{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2025-12-14T01:33:56.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2025-12-14T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":44817,"title":"Wrecked Angles?","description":"It's time for some simple geometry fun to start off the new year.\r\n\r\nYou will be given the perimeter P and the area A of a rectangle.  With these two values, calculate the area of the circle that circumscribes this rectangle.  This means we're looking for the area of the circle that touches this rectangle only at the four vertices of the rectangle.\r\n\r\nGood luck, and Happy 2019!","description_html":"\u003cp\u003eIt's time for some simple geometry fun to start off the new year.\u003c/p\u003e\u003cp\u003eYou will be given the perimeter P and the area A of a rectangle.  With these two values, calculate the area of the circle that circumscribes this rectangle.  This means we're looking for the area of the circle that touches this rectangle only at the four vertices of the rectangle.\u003c/p\u003e\u003cp\u003eGood luck, and Happy 2019!\u003c/p\u003e","function_template":"function y = wrecked_angles(P,A)\r\n  y = x;\r\nend","test_suite":"%%\r\nP=14;\r\nA=12;\r\ny=wrecked_angles(P,A);\r\ny_correct = 20.63495408493621;\r\njunk=abs(y-y_correct);\r\nassert(junk-1\u003c1e-10);\r\n%%\r\nP=34;\r\nA=60;\r\ny=wrecked_angles(P,A);\r\ny_correct = 131.7322896141688;\r\njunk=abs(y-y_correct);\r\nassert(junk-1\u003c1e-10);\r\n%%\r\nP=62;\r\nA=168;\r\ny=wrecked_angles(P,A);\r\ny_correct = 590.8738521234052;\r\njunk=abs(y-y_correct);\r\nassert(junk-100\u003c1e-10);\r\n%%\r\ns1=100;\r\ntotalsum=zeros(1,s1);\r\nfor s2=1:s1\r\n    P=2*(s1+s2);\r\n    A=s1*s2;\r\n    totalsum(s2)=wrecked_angles(P,A);\r\nend\r\ns=sum(totalsum);\r\ns_correct=1051137.631982975;\r\ns_junk=abs(s-s_correct);\r\nassert(s_junk\u003c1e-8);\r\n\r\nd=max(totalsum)-min(totalsum);\r\nd_correct=7853.196235811095;\r\nd_junk=abs(d-d_correct);\r\nassert(d_junk\u003c1e-8);\r\n%%\r\ns1=wrecked_angles(32,64);\r\ns2=wrecked_angles(72,288);\r\nP=2*(s1+s2);\r\nA=s1*s2;\r\ny=wrecked_angles(P,A);\r\ny_correct=259088.4479405854;\r\njunk=abs(y-y_correct);\r\nassert(junk\u003c1e-10);","published":true,"deleted":false,"likes_count":0,"comments_count":5,"created_by":1615,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":21,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":72,"created_at":"2019-01-03T14:27:57.000Z","updated_at":"2026-01-21T13:24:31.000Z","published_at":"2019-01-03T14:27:57.000Z","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\u003eIt's time for some simple geometry fun to start off the new year.\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\u003eYou will be given the perimeter P and the area A of a rectangle. With these two values, calculate the area of the circle that circumscribes this rectangle. This means we're looking for the area of the circle that touches this rectangle only at the four vertices 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\u003eGood luck, and Happy 2019!\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":60301,"title":"Compute the area of a lune","description":"Write a function to compute the area of the shaded moon-shaped region in the figure below—that is, the area of a smaller circle that does not overlap with a larger circle. The input will be the radius  of the smaller circle, the radius  of the larger circle, and the separation  between centers of the circles. \r\n","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: 405.7px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 202.85px; transform-origin: 407px 202.85px; 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: 384px 31.5px; text-align: left; transform-origin: 384px 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: 377.175px 8px; transform-origin: 377.175px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the area of the shaded moon-shaped region in the figure below—that is, the area of a smaller circle that does not overlap with a larger circle. The input will be the radius \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ea\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 98.7917px 8px; transform-origin: 98.7917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of the smaller circle, the radius \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eb\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 41.225px 8px; transform-origin: 41.225px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of the larger circle, and the separation \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ec\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 98.4px 8px; transform-origin: 98.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e between centers of the circles. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 333.7px; 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\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = luneArea(a,b,c)\r\n%  a = radius of smaller circle\r\n%  b = radius of larger circle\r\n%  c = distance between the centers of the circles\r\n   y = (b-a)*(b+c)/2;\r\nend","test_suite":"%%\r\na = 1; \r\nb = 1.2;\r\nc = 0.9; \r\nA = luneArea(a,b,c);\r\nA_correct = 1.285341014608472;\r\nassert(abs(A-A_correct)/A_correct\u003c1e-13)\r\n\r\n%%\r\na = 4; \r\nb = 5;\r\nc = 3; \r\nA = luneArea(a,b,c);\r\nA_correct = 13.950360778678039;\r\nassert(abs(A-A_correct)/A_correct\u003c1e-13)\r\n\r\n%%\r\na = exp(1); \r\nb = pi;\r\nc = -psi(1); \r\nA = luneArea(a,b,c);\r\nA_correct = 0.443456401155954;\r\nassert(abs(A-A_correct)/A_correct\u003c1e-13)\r\n\r\n%%\r\na = 3; \r\nb = 4;\r\nc = 1.01; \r\nA = luneArea(a,b,c);\r\nA_correct = 0.0065019633283;\r\nassert(abs(A-A_correct)/A_correct\u003c8e-12)\r\n\r\n%%\r\na = 1/sqrt(2); \r\nb = 1;\r\nc = a; \r\nA = luneArea(a,b,c);\r\nA_correct = 1/2;\r\nassert(abs(A-A_correct)/A_correct\u003c1e-13)\r\n\r\n%% \r\na = 5*rand;\r\nb = a*sqrt(2);\r\nc = a; \r\nA = luneArea(a,b,c);\r\nA_correct = b^2/2;\r\nassert(abs(A-A_correct)/A_correct\u003c1e-13)","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":46909,"edited_by":46909,"edited_at":"2024-06-01T23:28:36.000Z","deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":"2024-06-01T23:28:36.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2024-05-13T12:25:08.000Z","updated_at":"2026-01-04T10:52:42.000Z","published_at":"2024-05-13T12:25:26.000Z","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\u003eWrite a function to compute the area of the shaded moon-shaped region in the figure below—that is, the area of a smaller circle that does not overlap with a larger circle. The input will be the radius \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\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e of the smaller circle, the radius \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\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e of the larger circle, and the separation \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\u003ec\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e between centers of the circles. \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=\\\"328\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"438\\\"/\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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Angles?","description":"It's time for some simple geometry fun to start off the new year.\r\n\r\nYou will be given the perimeter P and the area A of a rectangle.  With these two values, calculate the area of the circle that circumscribes this rectangle.  This means we're looking for the area of the circle that touches this rectangle only at the four vertices of the rectangle.\r\n\r\nGood luck, and Happy 2019!","description_html":"\u003cp\u003eIt's time for some simple geometry fun to start off the new year.\u003c/p\u003e\u003cp\u003eYou will be given the perimeter P and the area A of a rectangle.  With these two values, calculate the area of the circle that circumscribes this rectangle.  This means we're looking for the area of the circle that touches this rectangle only at the four vertices of the rectangle.\u003c/p\u003e\u003cp\u003eGood luck, and Happy 2019!\u003c/p\u003e","function_template":"function y = wrecked_angles(P,A)\r\n  y = x;\r\nend","test_suite":"%%\r\nP=14;\r\nA=12;\r\ny=wrecked_angles(P,A);\r\ny_correct = 20.63495408493621;\r\njunk=abs(y-y_correct);\r\nassert(junk-1\u003c1e-10);\r\n%%\r\nP=34;\r\nA=60;\r\ny=wrecked_angles(P,A);\r\ny_correct = 131.7322896141688;\r\njunk=abs(y-y_correct);\r\nassert(junk-1\u003c1e-10);\r\n%%\r\nP=62;\r\nA=168;\r\ny=wrecked_angles(P,A);\r\ny_correct = 590.8738521234052;\r\njunk=abs(y-y_correct);\r\nassert(junk-100\u003c1e-10);\r\n%%\r\ns1=100;\r\ntotalsum=zeros(1,s1);\r\nfor s2=1:s1\r\n    P=2*(s1+s2);\r\n    A=s1*s2;\r\n    totalsum(s2)=wrecked_angles(P,A);\r\nend\r\ns=sum(totalsum);\r\ns_correct=1051137.631982975;\r\ns_junk=abs(s-s_correct);\r\nassert(s_junk\u003c1e-8);\r\n\r\nd=max(totalsum)-min(totalsum);\r\nd_correct=7853.196235811095;\r\nd_junk=abs(d-d_correct);\r\nassert(d_junk\u003c1e-8);\r\n%%\r\ns1=wrecked_angles(32,64);\r\ns2=wrecked_angles(72,288);\r\nP=2*(s1+s2);\r\nA=s1*s2;\r\ny=wrecked_angles(P,A);\r\ny_correct=259088.4479405854;\r\njunk=abs(y-y_correct);\r\nassert(junk\u003c1e-10);","published":true,"deleted":false,"likes_count":0,"comments_count":5,"created_by":1615,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":21,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":72,"created_at":"2019-01-03T14:27:57.000Z","updated_at":"2026-01-21T13:24:31.000Z","published_at":"2019-01-03T14:27:57.000Z","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\u003eIt's time for some simple geometry fun to start off the new year.\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\u003eYou will be given the perimeter P and the area A of a rectangle. With these two values, calculate the area of the circle that circumscribes this rectangle. This means we're looking for the area of the circle that touches this rectangle only at the four vertices 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\u003eGood luck, and Happy 2019!\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":60301,"title":"Compute the area of a lune","description":"Write a function to compute the area of the shaded moon-shaped region in the figure below—that is, the area of a smaller circle that does not overlap with a larger circle. The input will be the radius  of the smaller circle, the radius  of the larger circle, and the separation  between centers of the circles. \r\n","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: 405.7px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 202.85px; transform-origin: 407px 202.85px; 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: 384px 31.5px; text-align: left; transform-origin: 384px 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: 377.175px 8px; transform-origin: 377.175px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the area of the shaded moon-shaped region in the figure below—that is, the area of a smaller circle that does not overlap with a larger circle. The input will be the radius \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ea\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 98.7917px 8px; transform-origin: 98.7917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of the smaller circle, the radius \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eb\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 41.225px 8px; transform-origin: 41.225px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of the larger circle, and the separation \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ec\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 98.4px 8px; transform-origin: 98.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e between centers of the circles. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 333.7px; 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 166.85px; text-align: left; transform-origin: 384px 166.85px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"438\" height=\"328\" style=\"vertical-align: baseline;width: 438px;height: 328px\" 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\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = luneArea(a,b,c)\r\n%  a = radius of smaller circle\r\n%  b = radius of larger circle\r\n%  c = distance between the centers of the circles\r\n   y = (b-a)*(b+c)/2;\r\nend","test_suite":"%%\r\na = 1; \r\nb = 1.2;\r\nc = 0.9; \r\nA = luneArea(a,b,c);\r\nA_correct = 1.285341014608472;\r\nassert(abs(A-A_correct)/A_correct\u003c1e-13)\r\n\r\n%%\r\na = 4; \r\nb = 5;\r\nc = 3; \r\nA = luneArea(a,b,c);\r\nA_correct = 13.950360778678039;\r\nassert(abs(A-A_correct)/A_correct\u003c1e-13)\r\n\r\n%%\r\na = exp(1); \r\nb = pi;\r\nc = -psi(1); \r\nA = luneArea(a,b,c);\r\nA_correct = 0.443456401155954;\r\nassert(abs(A-A_correct)/A_correct\u003c1e-13)\r\n\r\n%%\r\na = 3; \r\nb = 4;\r\nc = 1.01; \r\nA = luneArea(a,b,c);\r\nA_correct = 0.0065019633283;\r\nassert(abs(A-A_correct)/A_correct\u003c8e-12)\r\n\r\n%%\r\na = 1/sqrt(2); \r\nb = 1;\r\nc = a; \r\nA = luneArea(a,b,c);\r\nA_correct = 1/2;\r\nassert(abs(A-A_correct)/A_correct\u003c1e-13)\r\n\r\n%% \r\na = 5*rand;\r\nb = a*sqrt(2);\r\nc = a; \r\nA = luneArea(a,b,c);\r\nA_correct = b^2/2;\r\nassert(abs(A-A_correct)/A_correct\u003c1e-13)","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":46909,"edited_by":46909,"edited_at":"2024-06-01T23:28:36.000Z","deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":"2024-06-01T23:28:36.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2024-05-13T12:25:08.000Z","updated_at":"2026-01-04T10:52:42.000Z","published_at":"2024-05-13T12:25:26.000Z","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\u003eWrite a function to compute the area of the shaded moon-shaped region in the figure below—that is, the area of a smaller circle that does not overlap with a larger circle. The input will be the radius \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\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e of the smaller circle, the radius \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\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e of the larger circle, and the separation \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\u003ec\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e between centers of the circles. \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=\\\"328\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"438\\\"/\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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