps,0.135);\r\n ps = subtract(ps,nsidedpoly(17,'Center',[43, -220],'SideLength', 1.7));\r\n ps = subtract(ps,nsidedpoly(17,'Center',[20, -220],'SideLength', 1.7));\r\n [P, A, Cx, Cy] = PolyShape_01(ps);\r\n assert(isequal(round(P,4),235.055))\r\n assert(isequal(round(A,4),2319.9976))\r\n assert(isequal(round(Cx,4),34.448))\r\n assert(isequal(round(Cy,4),-226.6146))\r\n\r\n \r\n%% Test 6\r\n ps = nsidedpoly(13,'Center',[17, 47],'SideLength', 101);\r\n ps = translate(ps,[237,-1723]);\r\n ps = scale(ps,0.135);\r\n ps = subtract(ps,nsidedpoly(17,'Center',[43, -220],'SideLength', 1.7));\r\n ps = subtract(ps,nsidedpoly(17,'Center',[20, -220],'SideLength', 1.7));\r\n ps = subtract(ps,polyshape([20 30.1 40.1 45.1 50 45.2 40.2 30.2 27.2],[-235 -239 -239 -237 -235 -239 -241 -240.5 -240]));\r\n [P, A, Cx, Cy] = PolyShape_01(ps);\r\n assert(isequal(round(P,4),300.0489))\r\n assert(isequal(round(A,4),2274.2476))\r\n assert(isequal(round(Cx,4),34.4235))\r\n assert(isequal(round(Cy,4),-226.367))\r\n \r\n \r\n ","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":20795,"edited_by":20795,"edited_at":"2024-06-28T13:41:58.000Z","deleted_by":null,"deleted_at":null,"solvers_count":10,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-06-26T18:00:30.000Z","updated_at":"2026-03-18T15:16:22.000Z","published_at":"2024-06-26T18:18:37.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eReturn the perimeter (P) of a polyshape object, which is the sum of the lengths of its boundaries.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eReturn the total area (A) of a polyshape object, which is the sum of the areas of the solid regions that make up the polyshape.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eReturn the x-coordinate (Cx) and the y-coordinate (Cy) of the centroid of a polyshape. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61070,"title":"Square area to triangle area","description":"Given the area, A, of a square with side length, c, if a right angle triangle has the same area A and the hypothenuse length 2c (two times the square side), then find the height, h, of the triangle.\r\nForbidden functions / expressions\r\nregexp\r\nassignin\r\nstr2num\r\necho","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 163.75px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 81.875px; transform-origin: 408px 81.875px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven the area, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, of a square with side length, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ec\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, if a right angle triangle has the same area \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and the hypothenuse length \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e2c \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e(two times the square side), then find the height, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eh\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, of the triangle.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eForbidden functions / expressions\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.75px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 392px 40.875px; transform-origin: 392px 40.875px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2125px; text-align: left; transform-origin: 364px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eregexp\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2125px; text-align: left; transform-origin: 364px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eassignin\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2125px; text-align: left; transform-origin: 364px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003estr2num\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2125px; text-align: left; transform-origin: 364px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eecho\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function h = find_height(A)\r\n h = A;\r\nend","test_suite":"%%\r\nA = 8;\r\nh_correct = 4;\r\nassert(isequal(find_height(A),h_correct))\r\n\r\n%%\r\nfiletext = fileread('find_height.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\nA = 9;\r\nh_correct = 3*sqrt(2);\r\ntolerance = 1e-12;\r\nassert(abs(find_height(A)-h_correct)\u003ctolerance)\r\n\r\n%%\r\nA = 15;\r\nh_correct = sqrt(30);\r\ntolerance = 1e-12;\r\nassert(abs(find_height(A)-h_correct)\u003ctolerance)\r\n\r\n%%\r\nA = 16;\r\nh_correct = 4*sqrt(2);\r\ntolerance = 1e-12;\r\nassert(abs(find_height(A)-h_correct)\u003ctolerance)\r\n\r\n%%\r\nA = 18;\r\nh_correct = 6;\r\nassert(isequal(find_height(A),h_correct))\r\n\r\n%%\r\nA = 32;\r\nh_correct = 8;\r\nassert(isequal(find_height(A),h_correct))\r\n\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":5,"created_by":4993982,"edited_by":4993982,"edited_at":"2025-11-09T16:09:35.000Z","deleted_by":null,"deleted_at":null,"solvers_count":22,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-11-09T13:39:12.000Z","updated_at":"2026-04-12T13:53:34.000Z","published_at":"2025-11-09T16:09:35.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven the area, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, of a square with side length, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ec\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, if a right angle triangle has the same area \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and the hypothenuse length \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2c \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e(two times the square side), then find the height, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, of the triangle.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eForbidden functions / expressions\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eregexp\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eassignin\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003estr2num\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eecho\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":45538,"title":"Find the area of ​​the square","description":"There are *n²* circles inscribed in the square ABCD. The perimeter of each circle is *aπ*\r\n\r\n\u003c\u003chttp://imgfz.com/i/3wzCeAT.png\u003e\u003e\r\n\r\nGiven *n* and *a*, find the area of ​​the square.","description_html":"\u003cp\u003eThere are \u003cb\u003en²\u003c/b\u003e circles inscribed in the square ABCD. The perimeter of each circle is \u003cb\u003eaπ\u003c/b\u003e\u003c/p\u003e\u003cimg src = \"http://imgfz.com/i/3wzCeAT.png\"\u003e\u003cp\u003eGiven \u003cb\u003en\u003c/b\u003e and \u003cb\u003ea\u003c/b\u003e, find the area of ​​the square.\u003c/p\u003e","function_template":"function y = squartArea(n,a)\r\n y = n+a;\r\nend","test_suite":"%%\r\na = 8;\r\nn = 5;\r\ny = 1600;\r\nassert(isequal(squartArea(n,a),y))\r\n%%\r\na = 0;\r\nn = 10;\r\ny = 0;\r\nassert(isequal(squartArea(n,a),y))\r\n%%\r\na = 100/pi;\r\nn = 6;\r\ny = 36476;\r\ntolerance = 1e-12; \r\nassert(abs(36476-y)\u003ctolerance)\r\n%%\r\na = 15;\r\nn = 0;\r\ny = 0;\r\nassert(isequal(squartArea(n,a),y))\r\n%%\r\na = 10;\r\nn = 2;\r\ny = 400;\r\nassert(isequal(squartArea(n,a),y))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":446926,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":60,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-05-18T03:38:49.000Z","updated_at":"2026-03-05T11:06:44.000Z","published_at":"2020-05-18T03:38:49.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/media/image1.png\"}],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThere are\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en²\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e circles inscribed in the square ABCD. The perimeter of each circle is\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eaπ\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, find the area of the square.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray 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the Area of the Ring","description":"\r\nYou have Ring which consist of inner and outer Circles with Radius r and R which are not given but you'll be given Hprizontal distance d which is Tangent to inner circle .\r\nCalculate the Area of the Ring","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 312.033px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.5px 156.017px; transform-origin: 406.5px 156.017px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 231.033px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 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\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 21px; text-align: left; transform-origin: 383.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 192.067px 7.81667px; transform-origin: 192.067px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou have Ring which consist of inner and outer Circles with \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 126.742px 7.81667px; transform-origin: 126.742px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eRadius r and R which are not given \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 59.1833px 7.81667px; transform-origin: 59.1833px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ebut you'll be given Hprizontal distance d which is Tangent to inner circle .\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 10.5px; text-align: left; transform-origin: 383.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 96.5917px 7.81667px; transform-origin: 96.5917px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCalculate the Area of the Ring\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function area = your_fcn_name(d)\r\n area = d;\r\nend","test_suite":"%%\r\nd = 3;\r\narea_correct = 28.2743;\r\ntolerance = 1e-4;\r\nassert(abs(your_fcn_name(d)-area_correct)\u003ctolerance)\r\n%%\r\nd = 5;\r\narea_correct = 78.5398;\r\ntolerance = 1e-4;\r\nassert(abs(your_fcn_name(d)-area_correct)\u003ctolerance)\r\n%%\r\nd = 8;\r\narea_correct = 201.0619;\r\ntolerance = 1e-4;\r\nassert(abs(your_fcn_name(d)-area_correct)\u003ctolerance)\r\n%%\r\nd = 15;\r\narea_correct = 706.8583;\r\ntolerance = 1e-4;\r\nassert(abs(your_fcn_name(d)-area_correct)\u003ctolerance)\r\n%%\r\nd = 17;\r\narea_correct = 907.9203;\r\ntolerance = 1e-4;\r\nassert(abs(your_fcn_name(d)-area_correct)\u003ctolerance)","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":4033021,"edited_by":223089,"edited_at":"2024-06-12T15:22:45.000Z","deleted_by":null,"deleted_at":null,"solvers_count":21,"test_suite_updated_at":"2024-06-12T15:22:45.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2024-04-07T14:03:59.000Z","updated_at":"2026-03-05T11:47:22.000Z","published_at":"2024-04-07T14:20:37.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"225\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"225\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou have Ring which consist of inner and outer Circles with \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eRadius r and R which are not given \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003ebut you'll be given Hprizontal distance d which is Tangent to inner circle .\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate the Area of the 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":44742,"title":"Find the area of a triangle having vertices (A,B), (C,D), and (E,F)","description":"Find the area of a triangle using if we have the three vertices of the triangle","description_html":"\u003cp\u003eFind the area of a triangle using if we have the three vertices of the triangle\u003c/p\u003e","function_template":"function A = triarea(x1,y1,x2,y2,x3,y3)\r\nA=b*h/2","test_suite":"%%\r\nx1 = 1;y1=1;x2=0;y2=0;x3=2;y3=0;\r\ny_correct = 1;\r\nassert(isequal(triarea(x1,y1,x2,y2,x3,y3),y_correct))\r\n%%\r\nx1 = 2;y1=1;x2=5;y2=1;x3=4;y3=3;\r\ny_correct = 3;\r\nassert(isequal(triarea(x1,y1,x2,y2,x3,y3),y_correct))\r\n%%\r\nx1 = 4;y1=0;x2=7;y2=2;x3=2;y3=3;\r\ny_correct = 6.5;\r\nassert(isequal(triarea(x1,y1,x2,y2,x3,y3),y_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":38144,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":44,"test_suite_updated_at":"2018-10-04T21:31:40.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2018-10-04T21:07:54.000Z","updated_at":"2026-03-05T11:56:43.000Z","published_at":"2018-10-04T21:31:40.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind the area of a triangle using if we have the three vertices of the triangle\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":50452,"title":"Calculate Triangle Area: A, B and Beta is given","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 275px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 137.5px; transform-origin: 407px 137.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eCalculate Triangle Area: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eA\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eB\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eBeta\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e [degree] is given as follows:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 215px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; 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AD0YN687kBnF+7HgGhk6HQXpFr6X9X8PcNG7yIzidqy4Bd34JFtAK4rNzavR573s/UgM76khQ6ejI0g3ryvPIDGKxSew5JJltNHeilAIlxU2Abp/f6E/Q16UeQFLLtHHAlpRlnIBeq9Pd+ILSAsDb6kBC+hBhEIEZLkA3R83r5fLKfETyoziK1hzh3TjVSDTcdy8D4QfAvRvlDPivYsoM4pHsegKWECPIhSiwubmtbPOvewFRrVrS4oyw1tqSDdeHfx08/peOSFOLLBS412suiFNroQydFoNGnaatwPU4eZ10XvlhNiUslKjiGU3oBsvvvqqwN28jnsVoP+onA5vXlBXasjQaeXgbl7ePumv/LicDreWXxhvHgYLaN0F6MY3IRSUIPen/0T35ezZcSy55KlyNvx6XvnFUcqM4hW07gKq4WtsAa0i1W8b3vYp1xvZ8FXjlefUgAV0G0JBAZZXF8496u5eKSfDi+YrKzU+a0YukG68ahRYu82j7u5WIxmuN19aqUGRc5bTf18soFWBH57e3eDtrMoFvynnwjP02mtqSDdeKbh6w7uJxveNXLiGXlup8WUKnZKjDzU55qoC/PxSPTaylxob1p8hMHpsBsZG1gXSjVeGNLOQrU9GbHRbP74SwQuUGS5TI0sj12XodORkOqhdQUzV5+T2OaPa9QiCSmp8B7EzYAEt3fiI4S5uk/WO33jGyIS7bgWvm4nh8rSBDJ1WAj5GcqKz3j3BjcgFG65So51+mOSbyalMjvVLDtc/zWner5ALNn6IrztBLKCjh59+PezHDLjbjDw4cbSCJSp3c9qgmX4esYCODN5+3+/LgeMFJ8ppYDTjLbZTZrhKDenGRwt38/NrDMsWIw2qN6pWalh1Dgesox+pBaEQLg2s8FmvDrTCpcbnx5tGM97CSg0Xpw2kGx8hjeQTAHw8CW0mAqtuuU+NVfRTydDp8OGnoH01o7/GqHadqHrSmEmN1xHXRrrxEcHnAE71+2qN+ZyRBD9FQFip4fi0gQydjgbuhOH3OJ6bzCTYhIgwa6NlzrD3kjkYMn80sYAOl2wPHQcjfB9IfYkh07ArM35trpVx2JWXodMRkOtjFXHfx9gveJFygJXE6Y3EwOHutc/86abjNSk73nA7Nn/naBjM+4b1/nDijkuwlrpsk1EBA1suw+pciAV02OTZDI39Lf7XDDYhAQwq7xvWIRTiKazORRf9hCsQCgHDpcDB+AI/iJ6JwY1YuwIxuAPLcyDd+FDhx1gDGObmI7CAXoNQCJJ1XAqstp0BuvFiAR0CXAqsvKGnDJ0OCZsU2M+KeEBQIosFdMDwacJ1SoHDQSygw4D7aU32LMa60oybP+xx6cYHCB/oN9EVj4aEWEAHDpcCx8fYFRbQ0o0PivyQ71LgcJBufLAUeEXc73n0QQIL6Fg8FcUPXhHfHav6gHTjA4RLgXcpXRGfTa/5U8vQ6QBo3GteWxCMKVKAoBs/jFDwi3QzlwLHyBYcyNDpQMjwinh/DN+U0Y3fiVDwBZsUOA4V8dmIBbT/ZHt4RTymSmyygN6LSKif3NZgpcBhId14n+HGWIfb4ltipt2VWED7hE0KHJ+K+GykG+8nhTFeEcdyPCH1qhxz9YMGXhGP+YO9dON9Yy2XAsdefz1s/h4ydLpuuBR4JP71Q1hA9yIUvJFupQoA4etwjMiQodM+kGmPnRS4NotpBz6AUPBAllfEexLyZyYW0PVikwJ3J+WhLUO/llhAeyXXT7P+Cc8Wmwoi3fi6yA/GVApcmzRZ2Xs0htSdFbwi3pSoIzzSjfcOlwLvSVpzkoo0MnTaPQ102A+MJ+6PS7rxHmncQ1eOiJ0U2AEydNoL6SYuBU7ifKs19MuJBbQbbMMxBpJZEZKh067hUuDTyaiIz2YF/X5dCIWaZLsTIQWujVhAuyPXy6XAC7GePJZSvaYPoTA3Np+89iR/DEs33gVcCnwwSRXx2cACegihMAeF0QRJgWtD3XixgK7NGi4FXovlxCJDpx3Ch2OMadBuQjdeLKDnhkuBR3UQL4gFtAPSrQfNq0QkQwpcmxb6ddchFGaTaeNSYF38g6QbX4OFXArcq80eHxbQzQgFGzYpcHIr4rORbvxc5PqTMRzDC7CAbkcoVJMfSKwU2AHSjT8vy7kUuFmzN9Y8/d4ydHoWXAq8Vz9lJHXjT0s33kbDLvPCgLgPx/CCDJ0+J428Iq7lqS3qxk9LN76KNK+I79DzOJ9YQM/CJgUe1LUdDQvo+E3LDopMBx3vJBIyHMML0o3nZLs0kQLXpo2ugVhAm+R4RbxD512bdOOrsEmBtaqIz6aJLoMcczWkwNWJcUizivhspBsPCiNaSYFrs5auhPZDp1dzKbBImiwL6GOav3dyKfBOmTxTRoZOl2ncR1fBZFrPivhsRs3LcVLjJ/F0K6+IyzkcQnsL6MxGLgVehnVhkK6IrhbQNp+8rdJgrKB3N55LgU/qXBGfzVbzokxr+S6a69NXClwbjbvxeV4Rb5XE4Gg7dNrmk9ciZyxs6NqN51LgfVIRn42eQ6cbyHQQ6CgFdgDt6PWygF7PpcAyMuKcaDh0mkuBh6Uifh6ocXAIUfKxSYGHpCJ+PjSzgM50HKNf2ERjKbAD6GDWhB77tmwnlwLr2hlwhE7d+MVcCtwpFfE5gQV0cmcnV+BS4GNSEa8BuvHJt4DOD/GKuBQ+a6HJ0OnCsEiBXYJufMItoFdxKfB6LAtzoYMFNJcC75KKuCMW0hP7CMIk0rjX/BWBSIGdkvRufLpFpMDegAX0LoRJI8Mr4v2SGM5JdDfeJgXuk4q4G2gG+z5EiSLbc9L85Qith2N4Ibnd+NxWkQLXBXlcJ2/o9DIuBd4oieEWdOM3IkwKNimwVMQ94GHo9MVXf2nDvbffvPJTiNWjMCYV8bpBN74TYW0+tfmNksXbdy/BqlI08Iq4FD694dIC+qrHP0JaEB89PB9fUYZ1XAq8GsuCS2ABvRVhLW7+0EyIT579wX2/NF+VSk+qlRtcCjwiFXHPuOvG30vZcOCq8uv5j1FQeoC+pgLp1kPm70NMSUW8DrK0v3NoAX0f5cKBRWa0BB8tH6rytpHp4BVxKXzWg6tu/FeQCp9GfIDi0krE0ZLlFfEeSYy6yFAZ2dkx18tPUSbcgzj1C4pL30YcJTafvC6piNeJq278s5QIpy5EXHnXuBNxdHAp8HGpiNdNmo7pOBs6vRKJ8APEqZS1jf0i4qjID4oU2G9gAb0W4dw8SnnwSaXI9RlaKJXoqTQqVvCKeKMkhh+4GTpt7UeeR5xKfY0WSkcQRwIfjrFbKuL+sJ6upzMLaJQ0qp45X8XKBsQRwKXA41IR9wu6rg678VYiVD5PvoWFXyAOn0aSEwCRAvvHarqkziyglyAR3kCcWvQWLXz0GSyETLqZS4HFD8xHXHXjrfeIhxEvQQvl1JewEC624RgDUhH3k+V0WbsR1sBqmNxC4effofDVyykOF5sUWCriPuOuG49UKBlF8ou/9RhtVz75caX8FSLZHl4Rl8Knz7gbOn2VmQql0jvl19s+oden7oviLSPXy6XAGox9CBt33fgNlA2lp8uv3zdfvfXtKN4xlnIpcJtUxP3H5dDph810KJU2p1JX06tT3w0/NbgU+KBUxAOhmy6v0y2f1Um7LpX61D0I3gm5rVYYFSlwCLgcOr0IjxefULvkFpIBlh4KUcSzhlfEnfV9BPe00xV2Kqm9gVKhdADxSqTKo4gDZy2XAot1dWC4tYC+mzKh9GPEVhu29HnEwcKlwKNSEQ+QZrrKjkcWPY1M+Bbi1HVYCKGBkm6l49qEDMcIGDfdeANI/0qVfonVUikFfYAt0y5S4DCBBXQLwppYop1TiMtgJWCF10JeEe+VxAgaeqZzbgFt9daMghfAysxHTADYpMDdUhEPHNdDp3+MPLgbcdUHSnCpkes/TT+niQzHCAWqELiwgLZkPDcgrpREzRpYIOQHRAocPq4toC/kBS+D22mlVAqmw7acS4GbJDHCYci83lPOP7mtnapV8Cpj1TWMTqzvcCnwHqmIh4V7C+jNyIOZ2ueFlnxj5lCKbzSMmz8fkOEYIQIL6KUIHWAVvGaOxH8XKzOHUvyikVfEpfAZIh4soK23iG2IU0usEpilFPWJdBOXAq/AuhAKnXTdXVz1TyMPSkfwGLrI2rG85Gvn1SYFHpSKeLh4sID+OhKhVPpL8/NjpZUZb/hZJc900Dhs4rRUxENnI116Nw93DyETynz02A8eeB5b2dKTPmZGtlukwBGDbvwehI6whnZx3vk6vuwDOV4R75DEiAAPQ6cvtGYl3LzNevosndr2Jf8eM/hwjMPtUhGPBNoBHETkiC8iHQ6kUvOvumHD5s233PBpHx8/uRT4kFTEI8KLBbRVw6hsXf2kMCJSYDUgC+jjrv4yn0RqBDCxazWXAq/DshA+niyg30ZqXI3YN/hwjDGpiEfJiHkT3FlAX47MeB+xX3ApsFTEo8V1N97AGsv0LGJfSLfyirgUPiNmwLwRLi2gH0Bq+NhjzbRxKbCLTp8QCO678QYvITVuRlw3tuEYW6UiHj295r1waQE93yp4XYyFOrFJgaUirgKwgB5G6JDPIzMqM7zqItfPK+JS+FQCbxbQVsHrMcT1kOcV8VZJDDVI0ye8Wwvox5Ea9Q9MsPnkNUtFXBWYBfSi6zbfa3LnDTU66ytvIOp91OBS4L1SEVcIshfal5q/8vZtB0qvPf6oyZOvffLOsw/cEvSU8Qaq0AORAisFuvF/dM/bB7bd+cWqVJh/9dfvff79R2dOH/nPel4RX4VlQQ32GnflP/7hw4fP2Qq5/O4jR+4J5rRRmlfEd0hFXDGMbvy//+///cX5Hxmu2/bhff4PbrNJgYekIq4cxkPgv/z27+bcLl7+5Ftfw0ufyHSQFw8hwzFUxGE3/itHnrYs93wg2yVSYPVxOnT6wnvfvx0v62Uxr4h3SmIoyTIqNjmxgL767YohYz3YpMBSEVcVN0Onl7zxEF55J7+DV8Sl8Kkqi+lGDSKswcUv1ekSXxgWKXBccGUBnUotevr5Oqqjq7gU2PH8SSECMvQ8OIqwNvOffByvXMOlwDulIq427rvxi17ztk9p3Ef/KUKkwKoDC+hxhI64+tRKvHJOukWkwDED3Xh3VgAbrFkaTsls5FLgZVgXFIb+lp0PnSYed/W4YZMC90lFPA6gG9+E0CmLjjjvp2R7TtJ/xOSkVMRjAm0ZHFpAV3HLq3hRi1yfSIFjyRq6Y20InTP/LUfqnmW8Ir5REiM2UAHKoQU047tVw+rPh00K3CIV8fgAC+guhG5Y9P5VeHU+CmPVibFPKuKxwp0FNOe+uYetNOw0vzcQKXDMyNGfdR9Cdyz5cI4TBuu4FNipv5+gCu4soO388rxHoLkUeFgq4rEjS2YzboZOV/PQfXjBsUmBpSIeR6gbf9brvfvaS3hRTaaDV8Sl8BlHPAydZiz5aNbpg2wnlwIvxroQL2AB7f202BGbH6NtOEaXVMRjilsL6Nk8uhkvTLgU+JhUxOMLLKDrmMZ5b5VnfH5IpMCJwVs3vpqZ1CjwinijJEacWUe30bEF9DmwUoMPx9gtFfGY47UbX8XtZmpwKfAuqYjHnVV0J90NnbaxoZwajeb4BQuRAicA7934GTb8eTOXAi/HF4QYk6e76W7otI3Mn/09fReTqX6piCcCsoA+XUdRKtMx8bv/Mr+LwaRUxBOCt6HTVWR7Js6e/Z/fmt/FqIhL4TMp9Jl31I0FNCO31ayI//7fzG8jUuAE4cECuoqlqIj/6++N/324TRIjQXSZt9aNBfQMM1Lg3/732bP7pSKeKOroxhdGZyri//k7GY6RNNro1q5B6JwGXhH/AywLScFrN34tlwK7zyxBdTxYQJfhUuARqYgnEQ/d+HQrjbcnZDhGQnFvAZ1pFymwFoybN9i5BXSWD8fokcRIKi4toG1S4G6piCeXUfMeTzorYeb66RQTcVwq4knGjQV0flCkwBoxaN7mKQdnh1ZwKXCTJEaycdyN51LgPVIRTzywgK41m7GBtjFgXKTAyQfd+BoW0I17zH8FRAqsBQ6GTqebuBTYU+deiBvoxu9EeA5swzEGpCKuCcwC+hzwqcCnpSKuD/SOsBeRnWw3r4hL4VMf5uzG53pZRbxjIdYFHaAziIcQMWw+ee1SEdeK83fj+VTgg1IR1w2a8Tox674XRlhFXAqf2nGebvwaLgV2Z5kjJIJh897bhk7z4RhjUhHXEXTjexGacCnwqFTE9WTW0Ol060FziRApsLbAAnoAYSrTxqXAXk9GC7GHW0Av5FLgXqmI6wssoEfMwCYFloq41lR143P9vCIuhU+tSR8382C8vFEZECmwUIXVjV/OpcDNkhjaQ9vUv2aFz71SEResbnw14pMnGDAZsIFIgQUTWEBbTO+QxBCIv0JOmEwNSkVcACuQFAYyHEOoAh5rZUQKLHAKI/9sJMZEhySGYOdPzp79G6mIC+cgveuPpfApcFKp/wfUk0GGNJB3NQAAAABJRU5ErkJggg==\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e Round the answer to four decimal places\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = AreaTriangle(A, B, Beta)\r\n\r\nend","test_suite":"%% \r\nA = 4; B = 4; Beta = 45; % [degree]\r\n\r\ny_correct = 8\r\nassert(isequal(AreaTriangle(A, B, Beta),y_correct))\r\n\r\n%%\r\nA = 6.39; B = 4.9; Beta = 32.9; % [degree]\r\n\r\ny_correct = 15.3134\r\nassert(isequal(AreaTriangle(A, B, Beta),y_correct))\r\n\r\n%%\r\nA = 257; B = 567; Beta = 23.8; % [degree]\r\n\r\ny_correct = 41099.6329\r\nassert(isequal(AreaTriangle(A, B, Beta),y_correct))\r\n\r\n%%\r\nA = 2*pi; B = 3*pi; Beta = 56.3; % [degree]\r\n\r\ny_correct = 29.6088\r\nassert(isequal(AreaTriangle(A, B, Beta),y_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":487522,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":24,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-02-18T16:37:21.000Z","updated_at":"2026-03-14T18:27:52.000Z","published_at":"2021-02-18T16:44:29.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate Triangle Area: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eB\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eBeta\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e [degree] is given as follows:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"209\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"269\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e Round the answer to four decimal 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VI0ye8Wwvox5Ea9Q9MsPnkNUtFXBWYBfSi6zbfa3LnDTU66ytvIOp91OBS4L1SEVcIshfal5q/8vZtB0qvPf6oyZOvffLOsw/cEvSU8Qaq0AORAisFuvF/dM/bB7bd+cWqVJh/9dfvff79R2dOH/nPel4RX4VlQQ32GnflP/7hw4fP2Qq5/O4jR+4J5rRRmlfEd0hFXDGMbvy//+///cX5Hxmu2/bhff4PbrNJgYekIq4cxkPgv/z27+bcLl7+5Ftfw0ufyHSQFw8hwzFUxGE3/itHnrYs93wg2yVSYPVxOnT6wnvfvx0v62Uxr4h3SmIoyTIqNjmxgL767YohYz3YpMBSEVcVN0Onl7zxEF55J7+DV8Sl8Kkqi+lGDSKswcUv1ekSXxgWKXBccGUBnUotevr5Oqqjq7gU2PH8SSECMvQ8OIqwNvOffByvXMOlwDulIq427rvxi17ztk9p3Ef/KUKkwKoDC+hxhI64+tRKvHJOukWkwDED3Xh3VgAbrFkaTsls5FLgZVgXFIb+lp0PnSYed/W4YZMC90lFPA6gG9+E0CmLjjjvp2R7TtJ/xOSkVMRjAm0ZHFpAV3HLq3hRi1yfSIFjyRq6Y20InTP/LUfqnmW8Ir5REiM2UAHKoQU047tVw+rPh00K3CIV8fgAC+guhG5Y9P5VeHU+CmPVibFPKuKxwp0FNOe+uYetNOw0vzcQKXDMyNGfdR9Cdyz5cI4TBuu4FNipv5+gCu4soO388rxHoLkUeFgq4rEjS2YzboZOV/PQfXjBsUmBpSIeR6gbf9brvfvaS3hRTaaDV8Sl8BlHPAydZiz5aNbpg2wnlwIvxroQL2AB7f202BGbH6NtOEaXVMRjilsL6Nk8uhkvTLgU+JhUxOMLLKDrmMZ5b5VnfH5IpMCJwVs3vpqZ1CjwinijJEacWUe30bEF9DmwUoMPx9gtFfGY47UbX8XtZmpwKfAuqYjHnVV0J90NnbaxoZwajeb4BQuRAicA7934GTb8eTOXAi/HF4QYk6e76W7otI3Mn/09fReTqX6piCcCsoA+XUdRKtMx8bv/Mr+LwaRUxBOCt6HTVWR7Js6e/Z/fmt/FqIhL4TMp9Jl31I0FNCO31ayI//7fzG8jUuAE4cECuoqlqIj/6++N/324TRIjQXSZt9aNBfQMM1Lg3/732bP7pSKeKOroxhdGZyri//k7GY6RNNro1q5B6JwGXhH/AywLScFrN34tlwK7zyxBdTxYQJfhUuARqYgnEQ/d+HQrjbcnZDhGQnFvAZ1pFymwFoybN9i5BXSWD8fokcRIKi4toG1S4G6piCeXUfMeTzorYeb66RQTcVwq4knGjQV0flCkwBoxaN7mKQdnh1ZwKXCTJEaycdyN51LgPVIRTzywgK41m7GBtjFgXKTAyQfd+BoW0I17zH8FRAqsBQ6GTqebuBTYU+deiBvoxu9EeA5swzEGpCKuCcwC+hzwqcCnpSKuD/SOsBeRnWw3r4hL4VMf5uzG53pZRbxjIdYFHaAziIcQMWw+ee1SEdeK83fj+VTgg1IR1w2a8Tox674XRlhFXAqf2nGebvwaLgV2Z5kjJIJh897bhk7z4RhjUhHXEXTjexGacCnwqFTE9WTW0Ol060FziRApsLbAAnoAYSrTxqXAXk9GC7GHW0Av5FLgXqmI6wssoEfMwCYFloq41lR143P9vCIuhU+tSR8382C8vFEZECmwUIXVjV/OpcDNkhjaQ9vUv2aFz71SEResbnw14pMnGDAZsIFIgQUTWEBbTO+QxBCIv0JOmEwNSkVcACuQFAYyHEOoAh5rZUQKLHAKI/9sJMZEhySGYOdPzp79G6mIC+cgveuPpfApcFKp/wfUk0GGNJB3NQAAAABJRU5ErkJggg==\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":2284,"title":"Find the area of the four walls ","description":"If length, breadth and height of the walls are given, find the area of the four walls.","description_html":"\u003cp\u003eIf length, breadth and height of the walls are given, find the area of the four walls.\u003c/p\u003e","function_template":"function a = your_fcn_name(l,b,h)\r\n %your code\r\nend","test_suite":"%%\r\nl = 1;\r\nb = 1;\r\nh = 1;\r\ny_correct = 4;\r\nassert(isequal(your_fcn_name(l,b,h),y_correct))\r\n\r\n%%\r\nl = 20;\r\nb = 10;\r\nh = 15;\r\ny_correct = 900;\r\nassert(isequal(your_fcn_name(l,b,h),y_correct))\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":2,"created_by":22816,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":292,"test_suite_updated_at":"2014-04-14T15:16:41.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2014-04-14T05:59:25.000Z","updated_at":"2026-03-05T16:44:02.000Z","published_at":"2014-04-14T05:59:25.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf length, breadth and height of the walls are given, find the area of the four walls.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":56255,"title":"Area under the curve","description":"Compute area under the curve specified by points stored in y, where y is in range (0,inf) and x time step is 1. \r\nnote: please round the result to 4 decimals.\r\nexample: y=[1 2 3 5 8 9 10]\r\n area=32.5000","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 111px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 55.5px; transform-origin: 407px 55.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eCompute area under the curve specified by points stored in \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003ey, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003ey\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e is in range (0,inf) and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003ex\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e time step is 1. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; \"\u003enote: please round the result to 4 decimals.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eexample: y=[1 2 3 5 8 9 10]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e area=32.5000\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function area = your_fcn_name(y)\r\n area= 'Your solution'\r\nend","test_suite":"%%\r\nx = [1 2 3 5 8 9 10];\r\ny_correct = 32.5000;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\n\r\nx = [43 10 27 16 29 45 53 46 88 52 95 64 96 25 68 29 68];\r\ny_correct = 798.5000;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\n\r\nx=[70 7 26 23 67 85 35 79 68 1];\r\ny_correct = 425.5000;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\n\r\nx=[0.993183755212665 0.480756369506705 0.827750131864470 0.603238265822881 0.817841681068066 0.955547170535556 0.650378193390669 0.627647346270777 0.646563331304310 0.062133128691720];\r\ny_correct = 6.1374;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":3,"created_by":1739584,"edited_by":1739584,"edited_at":"2022-10-10T12:14:42.000Z","deleted_by":null,"deleted_at":null,"solvers_count":26,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-10-10T12:13:31.000Z","updated_at":"2026-03-05T14:10:14.000Z","published_at":"2022-10-10T12:14:42.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCompute area under the curve specified by points stored in \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e is in range (0,inf) and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e time step is 1. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003enote: please round the result to 4 decimals.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003eexample: y=[1 2 3 5 8 9 10]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e area=32.5000\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":425,"title":"ranch area?","description":"Your friend has a ranch with four distinct boundary lines. Three boundary lines are ideal straight roads: (1) North Club Road, (2) East Cathedral Road, and (3) North Market Road. The fourth boundary line is the Threadwater Canal. The length of the second boundary line is exactly one mile. You have visualized that any point on the Threadwater Canal is defined by cartesian coordinates x and y in miles, where x is its distance from North Club Road, and y is its distance from East Cathedral Road. A surveyor has found the function y(x) for you. She also told you that one square mile is 640 acres. She wants you to calculate the area of this ranch in acres.","description_html":"\u003cp\u003eYour friend has a ranch with four distinct boundary lines. Three boundary lines are ideal straight roads: (1) North Club Road, (2) East Cathedral Road, and (3) North Market Road. The fourth boundary line is the Threadwater Canal. The length of the second boundary line is exactly one mile. You have visualized that any point on the Threadwater Canal is defined by cartesian coordinates x and y in miles, where x is its distance from North Club Road, and y is its distance from East Cathedral Road. A surveyor has found the function y(x) for you. She also told you that one square mile is 640 acres. She wants you to calculate the area of this ranch in acres.\u003c/p\u003e","function_template":"function acres = ranch(y)\r\n acres=y(1)^2;\r\nend","test_suite":"%%\r\ny=@(x)1+x/10^10;\r\nacres=round(ranch(y));\r\nacres_correct = 640;\r\nassert(acres==acres_correct)\r\n%%\r\ny=@(x)0.5+x/10^10;\r\nacres=round(ranch(y));\r\nacres_correct = 320;\r\nassert(acres==acres_correct)\r\n%%\r\ny=@(x)1+x;\r\nacres=round(ranch(y));\r\nacres_correct = 960;\r\nassert(acres==acres_correct)\r\n%%\r\ny=@(x)2+sin(x);\r\nacres=round(ranch(y));\r\nacres_correct = 1574;\r\nassert(acres==acres_correct)\r\n%%\r\ny=@(x)3+cos(x);\r\nacres=round(ranch(y));\r\nacres_correct = 2459;\r\nassert(acres==acres_correct)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":166,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":52,"test_suite_updated_at":"2012-02-29T07:24:36.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-02-29T03:37:08.000Z","updated_at":"2026-03-19T18:32:18.000Z","published_at":"2012-02-29T07:24:36.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYour friend has a ranch with four distinct boundary lines. Three boundary lines are ideal straight roads: (1) North Club Road, (2) East Cathedral Road, and (3) North Market Road. The fourth boundary line is the Threadwater Canal. The length of the second boundary line is exactly one mile. You have visualized that any point on the Threadwater Canal is defined by cartesian coordinates x and y in miles, where x is its distance from North Club Road, and y is its distance from East Cathedral Road. A surveyor has found the function y(x) for you. She also told you that one square mile is 640 acres. She wants you to calculate the area of this ranch in acres.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":60166,"title":"Recursive triangle area","description":"Given triangle 1 with sides of length a, b, and c. Triangle 2 is constructed within triangle 1 by bisecting each side. Triangle 3 is constructed within triangle 2 by bisecting each of triangle 2's sides. And so on. \r\nFind the area of triangle n.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 71.9661px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 359.492px 35.9766px; transform-origin: 359.499px 35.9831px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 41.9792px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 336.497px 20.9896px; text-align: left; transform-origin: 336.497px 20.9896px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven triangle 1 with sides of length a, b, and c. Triangle 2 is constructed within triangle 1 by bisecting each side. Triangle 3 is constructed within triangle 2 by bisecting each of triangle 2's sides. And so on. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9896px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 336.497px 10.4948px; text-align: left; transform-origin: 336.497px 10.4948px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFind the area of triangle n.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function area = your_fcn_name(a,b,c,n)\r\n area = a+b+c+n;\r\nend","test_suite":"%%\r\na=1;b=1;c=sqrt(2);n=1;\r\ny_correct = 0.50;\r\nassert(your_fcn_name(a,b,c,n) - y_correct \u003c y_correct/1000)\r\n\r\n\r\n%%\r\na=100;b=100;c=100;n=2;\r\ny_correct = 1082.53;\r\nassert(your_fcn_name(a,b,c,n) - y_correct \u003c y_correct/1000)\r\n\r\n\r\n%%\r\na=13;b=33;c=44;n=4;\r\ny_correct = 2.0540;\r\nassert(your_fcn_name(a,b,c,n) - y_correct \u003c y_correct/1000)","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":3293343,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":16,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-04-30T18:08:43.000Z","updated_at":"2026-03-11T15:33:11.000Z","published_at":"2024-04-30T18:08:43.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven triangle 1 with sides of length a, b, and c. Triangle 2 is constructed within triangle 1 by bisecting each side. Triangle 3 is constructed within triangle 2 by bisecting each of triangle 2's sides. And so on. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind the area of triangle n.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":2944,"title":"Areas","description":"Given certain dimensions determine the area of that shape. If given only one value assume its the radius. Use round(x) to round each area\r\n\r\nx= [2 2 4 4]\r\n\r\narea = 8 \r\n\r\nx=[3 4 5]\r\n\r\narea = 6","description_html":"\u003cp\u003eGiven certain dimensions determine the area of that shape. If given only one value assume its the radius. Use round(x) to round each area\u003c/p\u003e\u003cp\u003ex= [2 2 4 4]\u003c/p\u003e\u003cp\u003earea = 8\u003c/p\u003e\u003cp\u003ex=[3 4 5]\u003c/p\u003e\u003cp\u003earea = 6\u003c/p\u003e","function_template":"function y = your_fcn_name(x)\r\n y = round(x);\r\nend","test_suite":"%%\r\nx = 5;\r\ny_correct = 79;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n%%\r\nx = [2 2 2 2];\r\ny_correct = 4;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n%%\r\nx = [5 12 13];\r\ny_correct = 30;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n%%\r\nx = [2 6 2 6];\r\ny_correct = 12;\r\nassert(isequal(your_fcn_name(x),y_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":33703,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":83,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2015-02-04T17:37:46.000Z","updated_at":"2026-04-02T10:14:43.000Z","published_at":"2015-02-04T17:37:46.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven certain dimensions determine the area of that shape. If given only one value assume its the radius. Use round(x) to round each area\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ex= [2 2 4 4]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003earea = 8\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ex=[3 4 5]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003earea = 6\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":45337,"title":"Area-03","description":"There are two circles of equal size are inscribed inside a square. They are tangent to each other.\r\n\r\n\u003chttps://serving.photos.photobox.com/4629487514d477b90123a8d594e9bdaa5ddba8e2ac82569375c49cd5551dd3acffb751ed.jpg\u003e\r\n\r\nGiven the side length of the square, find the radius of the circles.","description_html":"\u003cp\u003eThere are two circles of equal size are inscribed inside a square. They are tangent to each other.\u003c/p\u003e\u003cp\u003e\u003ca href = \"https://serving.photos.photobox.com/4629487514d477b90123a8d594e9bdaa5ddba8e2ac82569375c49cd5551dd3acffb751ed.jpg\"\u003ehttps://serving.photos.photobox.com/4629487514d477b90123a8d594e9bdaa5ddba8e2ac82569375c49cd5551dd3acffb751ed.jpg\u003c/a\u003e\u003c/p\u003e\u003cp\u003eGiven the side length of the square, find the radius of the circles.\u003c/p\u003e","function_template":"function y =inscribed_circle_3(a)\r\n y = x;\r\nend","test_suite":"%%\r\na = 1;\r\ny_correct = .2929;\r\nassert(abs(inscribed_circle_3(a)-y_correct)\u003c0.001)\r\n\r\n%%\r\na = 10;\r\ny_correct = 2.9289;\r\nassert(abs(inscribed_circle_3(a)-y_correct)\u003c0.001)\r\n\r\n%%\r\na = 23.6;\r\ny_correct = 6.9123;\r\nassert(abs(inscribed_circle_3(a)-y_correct)\u003c0.001)\r\n\r\n%%\r\na = 0;\r\ny_correct = 0;\r\nassert(abs(inscribed_circle_3(a)-y_correct)\u003c0.001)\r\n\r\n%%\r\na = pi;\r\ny_correct = 0.9202;\r\nassert(abs(inscribed_circle_3(a)-y_correct)\u003c0.001)","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":363598,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":32,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-02-17T06:35:50.000Z","updated_at":"2025-12-07T20:32:03.000Z","published_at":"2020-02-17T06:36:40.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThere are two circles of equal size are inscribed inside a square. They are tangent to each other.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://serving.photos.photobox.com/4629487514d477b90123a8d594e9bdaa5ddba8e2ac82569375c49cd5551dd3acffb751ed.jpg\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026lt;https://serving.photos.photobox.com/4629487514d477b90123a8d594e9bdaa5ddba8e2ac82569375c49cd5551dd3acffb751ed.jpg\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026gt;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven the side length of the square, find the radius of the circles.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":45334,"title":"Area-02","description":"Given the radius of the circle inscribed in a square, find the area of the square that can be fitted perfectly in the corner.\r\n\r\n\u003chttps://serving.photos.photobox.com/951462430971a9cfd5dff5f0f3e94dee75ee1bb89ddb5e3e47e18f79b04d3cd720c92cb2.jpg\u003e","description_html":"\u003cp\u003eGiven the radius of the circle inscribed in a square, find the area of the square that can be fitted perfectly in the corner.\u003c/p\u003e\u003cp\u003e\u003ca href = \"https://serving.photos.photobox.com/951462430971a9cfd5dff5f0f3e94dee75ee1bb89ddb5e3e47e18f79b04d3cd720c92cb2.jpg\"\u003ehttps://serving.photos.photobox.com/951462430971a9cfd5dff5f0f3e94dee75ee1bb89ddb5e3e47e18f79b04d3cd720c92cb2.jpg\u003c/a\u003e\u003c/p\u003e","function_template":"function y = inscribed_circle_2(r)\r\n y = x;\r\nend","test_suite":"%%\r\nr=1;\r\ny_correct = 0.0858;\r\nassert(abs(inscribed_circle_2(r)-y_correct)\u003c0.001)\r\n%%\r\nr=11;\r\ny_correct = 10.3802;\r\nassert(abs(inscribed_circle_2(r)-y_correct)\u003c0.001)\r\n%%\r\nr=45.98;\r\ny_correct = 181.3663;\r\nassert(abs(inscribed_circle_2(r)-y_correct)\u003c0.001)\r\n%%\r\nr=0;\r\ny_correct = 0;\r\nassert(abs(inscribed_circle_2(r)-y_correct)\u003c0.001)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":363598,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":42,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-02-16T18:38:38.000Z","updated_at":"2025-08-03T22:41:51.000Z","published_at":"2020-02-16T18:39:11.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven the radius of the circle inscribed in a square, find the area of the square that can be fitted perfectly in the corner.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://serving.photos.photobox.com/951462430971a9cfd5dff5f0f3e94dee75ee1bb89ddb5e3e47e18f79b04d3cd720c92cb2.jpg\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026lt;https://serving.photos.photobox.com/951462430971a9cfd5dff5f0f3e94dee75ee1bb89ddb5e3e47e18f79b04d3cd720c92cb2.jpg\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026gt;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":50504,"title":"Find the area between curves (P3)","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 541px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 270.5px; transform-origin: 407px 270.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20px; border-block-end-color: rgb(60, 60, 60); border-block-start-color: rgb(60, 60, 60); border-bottom-color: rgb(60, 60, 60); border-inline-end-color: rgb(60, 60, 60); border-inline-start-color: rgb(60, 60, 60); border-left-color: rgb(60, 60, 60); border-right-color: rgb(60, 60, 60); border-top-color: rgb(60, 60, 60); caret-color: rgb(60, 60, 60); color: rgb(60, 60, 60); column-rule-color: rgb(60, 60, 60); font-family: Helvetica, Arial, sans-serif; font-size: 20px; font-weight: 700; line-height: 20px; margin-block-end: 5px; margin-block-start: 3px; margin-bottom: 5px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 3px; outline-color: rgb(60, 60, 60); perspective-origin: 384px 10px; text-align: left; text-decoration: none; text-decoration-color: rgb(60, 60, 60); transform-origin: 384px 10px; white-space: pre-wrap; margin-left: 4px; margin-top: 3px; margin-bottom: 5px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eArea between curves - Problem 3\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFind the area enclosed by the curves \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"94.5\" height=\"19\" style=\"width: 94.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"62.5\" height=\"19\" style=\"width: 62.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e for different \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ea\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eb\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e coefficients\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 426px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 213px; text-align: left; transform-origin: 384px 213px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline\" 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width=\"87.5\" height=\"18\" style=\"width: 87.5px; height: 18px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = AreaCurves(a, b)\r\n \r\nend","test_suite":"%%\r\nfiletext = fileread('AreaCurves.m');\r\nfor ii = [0.4208, 0.5101, 0.2569, 0.1252, 1.1838]\r\n assert(isempty(strfind(filetext, num2str(ii))),'Do NOT use provided answers in your solution')\r\nend\r\nassert(isempty(strfind(filetext, 'if')),'if: Forbidden')\r\nassert(isempty(strfind(filetext, 'switch')),'switch: Forbidden')\r\n%%\r\na = 1; \r\nb = 0.5;\r\n\r\ny_correct = 0.4208;\r\nassert(abs(AreaCurves(a,b)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = 2; \r\nb = 0.5; \r\n\r\ny_correct = 0.5101;\r\nassert(abs(AreaCurves(a,b)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = exp(1); \r\nb = 1; \r\n\r\ny_correct = 0.2569;\r\nassert(abs(AreaCurves(a,b)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = 0.5;\r\nb = 0.4;\r\n\r\ny_correct = 0.1252;\r\nassert(abs(AreaCurves(a,b)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = sqrt(2);\r\nb = 0.1;\r\n\r\ny_correct = 1.1838;\r\nassert(abs(AreaCurves(a,b)-y_correct)\u003c1e-4)\r\n\r\n","published":true,"deleted":false,"likes_count":4,"comments_count":0,"created_by":487522,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":18,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-02-19T18:50:42.000Z","updated_at":"2026-02-05T14:11:12.000Z","published_at":"2021-02-19T18:51:35.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"heading\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eArea between curves - Problem 3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind the area enclosed by the curves \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ef(x) = sin(ax)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eg(x) = bx\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e for different \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e coefficients\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml 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w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eg(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea=1 , 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cow is tied to an outside corner of a rectangular barn of size (a,b) with a rope of length l. What is the maximum area the cow can graze outside the barn?\r\n\r\n\u003chttps://serving.photos.photobox.com/495639807b8e93bb90ab3c212fe921e51fefc77e0b8756d28871096f5482839b5e5d4bb8.jpg\u003e\r\n\r\nNb.the test cases are simpler for this problem. They'll be enhanced in the next case.","description_html":"\u003cp\u003eA cow is tied to an outside corner of a rectangular barn of size (a,b) with a rope of length l. What is the maximum area the cow can graze outside the barn?\u003c/p\u003e\u003cp\u003e\u003ca href = \"https://serving.photos.photobox.com/495639807b8e93bb90ab3c212fe921e51fefc77e0b8756d28871096f5482839b5e5d4bb8.jpg\"\u003ehttps://serving.photos.photobox.com/495639807b8e93bb90ab3c212fe921e51fefc77e0b8756d28871096f5482839b5e5d4bb8.jpg\u003c/a\u003e\u003c/p\u003e\u003cp\u003eNb.the test cases are simpler for this problem. They'll be enhanced in the next case.\u003c/p\u003e","function_template":"function y = grazing_01(a,b,l)\r\n y = x;\r\nend","test_suite":"%%\r\nassert(abs(grazing_01(10,20,5)-58.9049)\u003c0.001)\r\n%%\r\nassert(abs(grazing_01(5,25,2)-9.4248)\u003c0.001)\r\n%%\r\nassert(abs(grazing_01(5,25,8)-157.8650)\u003c0.001)\r\n%%\r\nassert(abs(grazing_01(20,20,20)- 942.4778)\u003c0.001)\r\n%%\r\nassert(abs(grazing_01(10,20,0)-0)\u003c0.001)\r\n%%\r\nassert(abs(grazing_01(12,20,25)-1624.9888)\u003c0.001)\r\n\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":3,"created_by":363598,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":19,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-02-20T10:45:47.000Z","updated_at":"2026-01-29T12:35:16.000Z","published_at":"2020-02-20T11:20:35.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA cow is tied to an outside corner of a rectangular barn of size (a,b) with a rope of length l. What is the maximum area the cow can graze outside the barn?\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://serving.photos.photobox.com/495639807b8e93bb90ab3c212fe921e51fefc77e0b8756d28871096f5482839b5e5d4bb8.jpg\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026lt;https://serving.photos.photobox.com/495639807b8e93bb90ab3c212fe921e51fefc77e0b8756d28871096f5482839b5e5d4bb8.jpg\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026gt;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNb.the test cases are simpler for this problem. They'll be enhanced in the next case.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":61076,"title":"Covering rectangle area of a four-pointed star polygon","description":"Given the four-pointed star polygon formed by the rectangle, with dimensions l1xl2, and four triangles, with height, h, from their bases to the apices, find the rectangle, with dimensions y1xy2, such that has the same area of the given star polygon, and covers the given rectangle (cf. figure below). Given x=[l1 l2 h], return y=[y1 y2].\r\n\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 520.8px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 260.4px; transform-origin: 408px 260.4px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 31.5px; text-align: left; transform-origin: 385px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven the four-pointed star polygon formed by the rectangle, with dimensions \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003el1xl2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and four triangles, with height, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eh,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e from their bases to the apices, find the rectangle, with dimensions \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ey1xy2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, such that has the same area of the given star polygon, and covers the given rectangle (cf. figure below). Given \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ex=[l1 l2 h]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, return \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ey=[y1 y2]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 418.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 209.4px; text-align: left; transform-origin: 385px 209.4px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline\" 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wGJi+U4e9aLPsAPAYmL5Th7Fos+wA8CSYjbyqBR9hh0AFhabkUel6DPsALCw2Iw8ykSfYQeA5cVg5FEj+gw7AGzC7JFHjegz7ACwCbNHHgWiz7ADwFZMHXlkjz7DDgAbMm/kkT36DDsAbMi8kUfq6DPsALAtk0YeeaPPsAPA5swYeeSNPsMOAJszY+SRNPoMOwCgmTDyyBh9hh0A6GDsyCNj9Bl2AKCDsSOPdNFn2AGA0xg48sgVfYYdAOiWUSOPXNFn2AGAbhk18kgUfYYdAOiBISOPLNFn2AGAoKIfeWSJPsMOAAQV/cgjRfQZdgAgRFGOPOKjz7ADAGGJZuQRH32GHQAISzQjj+DoM+wAQAQiHnlERp9hBwAiFtnIIzL6paWle/fuZdgBgAg0NzcfOHCguLg4rM8SGf2ioqILL7zQ4XAIvAEAFOVwOC644IKioqKwPkvwpr906dKMjAyxNwCAchITEzMyMpYuXRruJwqOvtvtvuKKK+g+AIQlPT19xowZbrc73E8U/5bN9evXDxs2jJEHAELkcDiGDRu2bNmyCD5XfPQ1Rh4ACFnEw45Oiugz8gBAiCIednRSRF9j5AGAEEQz7Ohkib7GyAMAPYpy2NFJFH1GHgDoQZTDjk6i6GuMPABwBtEPOzq5oq8x8gBAF4YMOzrpos/IAwCnMWTY0UkXfY2RBwA6MWrY0ckYfY2RBwA0TTN02NFJGn1GHgDQDB12dJJGX2PkAWB7xg47OnmjrzHyALAxw4cdndTRZ+QBYFuGDzs6qaOvMfIAsCUzhh2d7NHXGHkA2IxJw45Ogegz8gCwFZOGHZ0C0dcYeQDYhnnDjk6N6GuMPABswNRhR6dM9Bl5AFieqcOOTpnoa4w8ACzN7GFHp1L0NUYeABYVg2FHp1j0GXkAWFIMhh2dYtHXGHkAWE5shh2detHXGHkAWEjMhh1deNHfuXPn2LFjN2/ebNI1IWLkAWAZMRt2dGFEv6GhYcmSJfX19eZdEzpGHgAWEMthRxdq9D0ez1133fXJJ5+Yek1YGHkAKC3Gw44uePRPnTr1/vvv5+Xl7d27NycnJwY3hYiRB4DSYjzs6IJHf9euXY8//nhCQsKqVatuuOGGGNwUOkYeAIqK/bCjCx79hISE22+/vaysbPz48TE4KFyMPACUI2TY+emHDvoROTk5Uq06p9FHnn/84x91dXWibwGAkAgZdnTBox8Zj8dTXFzc8U2Xy2XeT2/9+vUTJkzw+XzNzc0m/RAAYBRRw47OrC/O8nq9nb/pdDpN+oF0jDwAlCBw2PnpAJO+X5fLVVRUZNJ33hUjDwAlCBx2dEr+Zxi6xTt5AEhO7LCjs070NUYeABITPuzoLBV9vlwLgLSEDzs6S0VfY+QBICUZhh2d1aKvMfIAkIwkw44uvOjPmTNn//79kyZNMukaQzDyAJCKJMOOzoJP+hojDwBpyDPs6KwZfY2RB4AEpBp2dJaNPiMPAOGkGnZ0lo2+xsgDQCjZhh2dlaOvMfIAEETCYUdn8egz8gAQQsJhR2fx6GuMPABiTs5hR2f96GuMPABiSNphR2eL6DPyAIgZaYcdnS2irzHyAIgJmYcdnV2irzHyADCZ5MOOzkbRZ+QBYCrJhx2djaKv/d/Ik5KSIvoQAFaTkpIi+bCjs1f0NU1bunRpamqq6CsAWE1qaqrkw47OdtF3u90ul0v0FQCsJj8/X/JhR2e76GuadvPNN4s+AYDVKFF8zZ7RBwDbIvoAYCNEHwBsxO7RT0xMEn0CACXFx8fHxyeIviJsdo++pmm9e/cRfQIA9TgcKfHx6iVUvYuN5XRmDhgwIDExUfQhAFSSmJg4YMAApzNT9CFhs3v0NU2bPHkyD/sAQhcfH9+7d5/JkyeLPiQSRF9zOjPPP38w3QcQIocjZcSIn6v4mK8RfV1+fj4jD4BQ6MOOoo/5GtHvwMgDICilhx0d0f8JIw+AoJQednRE/78YeQD0QPVhR0f0/wcjD4BuWWDY0RH9/8HIA6BbFhh2dET/dIw8AE5jjWFHR/S7wcgDoINlhh0d0e8GIw+ADpYZdnREv3uMPAA0aw07OqJ/Row8gM1ZbNjREf0zYuQBbM5iw46O6PeEkQewLesNOzqiHwQjD2BDlhx2dEQ/CEYewIYsOezoiH5wjDyArVh12NER/ZAw8gA2YeFhR0f0Q8LIA9iEhYcdHdEPFSMPYHnWHnZ0RD8MjDyAhVl+2NER/TAw8gAWZvlhR0f0w8PIA1iSHYYdHdEPGyMPYDE2GXZ0RD9sjDyAxdhk2NER/Ugw8gCWYZ9hR0f0I8TIA1iArYYdHdGPECMPYAG2GnZ0RD9yjDyA0uw27OiIflQYeQBF2XDY0RH9qDDyAIqy4bCjI/rRYuQBlGPPYUdH9A3AyAMoxLbDjo7oG4CRB1CIbYcdHdE3BiMPoAQ7Dzs6om8YRh5AcjYfdnQhRd/r9RYWFg4bNiw7Ozs3N/fPf/5za2ur2Zcph5EHkJzNhx1d8Ojv2rVr2rRpH3744aWXXjpt2rRAILB48eJFixbR/a4YeQBpMezogkS/tbX15ZdfPn78+AsvvLBu3brly5eXlZXl5uZu2LChsrIyNieqhZEHkBDDTocg0d+/f39lZaXb7b766qv1V9LS0oqKipKTk99///329nbTD1QNIw8gIYadDkGi/+WXX9bX119++eUpKSkdL2ZlZTmdzi+++KKhocHk85TEyANIhWGnsyDRP3z4sKZpw4YN6/xicnLyWWeddfz4cb/fb+JpKmPkASTBsHOaINH/5ptvur7Yp0+fgQMH+v3+48ePm3OV8vSRx+FwiD4EsLvk5GSGnc6CTBDdvkUnLi4uPj7Ivy08Hk9xcXHHN10ul9vtjuA+deXn57/22v/zBAKaIyX4RwMwgScxUdO0zEyn6EMkEiT6SUlJXV9sb29va2vr+RO9Xm/nbzqddvybPnny5LKyssrGxra2tpaWFtHnADaSnJwcHx/ft29fd87wnJzhos+RSJDo/+xnP+v64okTJw4fPpyamtqvX78zfaLL5SoqKor2OsU5nZl33vlrj8dbVlb2ww8/NDc3kX7AbMnJycnJvc466yyXy0Xuuwop+nv37p00aVLHiy0tLT/88EO/fv1SU1PNvc4SSD8QG3ru+/fvT+57ECT6F1544YABAyorK++4446Od23u27fvwIED119/fXp6uvkXWgTpB8xD7kMXJPpOp3P06NHl5eWbN2++4YYb4uLifD5fSUlJW1vbTTfdFBcXF5srLYP0A8Yi9+EKEv2UlJR77713+/btv/3tb9evXz9o0KCKioojR44UFBTY7d04BiL9QPTIfWSCf9Xo6NGj33777T/84Q8VFRWVlZWDBg1avHjxzJkzu31jD0JH+oHIkPtohPSfCsjKynrllVfMPsWeSD8QOnIfPf77MFIg/UDPyL1RiL5ESD/QFbk3FtGXDukHdOTeDERfUqQfdkbuzUP0pUb6YTfk3mxEXwGkH3ZA7mOD6CuD9MOqyH0sEX3FkH5YCbmPPaKvJNIP1ZF7UYi+wkg/VETuxSL6yiP9UAW5lwHRtwjSD5mRe3kQfUsh/ZANuZcN0bcg0g8ZkHs5EX3LIv0QhdzLjOhbHOlHLJF7+RF9WyD9MBu5VwXRtxHSDzOQe7UQfdsh/TAKuVcR0bcp0o9okHt1EX1bI/0IF7lXHdEH6UdIyL01EH38hPTjTMi9ldg9+gd3f/bXP/5W9BVyGaBpyY2NjY2+tra2trZTos+BeImJSZqmDYjP3PfR5/s+En2NTHz134s+IWx2j76maQd3fyb6BBnFa1q86BsgixZN07SDu4+KvgMG4H/XAGCAzMxM0SeExI7Rz8/Pd7lcoq8AYB1Op9Ptdou+IiQ2nXeWLVtWVVUl+gr1eDye0tJSj8fT3Nzs8/lEnwPDpKWlORwOp9NZVFQk+hYl5efniz4hVDaNvtPpdDqdoq9QUlFRUWVl5UMPPXTgwIGGhga/3y/6IkQlNTU1LS3twgsvLCoqUqhciJhNo49ouN3u8vJy0q86cm9PRB8RIv3qIvd2RvQRFdKvFnIPog8DkH75kXvoiD4MQ/rlRO7RGdGHwUi/PMg9uiL6MAXpF4vc40yIPkxE+mOP3KNnRB+mI/2xQe4RCqKPGCH95iH3CB3RR0yRfmORe4SL6EMA0h89co/IEH0IQ/ojQ+4RDaIPwUh/6Mg9okf0IQXS3zNyD6MQfUiE9HdF7mEsog/pkH4duYcZiD4kZef0k3uYh+hDanZLP7mH2Yg+FGCH9JN7xAbRhzKsmn5yj1gi+lCMldJP7hF7RB9KUj395B6iEH0oTMX0k3uIRfShPFXST+4hA6IPi5A5/eQe8iD6sBTZ0k/uIRuiDwuSIf3kHnIi+rAsUekn95AZ0YfFxTL95B7yiw/ro3fu3Dl27NjNmzebdA1gEj39b7/99pgxYwYPHpyammrs95+amnreeeeNGTOmpKSkvLyc4kNaYTzpNzQ0LFmypL6+3rxrAFOZ8dTP0z3UEmr0PR5PYWHhZ599ZuCP7fF4NE1zOp0Gfp9S4ScoJ6PSb4HcK/pPMHT8BLsKPu+cOnXq/fffz8vL27t3b05OTuTXdVFaWlpaWmrgdygbfoIyi2bwscyYo/Q/wVDwE+wq+JP+rl27Hn/8cYfDsWrVqs8//3zXrl2RngdIJ9ynfgs83cPmgj/pJyQk3H777WVlZePHj4/BQUDshfLUb5mne9hc8Cf9nJwcY1cdQE5neurn6R5WYtb79D0eT3Fxcc8fU1lZadKPLgl+gorKz8+vrKysqqpKT08PBAIOh8PpdObn54fyq1otVv0n2IGfYAeXy+V2uzWTop+Zmal/7z0L5WOUxk9QXW6328I/uw6W/znyE+zQ8Q6fn6Lv9/tnz57d+V8abrd79erVkX0Ni03+BwMAygnvK3IBAEr76Uk/NTV13bp1Yk8BAJiNJ30AsBGiDwA2QvQBwEbi2tvbRd8AAIgRnvQBwEaIPgDYCNEHABuRJfp+v/+OO+6YP3++6EOMsXv37oKCgqFDhw4ZMmTKlCmbNm2y6u+dbN682eVy7dixQ/QhRmpvb6+urp4+ffrQoUOzs7PHjx+/ZMmSxsZG0XcZ5tSpUxs3bpwyZcqQIUOGDh06ffr06upqq/4S9fl8BQUFV1111ZEjR0TfYpg9e/aMGzcuu4uVK1cG/Vwpon/q1Kk33nijoqJC9CHG2Lx5c35+fk1NzcSJE6+77rrDhw/PnTt3zZo11vsf1ddff71kyZLm5mbRhxipvb19zZo1M2fO3LFjx8SJE6dNm9bW1rZq1aq5c+f6fD7R1xkgEAg89dRT999//+HDh6+77rqpU6fW1tbOnDnTkr9E29vbV69eXV1dLfoQg3k8nvr6+n79+jn/V1paWvBPbhft5MmTTz/9dHZ2dlZW1oMPPij6nGgdO3YsLy/v8ssv3759u/6Kx+OZNGnSuHHjamtrxd5mrJqamiuvvDIrK+uSSy75/PPPRZ9jmNra2nHjxk2aNGn//v36KydPnly4cGFWVtYf//hHsbcZ4tNPPx05cuSMGTOOHTumv6L/Es3Nzf3222/F3ma48vLyiy++OCsra8KECd9//73ocwzzyiuvZGdnb9myJYLPFfykv3v37ltvvfXVV18dPny4w+EQe4wh9D9c7Prrrx81apT+SmZm5v3333/06NEtW7aIvc0oTU1Nq1evvu2223788cesrCzR5xjsn//8Z11d3a9+9auOn1pKSspdd901YMCA6urq6P8gdeG++uorh8NRUFCQnp6uv5KZmXnttdd6vd7a2lqxtxmrrq7u2WefHT58+M9//nPRtxjsyy+/POuss84999wIPldk9P1+/+LFi3fu3Dlv3rwnn3wyKSlJ4DFG2bZtW2trq8vliouL63hx2LBhZ5999qeffvrjjz8KvM0on3zyyXPPPZeZmbl27doxY8aIPsdghw8fHjBgwPDhwzu/2KdPn169eok6yVizZs2qrq7Oy8vreCUQCBw4cMDhcPTr10/gYcYKBALFxcV1dXWPPPJISKOHOvx+v8fjOffccwcOHBjBpwt+0h8xYsTGjRvnzp2bnJws9hKjHD58OC0t7bQ/nL5fv34pKSn19fXWmL8dDsfChQv/8pe/DB06VPQtxvvd735XXV09duzYzi/+5z//F6EmRwAABQRJREFUOXjwYGZmZp8+fUQdZpK6urqnnnrqo48+mjhx4ogRI0SfY5iysrINGzbMnj3ben/wX2Njo9frTUtLKykpGTt2bHZ29tixY0N/r4FZf3JWKFJTUx999FGBBxjuxIkT3b5DoHfv3uedd96hQ4es8aSfm5ubm5sr+orY8Xq9L7zwQp8+fW6++ebO/wdOdUeOHJk+ffp3332nadq0adMWL16ckpIi+ihjeL3e559/Pjc397bbbjt16pTocwzm9Xrr6+u9Xu/+/fvdbnevXr0qKipWrVq1devWNWvWZGZm9vzpUrx7xzLa29sDgUC3fyk+nr/VSqqrq3vwwQf3798/d+7ccePGiT7HSD/88MPYsWOnTZt2zjnnbNiw4e677z548KDoowzQ2tq6YsWKxsbG+fPnW+ZfY50dP368V69eM2bMKC8vLykpWb58+ccffzxjxoyvvvrqxRdfPFOCOoh80reeuLi4xMTu/5a2tbXF+BhE7+uvv77vvvtqa2sLCwvvvPNOKz3ma5p20UUXLV++XNO01tbWRYsWvfnmmyUlJU899dSZfg2r4sMPP9ywYcPjjz9+0UUXib7FFJMmTdq+fXvnV1JSUu69996KioqKioojR44MGjSoh0+PxePnypUrO3/5wKhRoyz2tTwd+vTpc84553R9/eTJk4cOHerfv79lfjPQDv71r38VFBTs379/0aJFRUVF1nijQbeSkpLmzJlz3nnnVVdXNzQ0iD4nKvrXjkyePPmWW24RfUtMpaenDx48uLGxsb6+vuePVPtf6RK64IILfD7f999/P3LkyI4Xjx8/3tTUdPbZZ1vjbamW197eXlpa+thjj/Xq1evFF1/8xS9+YbFn/K769+8/ePDgQ4cOtSv+9Vn79u07ePDgwYMHN27ceNpfcrvdgwcPfuedd7p9MlOLz+dzOBxdH0QSExMTEhJ6/txYRH/OnDlz5syJwQ8kg9GjRyclJVVUVHQuxRdffHH06NHLL7+cJ30lfPjhh4899tg555zz0ksvWekNLZqmtbS0PPHEE1u2bFmxYkXndyh5vd59+/Y5nU7Vf4kOHDiwoKCg8yutra3l5eVNTU2TJk0699xzVX/wCgQCDzzwwKZNm1atWjVp0qSO171e7549e0J5HydP+ga7+OKLhwwZsnHjxhtvvPGyyy7TNM3r9a5YsSIjI+Oaa64RfR2Cq6mpeeKJJwYPHrx69WrrfelZcnLyyJEj33nnnZKSkhUrVuhvYPf5fM8//3x9ff3dd9+t+lv1R4wY8cwzz3R+xe/3z5492+v1Lly40ALP+ImJiddee+2mTZtef/31yy67TP8Ku4aGhqeffvrYsWOzZ8/u379/kO8hJnfaSEZGRmFh4bx582bNmjVhwoRevXpt3br1xIkTDz/8sCXf1W4xgUDgtdde07+i4o477jjtr44ePfrZZ59V/a36N91007///e8PPvjgmmuucbvdmqZt3brV7/dfd911s2bNEn0dgps6deqMGTPefPPNq6666qqrrtL+759gXl7ezJkzg3460TfeL3/5ywEDBixduvTjjz9ua2sbMmTIvHnzpk6davld2AKOHTtWU1OjadqJEydOnDhx2l91Op2qT96apqWlpS1btuzKK69cuXLlBx98oGnakCFDfvOb39xwww0W/s1qK0lKSnryySfHjh378ssvR/BPkD8uEQBshK8YAgAb+f/ypVejSmIHqAAAAABJRU5ErkJggg==\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = covering(x)\r\n y = x;\r\nend","test_suite":"%%\r\nx = [2 7 4];\r\ny_correct = [5 10];\r\nassert(isequal(covering(x),y_correct))\r\n\r\n%%\r\nx = [7 2 1];\r\ny_correct = [2.5 -2.5] + 1.5*sqrt(13);\r\ntolerance = 1e-12;\r\nassert(all(abs(covering(x)-y_correct)\u003ctolerance))\r\n\r\n%%\r\nx = [5 2 1];\r\ny_correct = [3 -3]/2 + sqrt(77)/2;\r\ntolerance = 1e-12;\r\nassert(all(abs(covering(x)-y_correct)\u003ctolerance))\r\n\r\n%%\r\nfiletext = fileread('covering.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\nx = [7 9 5];\r\ny_correct = [11 13];\r\nassert(isequal(covering(x),y_correct))\r\n\r\n%%\r\nx = [7 9 1];\r\ny_correct = [-1 1] + 4*sqrt(5);\r\ntolerance = 1e-12;\r\nassert(all(abs(covering(x)-y_correct)\u003ctolerance))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":1,"created_by":4993982,"edited_by":4993982,"edited_at":"2025-11-16T14:03:25.000Z","deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-11-15T16:57:30.000Z","updated_at":"2026-03-27T12:50:09.000Z","published_at":"2025-11-16T14:03:25.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven the four-pointed star polygon formed by the rectangle, with dimensions \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003el1xl2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, and four triangles, with height, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eh,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e from their bases to the apices, find the rectangle, with dimensions \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey1xy2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, such that has the same area of the given star polygon, and covers the given rectangle (cf. figure below). Given \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex=[l1 l2 h]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, return \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey=[y1 y2]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"413\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"508\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc 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- 01","description":"Find the area of a five-pointed star inscribed in a circle of radius r.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 21px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 10.5px; transform-origin: 407px 10.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 207.5px 8px; transform-origin: 207.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFind the area of a five-pointed star inscribed in a circle of radius r.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y =yoonir_02(r)","test_suite":"%%\r\nassert(abs(yoonir_02(10)-112.257)\u003c0.001)\r\n\r\n%%\r\nassert(abs(yoonir_02(3)-10.1031)\u003c0.001)\r\n\r\n%%\r\nassert(abs(yoonir_02(pi)-11.0793)\u003c0.001)\r\n\r\n%%\r\nassert(abs(yoonir_02(pi^5)-105126.4832)\u003c0.001)\r\n\r\n%%\r\nassert(abs(yoonir_02(1)-1.1226)\u003c0.001)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":363598,"edited_by":223089,"edited_at":"2023-01-14T09:16:04.000Z","deleted_by":null,"deleted_at":null,"solvers_count":24,"test_suite_updated_at":"2023-01-14T09:16:04.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2020-03-31T00:21:25.000Z","updated_at":"2026-01-03T15:34:12.000Z","published_at":"2020-03-31T00:21:25.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind the area of a five-pointed star inscribed in a circle of radius r.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":2239,"title":"Avalaible area: wall construction","description":"You need to build a wall to enclose a certain area. Calculate the available area after you build the wall. \r\n\r\nAssumptions\r\n\r\n* Wall could consist of multiple layers of material. example: a wall of 2 materials: rock of 1 meter thickness and wood of 0.5 meter thickness. The total thickness of the wall 1.5 meters.\r\n* x and y: the dimensions of the area before the wall is build. example: x=5m,y=4m. Total area 20m^2.\r\n\r\nExample\r\n\r\nArea of dimensions x=5m,y=5m and wall of 3 materials with thicknesses: 0.2m,0.1m,1m . Avalaible area after the wall is build : 5.76m^2\r\n\r\n \u003e\u003e AvailableArea(5,5,0.2,0.1,1) \r\n \u003e\u003e ans=5.76\r\n","description_html":"\u003cp\u003eYou need to build a wall to enclose a certain area. Calculate the available area after you build the wall.\u003c/p\u003e\u003cp\u003eAssumptions\u003c/p\u003e\u003cul\u003e\u003cli\u003eWall could consist of multiple layers of material. example: a wall of 2 materials: rock of 1 meter thickness and wood of 0.5 meter thickness. The total thickness of the wall 1.5 meters.\u003c/li\u003e\u003cli\u003ex and y: the dimensions of the area before the wall is build. example: x=5m,y=4m. Total area 20m^2.\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eExample\u003c/p\u003e\u003cp\u003eArea of dimensions x=5m,y=5m and wall of 3 materials with thicknesses: 0.2m,0.1m,1m . Avalaible area after the wall is build : 5.76m^2\u003c/p\u003e\u003cpre\u003e \u0026gt;\u0026gt; AvailableArea(5,5,0.2,0.1,1) \r\n \u0026gt;\u0026gt; ans=5.76\u003c/pre\u003e","function_template":"function A = AvailableArea(x,y,varargin)\r\n %A=..\r\nend","test_suite":"%%\r\ny_correct = 64;\r\nassert(isequal(AvailableArea(10,10,1),y_correct))\r\n\r\n%%\r\n\r\ny_correct = 3844;\r\nassert(isequal(AvailableArea(70,70,1,2,1),y_correct))\r\n\r\n%%\r\n\r\ny_correct = 49;\r\nassert(isequal(AvailableArea(9,9,1),y_correct))\r\n\r\n%%\r\n\r\ny_correct = 3900;\r\nassert(isequal(AvailableArea(75,70,1,3,1),y_correct))\r\n\r\n\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":24008,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":72,"test_suite_updated_at":"2014-03-10T20:27:07.000Z","rescore_all_solutions":false,"group_id":26,"created_at":"2014-03-08T16:23:45.000Z","updated_at":"2026-02-19T10:38:26.000Z","published_at":"2014-03-08T16:24:08.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou need to build a wall to enclose a certain area. Calculate the available area after you build the wall.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAssumptions\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWall could consist of multiple layers of material. example: a wall of 2 materials: rock of 1 meter thickness and wood of 0.5 meter thickness. The total thickness of the wall 1.5 meters.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ex and y: the dimensions of the area before the wall is build. example: x=5m,y=4m. Total area 20m^2.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eArea of dimensions x=5m,y=5m and wall of 3 materials with thicknesses: 0.2m,0.1m,1m . Avalaible area after the wall is build : 5.76m^2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ \u003e\u003e AvailableArea(5,5,0.2,0.1,1) \\n \u003e\u003e ans=5.76]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":49072,"title":"Area Conversion 2","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 21px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 332px 10.5px; transform-origin: 332px 10.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 309px 10.5px; text-align: left; transform-origin: 309px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eGiven an area in hectares, convert it to acres.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = convert_stuff(x)\r\n y = x*713*pi;\r\nend","test_suite":"%%\r\nx = 121;\r\ny_correct = 299.0031;\r\nassert(isequal(convert_stuff(x),y_correct))\r\n%%\r\nx = 333;\r\ny_correct = 822.8763;\r\nassert(isequal(convert_stuff(x),y_correct))\r\n%%\r\nx = 1.2;\r\ny_correct = 2.9653;\r\nassert(isequal(convert_stuff(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":6,"comments_count":2,"created_by":180632,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":834,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-12-22T21:57:51.000Z","updated_at":"2026-04-13T04:10:57.000Z","published_at":"2020-12-22T21:57:51.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven an area in hectares, convert it to acres.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":43029,"title":"Area of polygon","description":"Given the vertices in vectors X,Y, return the area of the polygon they define.","description_html":"\u003cp\u003eGiven the vertices in vectors X,Y, return the area of the polygon they define.\u003c/p\u003e","function_template":"function A = polygon_area(x,y)\r\n A = x+y;\r\nend","test_suite":"%%\r\nL=linspace(0,2.*pi,9);\r\nx = 1.2*cos(L)';\r\ny = 1.2*sin(L)';\r\na_correct = 4.072935;\r\nassert( abs(polygon_area(x,y)-a_correct) \u003c 1e-04 )\r\n%%\r\nx = (1:10)';\r\ny = [0,ones(1,9)]';\r\na_correct = 4;\r\nassert( isequal(polygon_area(x,y),a_correct) )\r\n%%\r\nx=[0,5,3]';\r\ny=[0,0,9]';\r\na_correct = 22.5;\r\nassert( abs(polygon_area(x,y)-a_correct) \u003c 1e-04 )\r\n%%\r\nx=[0,5,3,11]';\r\ny=[0,0,9,126]';\r\na_correct = 162;\r\nassert( isequal(polygon_area(x,y),a_correct) )","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":85738,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":45,"test_suite_updated_at":"2016-10-05T06:02:53.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2016-10-05T05:00:48.000Z","updated_at":"2025-10-28T03:21:32.000Z","published_at":"2016-10-05T06:02:53.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven the vertices in vectors X,Y, return the area of the polygon they define.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":61088,"title":"Covering a four-pointed star polygon by circles","description":"Given the area, A, of a star polygon formed by the rectangle, with dimensions L×2L, and four triangles, with height h from their bases to the vertices, consider the circles that cover the distances between opposite vertices (cf. figure below).\r\nGiven (A,h), return the 2x2 matrix M = [A1/π a1; A2/π a2], where\r\nin the first row (i=1), A1 stands for the area of the circle that covers the minimum distance (cf. left figure), and a1 stands for the logical 1 if A1 is smaller than or reaches the area A or a1 stands for the logical 0 if A1 surpasses A;\r\nin the second row (i=2), A2 stands for the area of the circle that covers the maximum distance (cf. right figure), and a2 has the same previous false-true meaning relative to the areas A2 and A. Obviously, that A2 \u003e A holds true, then a2 = 0.\r\ninput: (A, h)\r\noutput: M = [A1/π a1; A2/π 0]\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 748.987px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 408px 374.487px; transform-origin: 408px 374.494px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven the area, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, of a star polygon formed by the rectangle, with dimensions \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eL\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e×\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e2L\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and four triangles, with height \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eh\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e from their bases to the vertices, consider the circles that cover the distances between opposite vertices (cf. figure below).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(A,h)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, return the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ex\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e matrix \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eM = [A1/π a1; A2/π a2]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, where\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 102.188px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 51.0875px; transform-origin: 391px 51.0938px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 40.875px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 20.4375px; text-align: left; transform-origin: 363px 20.4375px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ein the first row \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(i=1)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e stands for the area of the circle that covers the minimum distance (cf. left figure), and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ea1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e stands for the logical \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e if \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is smaller than or reaches the area \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e or \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ea1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e stands for the logical \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e0\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e if \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e surpasses \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 61.3125px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 30.65px; text-align: left; transform-origin: 363px 30.6562px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ein the second row \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(i=2)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e stands for the area of the circle that covers the maximum distance (cf. right figure), and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ea2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e has the same previous false-true meaning relative to the areas \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Obviously, that A2 \u0026gt; A holds true, then \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ea2 = 0\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003einput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(A, h)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eoutput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eM = [A1/π a1; A2/π 0]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 484.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 242.4px; text-align: left; transform-origin: 384px 242.4px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cimg class=\"imageNode\" width=\"601\" height=\"479\" style=\"vertical-align: baseline;width: 601px;height: 479px\" 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\" alt=\"Covering by circles\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function M = covering_by_circles(A,h)\r\n M = x;\r\nend","test_suite":"%%\r\nA = 27;\r\nh = 1;\r\nM_correct = [6.25 1; 16 0];\r\nassert(isequal(covering_by_circles(A,h),M_correct))\r\n\r\n%%\r\nA = 36;\r\nh = 2;\r\nM_correct = [12.25 0; 25 0];\r\nassert(isequal(covering_by_circles(A,h),M_correct))\r\n\r\n%%\r\nA = 56;\r\nh = 2;\r\nM_correct = [16 1; 36 0];\r\nassert(isequal(covering_by_circles(A,h),M_correct))\r\n\r\n%%\r\nfiletext = fileread('covering_by_circles.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\nA = 68;\r\nh = 1.2;\r\nM_correct = [13.69 1; 38.44 0];\r\nassert(all(isapprox(covering_by_circles(A,h),M_correct), 'all'))\r\n\r\n%%\r\nA = 89;\r\nh = 2.6;\r\nM_correct = [26.01 1; 57.76 0];\r\nassert(all(isapprox(covering_by_circles(A,h),M_correct), 'all'))","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":4993982,"edited_by":4993982,"edited_at":"2025-11-30T13:14:56.000Z","deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-11-29T14:26:03.000Z","updated_at":"2026-03-22T14:02:11.000Z","published_at":"2025-11-30T13:14:56.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven the area, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, of a star polygon formed by the rectangle, with dimensions \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eL\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e×\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2L\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, and four triangles, with height \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e from their bases to the vertices, consider the circles that cover the distances between opposite vertices (cf. figure below).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(A,h)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, return the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e matrix \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eM = [A1/π a1; A2/π a2]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, where\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ein the first row \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(i=1)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e stands for the area of the circle that covers the minimum distance (cf. left figure), and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e stands for the logical \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e if \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is smaller than or reaches the area \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e or \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e stands for the logical \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e0\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e if \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e surpasses \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ein the second row \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(i=2)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e stands for the area of the circle that covers the maximum distance (cf. right figure), and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e has the same previous false-true meaning relative to the areas \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. Obviously, that A2 \u0026gt; A holds true, then \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea2 = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003einput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(A, h)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":45271,"title":"Calculate triangle area","description":"Imagine that you want to calculate the areas of some triangles given in matrix form. First the coordinates of the vertices of the triangles are in a matrix called coords where the line number represents the vertex number and the column number is the dimension, in this case it is equal to 2 (x, y). The way the nodes connect are found in the lnods matrix where the line number is the triangle number and the column number is the vertex number that makes up each triangle (v_i, v_j, v_k).","description_html":"\u003cp\u003eImagine that you want to calculate the areas of some triangles given in matrix form. First the coordinates of the vertices of the triangles are in a matrix called coords where the line number represents the vertex number and the column number is the dimension, in this case it is equal to 2 (x, y). The way the nodes connect are found in the lnods matrix where the line number is the triangle number and the column number is the vertex number that makes up each triangle (v_i, v_j, v_k).\u003c/p\u003e","function_template":"function y =areas(coords,lnods)\r\n y = ?;\r\nend","test_suite":"%%\r\ncoords=[0 0;1 0; 1 1; 0 1];\r\nlnods=[ 1 2 4; 2 3 4];\r\ny_correct = [0.500;0.500];\r\nassert(isequal(areas(coords,lnods),y_correct))\r\n%%\r\ncoords=[0 0;1 0; 1 1; 0 1; 0.5 0.5];\r\nlnods=[ 1 2 5; 2 3 5;3 4 5;4 1 5];\r\ny_correct = [0.2500;0.2500;0.2500;0.2500];\r\nassert(isequal(areas(coords,lnods),y_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":396229,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":18,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-01-19T02:12:33.000Z","updated_at":"2026-03-14T18:54:18.000Z","published_at":"2020-01-19T02:17:46.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eImagine that you want to calculate the areas of some triangles given in matrix form. First the coordinates of the vertices of the triangles are in a matrix called coords where the line number represents the vertex number and the column number is the dimension, in this case it is equal to 2 (x, y). The way the nodes connect are found in the lnods matrix where the line number is the triangle number and the column number is the vertex number that makes up each triangle (v_i, v_j, v_k).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":45407,"title":"Yoonir - 02","description":"Find the area of a six-pointed star inscribed in a circle of radius r.","description_html":"\u003cp\u003eFind the area of a six-pointed star inscribed in a circle of radius r.\u003c/p\u003e","function_template":"function y =yoonir_04(r)","test_suite":"%%\r\nassert(abs(yoonir_04(10)-173.2050)\u003c0.001)\r\n\t\r\n%%\r\nassert(abs(yoonir_04(20)-692.8203)\u003c0.001)\r\n\t\r\n%%\r\nassert(abs(yoonir_04(pi)-17.0946)\u003c0.001)\r\n\t\r\n%%\r\nassert(abs(yoonir_04(pi^4)-16434.6178)\u003c0.001)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":5,"created_by":363598,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":19,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-03-31T00:59:00.000Z","updated_at":"2026-01-29T14:02:37.000Z","published_at":"2020-03-31T00:59:00.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind the area of a six-pointed star inscribed in a circle of radius r.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":60999,"title":"Total Area Covered by Overlapping Polygons","description":"Given a variable length set of polygon vertex coordinates, compute the total area covered. For example, take two polygons with the following vertex coordinates:\r\np1=[0.2,0.2; 0.5,0.2; 0.5,0.5; 0.2,0.5];\r\np2=[0.4,0.4; 0.8,0.4; 0.8,0.8; 0.4,0.8];\r\n\r\nThe total area covered is the area of the first polygon plus the area of the second polygon minus the overlap. This comes out to 0.24 units.\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 617.571px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407.997px 308.778px; transform-origin: 407.997px 308.785px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42.017px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 21.0085px; text-align: left; transform-origin: 385px 21.0085px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven a variable length set of polygon vertex coordinates, compute the total area covered. For example, take two polygons with the following vertex coordinates:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0085px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.4972px; text-align: left; transform-origin: 385px 10.5043px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ep1=[0.2,0.2; 0.5,0.2; 0.5,0.5; 0.2,0.5];\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0085px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.4972px; text-align: left; transform-origin: 385px 10.5043px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ep2=[0.4,0.4; 0.8,0.4; 0.8,0.8; 0.4,0.8];\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 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\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42.017px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 21.0085px; text-align: left; transform-origin: 385px 21.0085px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe total area covered is the area of the first polygon plus the area of the second polygon minus the overlap. This comes out to 0.24 units.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0085px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.4972px; text-align: left; transform-origin: 385px 10.5043px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function A = lapgon(P)\r\n A=[];\r\nend","test_suite":"%% Test Case 1\r\nP{1}=[0.2,0.2;0.5,0.2;0.5,0.5;0.2,0.5];\r\nP{2}=[0.4,0.4;0.8,0.4;0.8,0.8;0.4,0.8];\r\n\r\nA=round(lapgon(P),6);\r\nA_correct=0.240000;\r\n\r\nassert(isequal(A,A_correct))\r\n\r\n%% Test Case 2\r\nP{1}=[0.1783,0.2985;0.3849,0.6214;0.8407,0.8054];\r\nP{2}=[0.1112,0.8761;0.8927,0.4062;0.6089,0.0228];\r\n\r\nA=round(lapgon(P),6);\r\nA_correct=0.244813;\r\n\r\nassert(isequal(A,A_correct))\r\n\r\n%% Test Case 3\r\nP{1}=[0.5967,0.2763;0.3286,0.2200;0.7586,0.4690];\r\nP{2}=[0.4809,0.5456;0.5589,0.2875;0.5021,0.3001;0.2000,0.7725];\r\nP{3}=[0.4260,0.0843;0.0140,0.4489;0.5535,0.8630;0.4133,0.3718;0.8033,0.0733];\r\nP{4}=[0.0169,0.7757;0.1636,0.9072;0.7480,0.9785;0.2718,0.4179;0.8687,0.2735;0.0599,0.1064];\r\n\r\nA=round(lapgon(P),6);\r\nA_correct=0.459378;\r\n\r\nassert(isequal(A,A_correct))\r\n\r\n%% Test Case 4\r\ntheta=0:0.01:2*pi;\r\nP{1}(:,1)=0.35*cos(theta)+0.6;\r\nP{1}(:,2)=0.22*sin(theta)+0.5;\r\nP{2}=[0.1083,0.3508;0.7413,0.9426;0.2748,0.0933];\r\n\r\nA=round(lapgon(P),6);\r\nA_correct=0.307282;\r\n\r\nassert(isequal(A,A_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":4910069,"edited_by":4910069,"edited_at":"2025-09-12T18:34:35.000Z","deleted_by":null,"deleted_at":null,"solvers_count":7,"test_suite_updated_at":"2025-09-12T18:34:35.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2025-09-12T17:15:15.000Z","updated_at":"2026-03-19T16:19:38.000Z","published_at":"2025-09-12T18:28:07.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a variable length set of polygon vertex coordinates, compute the total area covered. For example, take two polygons with the following vertex coordinates:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ep1=[0.2,0.2; 0.5,0.2; 0.5,0.5; 0.2,0.5];\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ep2=[0.4,0.4; 0.8,0.4; 0.8,0.8; 0.4,0.8];\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"420\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"560\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe total area covered is the area of the first polygon plus the area of the second polygon minus the overlap. 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61081,"title":"Slicing the area of a regular polygon","description":"Given the area, A, of a regular polygon with n sides, each of length s, consider its decomposition in congruent isosceles triangles of base s and heigth h. Find the rectangle, with dimensions L×h, which covers all n triangles in their adjacent positions (n\u003e3, cf. figure below). Complete the problem by determining the area, A_r, of the rectangle.\r\nHint: Consider that we are slicing the polygon into triangular slices and put them into the rectangle.\r\ninput: (A, n)\r\noutput: y = [L h A_r]\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 575.8px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 287.9px; transform-origin: 408px 287.9px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 31.5px; text-align: left; transform-origin: 385px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven the area, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, of a regular polygon with \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e sides, each of length \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003es\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, consider its decomposition in congruent isosceles triangles of base \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003es\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and heigth \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eh\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Find the rectangle, with dimensions \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eL\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e×\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eh\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, which covers all \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e triangles in their adjacent positions (\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u0026gt;3,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e cf. figure below). Complete the problem by determining the area, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA_r\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, of the rectangle.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHint: Consider that we are slicing the polygon into triangular slices and put them into the rectangle.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003einput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(A, n)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eoutput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ey = [L h A_r]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 413.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 206.9px; text-align: left; transform-origin: 385px 206.9px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"501\" height=\"408\" style=\"vertical-align: baseline;width: 501px;height: 408px\" 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\" alt=\"Slicing square (n=4)\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = slicing(A,n)\r\n y = [L h A_r];\r\nend","test_suite":"%%\r\nA = 16;\r\nn = 4;\r\ny_correct = [10 2 20];\r\nassert(isequal(slicing(A,n),y_correct))\r\n\r\n%%\r\nA = 20;\r\nn = 5; \r\ny_correct = [10.22849568767431 2.34638608968871 24];\r\ntolerance = 1e-13;\r\nassert(all(abs(slicing(A,n)-y_correct)\u003ctolerance))\r\n\r\n%%\r\nfiletext = fileread('slicing.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\nA = 20;\r\nn = 6; \r\ny_correct = [7*sqrt(10*3^(-3/2)) sqrt(10*3^(-1/2)) 70/3];\r\ntolerance = 1e-13;\r\nassert(all(abs(slicing(A,n)-y_correct)\u003ctolerance))\r\n\r\n%%\r\nA = 32;\r\nn = 8; \r\ny_correct = [18*sqrt(sqrt(2)-1) 2/sqrt(sqrt(2)-1) 36];\r\ntolerance = 1e-13;\r\nassert(all(abs(slicing(A,n)-y_correct)\u003ctolerance))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":4993982,"edited_by":4993982,"edited_at":"2025-11-19T14:59:52.000Z","deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-11-18T11:18:12.000Z","updated_at":"2026-03-20T13:59:51.000Z","published_at":"2025-11-19T14:59:52.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven the area, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, of a regular polygon with \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e sides, each of length \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003es\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, consider its decomposition in congruent isosceles triangles of base \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003es\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and heigth \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. Find the rectangle, with dimensions \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eL\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e×\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, which covers all \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e triangles in their adjacent positions (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u0026gt;3,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e cf. figure below). Complete the problem by determining the area, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA_r\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, of the rectangle.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHint: Consider that we are slicing the polygon into triangular slices and put them into the rectangle.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003einput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(A, n)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eoutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey = [L h A_r]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"408\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"501\\\"/\u003e\u003cw:attr 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61086,"title":"Covering a four-pointed star polygon by rectangles","description":"Given the area, A, of a star polygon formed by the rectangle, with dimensions L×2L, and four triangles, with height h from their bases to the vertices, find the rectangles that have the same area, A, and cover the distance between opposite vertices (cf. figure below).\r\nGiven (A, L), return the 2x2 matrix M, where \r\nthe first row returns the dimensions, y1×y2, of the rectangle that covers the minimum distance (cf. left figure);\r\nthe second row returns the dimensions, z1×z2, of the rectangle that covers the maximum distance (cf. right figure).\r\ninput: (A, L)\r\noutput: M = [y1 y2; z1 z2]\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 635.675px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 408px 317.837px; transform-origin: 408px 317.837px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven the area, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, of a star polygon formed by the rectangle, with dimensions \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eL\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e×\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e2L\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and four triangles, with height \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eh\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e from their bases to the vertices, find the rectangles that have the same area, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and cover the distance between opposite vertices (cf. figure below).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(A, L)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, return the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ex\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e matrix \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eM\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, where \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 40.875px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 20.4375px; transform-origin: 391px 20.4375px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ethe first row returns the dimensions, y\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e×\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ey2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, of the rectangle that covers the minimum distance (cf. left figure);\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ethe second row returns the dimensions, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ez1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e×z\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, of the rectangle that covers the maximum distance (cf. right figure).\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003einput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(A, L)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eoutput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eM = [y1 y2; z1 z2]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 411.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 205.9px; text-align: left; transform-origin: 384px 205.9px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cimg class=\"imageNode\" width=\"508\" height=\"406\" style=\"vertical-align: baseline;width: 508px;height: 406px\" 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\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function M = covering_polygon(A,L)\r\n M = x;\r\nend","test_suite":"%%\r\nA = 27;\r\nL = 3;\r\nM_correct = [5 5.4; 3.375 8];\r\nassert(all(isapprox(covering_polygon(A,L),M_correct), 'all'))\r\n\r\n%%\r\nA = 36;\r\nL = 3;\r\nM_correct = [7 36/7; 3.6 10];\r\nassert(all(isapprox(covering_polygon(A,L),M_correct), 'all'))\r\n\r\n%%\r\nfiletext = fileread('covering_polygon.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\nA = 48;\r\nL = 4;\r\nM_correct = [20/3 36/5; 4.5 32/3];\r\nassert(all(isapprox(covering_polygon(A,L),M_correct), 'all'))\r\n\r\n%%\r\nA = 56;\r\nL = 4;\r\nM_correct = [8 7; 14/3 12];\r\nassert(all(isapprox(covering_polygon(A,L),M_correct), 'all'))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":4993982,"edited_by":4993982,"edited_at":"2025-11-28T15:21:25.000Z","deleted_by":null,"deleted_at":null,"solvers_count":10,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-11-27T15:06:59.000Z","updated_at":"2026-03-21T13:41:00.000Z","published_at":"2025-11-28T15:21:25.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven the area, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, of a star polygon formed by the rectangle, with dimensions \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eL\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e×\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2L\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, and four triangles, with height \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e from their bases to the vertices, find the rectangles that have the same area, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, and cover the distance between opposite vertices (cf. figure below).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(A, L)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, return the 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\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ez1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e×z\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, of the rectangle that covers the maximum distance (cf. right figure).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003einput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(A, L)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":45349,"title":"Area-07","description":"This is a follow up of the problem \r\n\r\n\u003chttps://www.mathworks.com/matlabcentral/cody/problems/45341-area-06\u003e\r\n\r\nin this case, find the total area of the lobes i.e. the area confined by the arcs drawn.","description_html":"\u003cp\u003eThis is a follow up of the problem\u003c/p\u003e\u003cp\u003e\u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/45341-area-06\"\u003ehttps://www.mathworks.com/matlabcentral/cody/problems/45341-area-06\u003c/a\u003e\u003c/p\u003e\u003cp\u003ein this case, find the total area of the lobes i.e. the area confined by the arcs drawn.\u003c/p\u003e","function_template":"function c= quarter_circle_02(r)\r\n y = x;\r\nend","test_suite":"%%\r\nr = 25;\r\nassert(abs(quarter_circle_02(r)-516.5287)\u003c0.001)\r\n%%\r\nr = 55.67;\r\nassert(abs(quarter_circle_02(r)-2561.2789)\u003c0.001)\r\n%%\r\nr = 42;\r\nassert(abs(quarter_circle_02(r)-1457.8505)\u003c0.001)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":4,"created_by":363598,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":18,"test_suite_updated_at":"2020-02-21T08:43:29.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2020-02-21T08:40:42.000Z","updated_at":"2026-03-11T09:28:14.000Z","published_at":"2020-02-21T08:43:29.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis is a follow up of the problem\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/45341-area-06\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026lt;https://www.mathworks.com/matlabcentral/cody/problems/45341-area-06\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026gt;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ein this case, find the total area of the lobes i.e. the area confined by the arcs drawn.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":50499,"title":"Find the area between curves (P2)","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 612.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 306.25px; transform-origin: 407px 306.25px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20px; border-block-end-color: rgb(60, 60, 60); border-block-start-color: rgb(60, 60, 60); border-bottom-color: rgb(60, 60, 60); border-inline-end-color: rgb(60, 60, 60); border-inline-start-color: rgb(60, 60, 60); border-left-color: rgb(60, 60, 60); border-right-color: rgb(60, 60, 60); border-top-color: rgb(60, 60, 60); caret-color: rgb(60, 60, 60); color: rgb(60, 60, 60); column-rule-color: rgb(60, 60, 60); font-family: Helvetica, Arial, sans-serif; font-size: 20px; font-weight: 700; line-height: 20px; margin-block-end: 5px; margin-block-start: 3px; margin-bottom: 5px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 3px; outline-color: rgb(60, 60, 60); perspective-origin: 384px 10px; text-align: left; text-decoration: none; text-decoration-color: rgb(60, 60, 60); transform-origin: 384px 10px; white-space: pre-wrap; margin-left: 4px; margin-top: 3px; margin-bottom: 5px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e Area between curves - Problem 2\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 32.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 16.25px; text-align: left; transform-origin: 384px 16.25px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e Find the area enclosed by the curves \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"63.5\" height=\"20\" style=\"width: 63.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"68\" height=\"32\" style=\"width: 68px; height: 32px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; 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\" 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src=\"data:image/png;base64,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\" width=\"32.5\" height=\"19\" style=\"width: 32.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"29.5\" height=\"19\" style=\"width: 29.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"76.5\" height=\"18\" style=\"width: 76.5px; height: 18px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = AreaCurves(a, n)\r\n \r\nend","test_suite":"%%\r\nfiletext = fileread('AreaCurves.m');\r\nfor ii = [0.5, 0.6667, 1.3606, 2.7754, 22.3242]\r\n assert(isempty(strfind(filetext, num2str(ii))),'Do NOT use provided answers in your solution')\r\nend\r\n\r\n%%\r\na = 1; \r\nn = 3;\r\n\r\ny_correct = 0.5;\r\nassert(abs(AreaCurves(a,n)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = 1; \r\nn = 5; \r\n\r\ny_correct = 0.6667;\r\nassert(abs(AreaCurves(a,n)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = 2; \r\nn = 2.5; \r\n\r\ny_correct = 1.3606;\r\nassert(abs(AreaCurves(a,n)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = pi;\r\nn = 3.1;\r\n\r\ny_correct = 2.7754;\r\nassert(abs(AreaCurves(a,n)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = exp(3);\r\nn = 12;\r\n\r\ny_correct = 22.3242;\r\nassert(abs(AreaCurves(a,n)-y_correct)\u003c1e-4)\r\n\r\n","published":true,"deleted":false,"likes_count":4,"comments_count":1,"created_by":487522,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":15,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-02-19T15:56:21.000Z","updated_at":"2025-08-25T11:22:08.000Z","published_at":"2021-02-19T15:59:16.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"heading\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e Area between curves - Problem 2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e Find the area enclosed by the curves \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ef(x) = x^{n}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eg(x) = ax^{\\\\frac{1}{n}}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e for different \\\"n\\\" and \\\"a\\\" coefficients\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"420\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"560\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e Plot of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ef(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eg(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea = 1, 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61071,"title":"Generalizing square area to triangle area","description":"Cody Problem 61070 asked for the height, h, of a right triangle that had the same area, A, of a square with side length, c, and the hypothenuse length was correlated to the square side by x = 2. \r\nNow, find the height, h, of the right triangle that has the same area, A, of a square with side length, c, and the hypothenuse length is xc, for an arbitrary number x \u003e 2. Here, the height stands for the smallest cathetus.\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 123px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 61.5px; transform-origin: 408px 61.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/61070-square-area-to-triangle-area\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eCody Problem 61070\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e asked for the height, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eh\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, of a right triangle that had the same area, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, of a square with side length, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ec\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and the hypothenuse length was correlated to the square side by \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ex = 2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eNow, find the height, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eh\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, of the right triangle that has the same area, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, of a square with side length, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ec\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and the hypothenuse length is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003exc\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, for an arbitrary number \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ex \u0026gt; 2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Here, the height stands for the smallest cathetus.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function h = find_height(A,x)\r\n h = x;\r\nend","test_suite":"%%\r\nA = 9;\r\nx = sqrt(5);\r\nh_correct = 3;\r\ntolerance = 1e-12;\r\nassert(abs(find_height(A,x)-h_correct)\u003ctolerance)\r\n\r\n%%\r\nA = 10;\r\nx = 3;\r\nh_correct = sqrt(5*(9-sqrt(65)));\r\ntolerance = 1e-12;\r\nassert(abs(find_height(A,x)-h_correct)\u003ctolerance)\r\n\r\n%%\r\nA = 16;\r\nx = sqrt(5);\r\nh_correct = 4;\r\nassert(isequal(find_height(A,x),h_correct))\r\n\r\n%%\r\nfiletext = fileread('find_height.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\nA = 16;\r\nx = 3; \r\nh_correct = 4*sqrt((9-sqrt(65))/2);\r\ntolerance = 1e-12;\r\nassert(abs(find_height(A,x)-h_correct)\u003ctolerance)\r\n\r\n%%\r\nA = 16;\r\nx = 5; \r\nh_correct = 4*sqrt((25 - sqrt(609))/2);\r\ntolerance = 1e-12;\r\nassert(abs(find_height(A,x)-h_correct)\u003ctolerance)\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":7,"created_by":4993982,"edited_by":4993982,"edited_at":"2025-11-13T10:09:54.000Z","deleted_by":null,"deleted_at":null,"solvers_count":15,"test_suite_updated_at":"2025-11-13T10:09:54.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2025-11-10T14:44:15.000Z","updated_at":"2026-04-08T08:26:51.000Z","published_at":"2025-11-12T17:58:52.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/61070-square-area-to-triangle-area\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eCody Problem 61070\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e asked for the height, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, of a right triangle that had the same area, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, of a square with side length, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ec\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, and the hypothenuse length was correlated to the square side by \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex = 2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNow, find the height, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, of the right triangle that has the same area, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, of a square with side length, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ec\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, and the hypothenuse length is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003exc\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, for an arbitrary number \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex \u0026gt; 2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. Here, the height stands for the smallest cathetus.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":45476,"title":"Inscribed circle in a triangle","description":"A circle of radius r is inscribed in a triangle. \r\n\r\nIn the figure, Ac=x and Bc=y. \r\nvalues of x \u0026 y are given.\r\n\r\nFind the area of the triangle.\r\n\r\n\u003chttps://www.analyzemath.com/Geometry_calculators/inscribed.gif\u003e\r\n\r\n\r\n \r\n","description_html":"\u003cp\u003eA circle of radius r is inscribed in a triangle.\u003c/p\u003e\u003cp\u003eIn the figure, Ac=x and Bc=y. \r\nvalues of x \u0026 y are given.\u003c/p\u003e\u003cp\u003eFind the area of the triangle.\u003c/p\u003e\u003cp\u003e\u003ca href = \"https://www.analyzemath.com/Geometry_calculators/inscribed.gif\"\u003ehttps://www.analyzemath.com/Geometry_calculators/inscribed.gif\u003c/a\u003e\u003c/p\u003e","function_template":"function y = ins_cir_tri(x,y,r)","test_suite":"%%\r\nassert(isequal(ins_cir_tri(20,30,10),600))\r\n\r\n%%\r\nassert(isequal(ins_cir_tri(15,10,5),150))\r\n\r\n%%\r\nassert(abs(ins_cir_tri(25,10,5)-194.4444)\u003c0.001)\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":4,"created_by":363598,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":14,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-04-24T17:06:12.000Z","updated_at":"2020-05-11T00:46:34.000Z","published_at":"2020-04-24T17:06:12.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA circle of radius r is inscribed in a triangle.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn the figure, Ac=x and Bc=y. values of x \u0026amp; y are given.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind the area of the triangle.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.analyzemath.com/Geometry_calculators/inscribed.gif\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026lt;https://www.analyzemath.com/Geometry_calculators/inscribed.gif\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026gt;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":61074,"title":"Height of a four-pointed star polygon","description":"Given the area A, of a rectangle with dimensions l1xl2, where the side lengths are integers and form the smallest possible perimeter, and given the total area A_t of the star polygon formed by the rectangle and four triangles (cf. the figure below), with height, h, from their bases to the apices, find the vector [l1 l2 h] such that l1\u003cl2.\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 490.8px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 245.4px; transform-origin: 408px 245.4px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 31.5px; text-align: left; transform-origin: 385px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven the area \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, of a rectangle with dimensions \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003el1xl2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, where the side lengths are integers and form the smallest possible perimeter, and given the total area \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA_t\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of the star polygon formed by the rectangle and four triangles (cf. the figure below), with height, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eh\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, from their bases to the apices, find the vector \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[l1 l2 h]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e such that \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003el1\u0026lt;l2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 418.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 209.4px; text-align: left; transform-origin: 385px 209.4px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"508\" height=\"413\" style=\"vertical-align: baseline;width: 508px;height: 413px\" 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\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = star_polygon(A,A_t)\r\n y = A;\r\nend","test_suite":"%%\r\nA = 10;\r\nA_t = 24;\r\ny_correct = [2 5 2];\r\nassert(isequal(star_polygon(A,A_t),y_correct))\r\n\r\n%%\r\nA = 11;\r\nA_t = 23;\r\ny_correct = [1 11 1];\r\nassert(isequal(star_polygon(A,A_t),y_correct))\r\n\r\n%%\r\nA = 72;\r\nA_t = 106;\r\ny_correct = [8 9 2];\r\nassert(isequal(star_polygon(A,A_t),y_correct))\r\n\r\n%%\r\nfiletext = fileread('star_polygon.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\nA = 156;\r\nA_t = 180;\r\ny_correct = [12 13 0.96];\r\nassert(isequal(star_polygon(A,A_t),y_correct))\r\n\r\n%%\r\nA = 168;\r\nA_t = 190;\r\ny_correct = [12 14 11/13];\r\nassert(isequal(star_polygon(A,A_t),y_correct))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":4993982,"edited_by":4993982,"edited_at":"2025-11-14T17:36:31.000Z","deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-11-13T17:02:46.000Z","updated_at":"2026-01-15T09:17:29.000Z","published_at":"2025-11-14T17:36:31.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven the area \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, of a rectangle with dimensions \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003el1xl2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, where the side lengths are integers and form the smallest possible perimeter, and given the total area \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA_t\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e of the star polygon formed by the rectangle and four triangles (cf. the figure below), with height, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, from their bases to the apices, find the vector \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[l1 l2 h]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e such that \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003el1\u0026lt;l2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"413\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"508\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" 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