{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-04-06T14:01:22.000Z","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":"2026-04-06T00:00:00.000Z","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":57765,"title":"Determine whether a hydrograph is a unit hydrograph","description":"A hydrograph describes the runoff response of a catchment or watershed to rainfall. It shows the runoff rate  (or flow or discharge) as a function of time  resulting from a given excess rainfall (expressed as a depth ) for a storm of a specified duration. A unit hydrograph results from unit excess rainfall (e.g.,  = 1 cm). \r\nWrite a function to determine whether a hydrograph is a unit hydrograph. Inputs to the function will be time  in minutes, the flow rate  in , and the catchment area  in . Allow for a tolerance of 0.01 cm in the excess rainfall depth.","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: 114px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 57px; transform-origin: 407px 57px; 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: 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: 333.467px 8px; transform-origin: 333.467px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA hydrograph describes the runoff response of a catchment or watershed to rainfall. It shows the runoff rate \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);\"\u003eQ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 35px 8px; transform-origin: 35px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (or flow or discharge) as a function of time \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);\"\u003et\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 188.267px 8px; transform-origin: 188.267px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e resulting from a given excess rainfall (expressed as a depth \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);\"\u003eP\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 82.8333px 8px; transform-origin: 82.8333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e) for a storm of a specified duration. 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: 50.575px 8px; transform-origin: 50.575px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eunit hydrograph \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 115.9px 8px; transform-origin: 115.9px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eresults from unit excess rainfall (e.g., \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);\"\u003eP\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 29.3583px 8px; transform-origin: 29.3583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e = 1 cm). \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: 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: 330.108px 8px; transform-origin: 330.108px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to determine whether a hydrograph is a unit hydrograph. Inputs to the function will be time \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);\"\u003et\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 49.3917px 8px; transform-origin: 49.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e in minutes, the flow rate \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);\"\u003eQ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9.33333px 8px; transform-origin: 9.33333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e in \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"m^3/s\" style=\"width: 33px; height: 19.5px;\" width=\"33\" height=\"19.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 79.3417px 8px; transform-origin: 79.3417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and the catchment area \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: 9.33333px 8px; transform-origin: 9.33333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e in \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"m^2\" style=\"width: 19.5px; height: 19px;\" width=\"19.5\" height=\"19\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 188.642px 8px; transform-origin: 188.642px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Allow for a tolerance of 0.01 cm in the excess rainfall depth.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function tf = isUnitHydrograph(t,Q,A)\r\n  tf = isequal(Q*t/A,1);\r\nend","test_suite":"%%\r\nA = 2250000;                                                        %  Area (m2)\r\nt = 0:30:390;                                                       %  Time (min)\r\nQ = [0 1.2 2.8 1.7 1.4 1.2 1.1 0.91 0.74 0.61 0.5 0.28 0.17 0];     %  Discharge (m3/s)\r\nassert(isUnitHydrograph(t,Q,A))\r\n\r\n%%\r\nA = 2250000;                                                        %  Area (m2)\r\nt = 0:40:520;                                                       %  Time (min)\r\nQ = [0 1.2 2.8 1.7 1.4 1.2 1.1 0.91 0.74 0.61 0.5 0.28 0.17 0];     %  Discharge (m3/s)\r\nassert(~isUnitHydrograph(t,Q,A))\r\n\r\n%%\r\nA = 2520000;                                                        %  Area (m2)\r\nt = 0:30:390;                                                       %  Time (min)\r\nQ = [0 1.2 2.8 1.7 1.4 1.2 1.1 0.91 0.74 0.61 0.5 0.28 0.17 0];     %  Discharge (m3/s)\r\nassert(~isUnitHydrograph(t,Q,A))\r\n\r\n%%\r\nA = 753601;                                                         %  Area (m2)\r\nt = linspace(0,180);                                                %  Time (min)\r\nQ = 0.1*t.*exp(-0.000398*t.^2);                                     %  Discharge (m3/s)\r\nassert(isUnitHydrograph(t,Q,A))\r\n\r\n%%\r\nA = 735601;                                                         %  Area (m2)\r\nt = linspace(0,180);                                                %  Time (min)\r\nQ = 0.1*t.*exp(-0.000398*t.^2);                                     %  Discharge (m3/s)\r\nassert(~isUnitHydrograph(t,Q,A))\r\n\r\n%%\r\nA = 2100000;                                                        %  Area (m2)\r\nt = 0:30:390;                                                       %  Time (min)\r\nQ = [0 1.4 3.2 1.5 1.2 1.1 1.0 0.66 0.49 0.36 0.28 0.25 0.17 0];    %  Discharge (m3/s)\r\nassert(isUnitHydrograph(t,Q,A))\r\n\r\n%%\r\nA = 2100000;                                                        %  Area (m2)\r\nt = 0:30:390;                                                       %  Time (min)\r\nQ = [0 1.4 2.3 1.5 1.2 1.1 1.0 0.66 0.49 0.36 0.28 0.25 0.17 0];    %  Discharge (m3/s)\r\nassert(~isUnitHydrograph(t,Q,A))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":2,"created_by":46909,"edited_by":46909,"edited_at":"2023-03-11T12:56:35.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-03-11T01:14:20.000Z","updated_at":"2023-03-11T12:56:36.000Z","published_at":"2023-03-11T01:14:26.000Z","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\u003eA hydrograph describes the runoff response of a catchment or watershed to rainfall. It shows the runoff rate \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\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e (or flow or discharge) as a function of time \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\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"t\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003et\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e resulting from a given excess rainfall (expressed as a depth \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\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"P\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eP\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e) for a storm of a specified duration. A \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eunit hydrograph \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eresults from unit excess rainfall (e.g., \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\u003eP\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e = 1 cm). \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\u003eWrite a function to determine whether a hydrograph is a unit hydrograph. Inputs to the function will be time \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\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"t\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003et\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e in minutes, the flow rate \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\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e in \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\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"m^3/s\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\rm m^3/s\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and the catchment area \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\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"A\\\"/\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 in \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\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"m^2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\rm m^2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Allow for a tolerance of 0.01 cm in the excess rainfall depth.\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\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":57765,"title":"Determine whether a hydrograph is a unit hydrograph","description":"A hydrograph describes the runoff response of a catchment or watershed to rainfall. It shows the runoff rate  (or flow or discharge) as a function of time  resulting from a given excess rainfall (expressed as a depth ) for a storm of a specified duration. A unit hydrograph results from unit excess rainfall (e.g.,  = 1 cm). \r\nWrite a function to determine whether a hydrograph is a unit hydrograph. Inputs to the function will be time  in minutes, the flow rate  in , and the catchment area  in . Allow for a tolerance of 0.01 cm in the excess rainfall depth.","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: 114px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 57px; transform-origin: 407px 57px; 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: 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: 333.467px 8px; transform-origin: 333.467px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA hydrograph describes the runoff response of a catchment or watershed to rainfall. It shows the runoff rate \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);\"\u003eQ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 35px 8px; transform-origin: 35px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (or flow or discharge) as a function of time \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);\"\u003et\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 188.267px 8px; transform-origin: 188.267px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e resulting from a given excess rainfall (expressed as a depth \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);\"\u003eP\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 82.8333px 8px; transform-origin: 82.8333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e) for a storm of a specified duration. 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: 50.575px 8px; transform-origin: 50.575px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eunit hydrograph \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 115.9px 8px; transform-origin: 115.9px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eresults from unit excess rainfall (e.g., \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);\"\u003eP\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 29.3583px 8px; transform-origin: 29.3583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e = 1 cm). \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: 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: 330.108px 8px; transform-origin: 330.108px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to determine whether a hydrograph is a unit hydrograph. Inputs to the function will be time \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);\"\u003et\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 49.3917px 8px; transform-origin: 49.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e in minutes, the flow rate \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);\"\u003eQ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9.33333px 8px; transform-origin: 9.33333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e in \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"m^3/s\" style=\"width: 33px; height: 19.5px;\" width=\"33\" height=\"19.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 79.3417px 8px; transform-origin: 79.3417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and the catchment area \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: 9.33333px 8px; transform-origin: 9.33333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e in \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"m^2\" style=\"width: 19.5px; height: 19px;\" width=\"19.5\" height=\"19\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 188.642px 8px; transform-origin: 188.642px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Allow for a tolerance of 0.01 cm in the excess rainfall depth.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function tf = isUnitHydrograph(t,Q,A)\r\n  tf = isequal(Q*t/A,1);\r\nend","test_suite":"%%\r\nA = 2250000;                                                        %  Area (m2)\r\nt = 0:30:390;                                                       %  Time (min)\r\nQ = [0 1.2 2.8 1.7 1.4 1.2 1.1 0.91 0.74 0.61 0.5 0.28 0.17 0];     %  Discharge (m3/s)\r\nassert(isUnitHydrograph(t,Q,A))\r\n\r\n%%\r\nA = 2250000;                                                        %  Area (m2)\r\nt = 0:40:520;                                                       %  Time (min)\r\nQ = [0 1.2 2.8 1.7 1.4 1.2 1.1 0.91 0.74 0.61 0.5 0.28 0.17 0];     %  Discharge (m3/s)\r\nassert(~isUnitHydrograph(t,Q,A))\r\n\r\n%%\r\nA = 2520000;                                                        %  Area (m2)\r\nt = 0:30:390;                                                       %  Time (min)\r\nQ = [0 1.2 2.8 1.7 1.4 1.2 1.1 0.91 0.74 0.61 0.5 0.28 0.17 0];     %  Discharge (m3/s)\r\nassert(~isUnitHydrograph(t,Q,A))\r\n\r\n%%\r\nA = 753601;                                                         %  Area (m2)\r\nt = linspace(0,180);                                                %  Time (min)\r\nQ = 0.1*t.*exp(-0.000398*t.^2);                                     %  Discharge (m3/s)\r\nassert(isUnitHydrograph(t,Q,A))\r\n\r\n%%\r\nA = 735601;                                                         %  Area (m2)\r\nt = linspace(0,180);                                                %  Time (min)\r\nQ = 0.1*t.*exp(-0.000398*t.^2);                                     %  Discharge (m3/s)\r\nassert(~isUnitHydrograph(t,Q,A))\r\n\r\n%%\r\nA = 2100000;                                                        %  Area (m2)\r\nt = 0:30:390;                                                       %  Time (min)\r\nQ = [0 1.4 3.2 1.5 1.2 1.1 1.0 0.66 0.49 0.36 0.28 0.25 0.17 0];    %  Discharge (m3/s)\r\nassert(isUnitHydrograph(t,Q,A))\r\n\r\n%%\r\nA = 2100000;                                                        %  Area (m2)\r\nt = 0:30:390;                                                       %  Time (min)\r\nQ = [0 1.4 2.3 1.5 1.2 1.1 1.0 0.66 0.49 0.36 0.28 0.25 0.17 0];    %  Discharge (m3/s)\r\nassert(~isUnitHydrograph(t,Q,A))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":2,"created_by":46909,"edited_by":46909,"edited_at":"2023-03-11T12:56:35.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-03-11T01:14:20.000Z","updated_at":"2023-03-11T12:56:36.000Z","published_at":"2023-03-11T01:14:26.000Z","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\u003eA hydrograph describes the runoff response of a catchment or watershed to rainfall. It shows the runoff rate \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\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e (or flow or discharge) as a function of time \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\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"t\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003et\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e resulting from a given excess rainfall (expressed as a depth \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\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"P\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eP\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e) for a storm of a specified duration. A \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eunit hydrograph \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eresults from unit excess rainfall (e.g., \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\u003eP\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e = 1 cm). \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\u003eWrite a function to determine whether a hydrograph is a unit hydrograph. Inputs to the function will be time \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\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"t\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003et\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e in minutes, the flow rate \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\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e in \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\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"m^3/s\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\rm m^3/s\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and the catchment area \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\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"A\\\"/\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 in \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\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"m^2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\rm m^2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Allow for a tolerance of 0.01 cm in the excess rainfall depth.\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\"}]}"}],"term":"tag:\"trapz\"","current_player_id":null,"fields":[{"name":"page","type":"integer","callback":null,"default":1,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":null,"prepend":true},{"name":"per_page","type":"integer","callback":null,"default":50,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":null,"prepend":true},{"name":"sort","type":"string","callback":null,"default":null,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":null,"prepend":true},{"name":"body","type":"text","callback":null,"default":"*:*","directive":null,"facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":false},{"name":"group","type":"string","callback":null,"default":null,"directive":"group","facet":true,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"difficulty_rating_bin","type":"string","callback":null,"default":null,"directive":"difficulty_rating_bin","facet":true,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"id","type":"integer","callback":null,"default":null,"directive":"id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"tag","type":"string","callback":null,"default":null,"directive":"tag","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"product","type":"string","callback":null,"default":null,"directive":"product","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"created_at","type":"timeframe","callback":{},"default":null,"directive":"created_at","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"profile_id","type":"integer","callback":null,"default":null,"directive":"author_id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"created_by","type":"string","callback":null,"default":null,"directive":"author","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"player_id","type":"integer","callback":null,"default":null,"directive":"solver_id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"player","type":"string","callback":null,"default":null,"directive":"solver","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"solvers_count","type":"integer","callback":null,"default":null,"directive":"solvers_count","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"comments_count","type":"integer","callback":null,"default":null,"directive":"comments_count","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"likes_count","type":"integer","callback":null,"default":null,"directive":"likes_count","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"leader_id","type":"integer","callback":null,"default":null,"directive":"leader_id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"leading_solution","type":"integer","callback":null,"default":null,"directive":"leading_solution","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true}],"filters":[{"name":"asset_type","type":"string","callback":null,"default":null,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":"\"cody:problem\"","prepend":true},{"name":"profile_id","type":"integer","callback":{},"default":null,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":"author_id","static":null,"prepend":true}],"query":{"params":{"per_page":50,"term":"tag:\"trapz\"","current_player":null,"sort":"map(difficulty_value,0,0,999) 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