{"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":51830,"title":"Find the number of days in a given year","description":"Given a year number (eg. 2000) as input, find how many days are there in the given year.","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: 331.5px 10.4px; transform-origin: 331.5px 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: 308.5px 10.4px; text-align: left; transform-origin: 308.5px 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=\"\"\u003eGiven a year number (eg. 2000) as input, find how many days are there in the given year.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = daysInTheYear(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = 2000;\r\ny_correct = 366;\r\nassert(isequal(daysInTheYear(x),y_correct))\r\n\r\n%%\r\nx = 1000;\r\ny_correct = 365;\r\nassert(isequal(daysInTheYear(x),y_correct))\r\n\r\n%%\r\nx = 2021;\r\ny_correct = 365;\r\nassert(isequal(daysInTheYear(x),y_correct))\r\n\r\n\r\n%%\r\nx = 2020;\r\ny_correct = 366;\r\nassert(isequal(daysInTheYear(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":14038,"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":"2021-06-02T07:51:08.000Z","updated_at":"2026-03-02T14:04:40.000Z","published_at":"2021-06-02T07:51:08.000Z","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 a year number (eg. 2000) as input, find how many days are there in the given year.\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":44514,"title":"Happy Free Wednesday!","description":"Just submit your solution on any Wednesday. \r\n\r\n*Related Challenges:*\r\n\r\n# Happy Free Wednesday!\r\n# Happy Free 2019!\r\n# Happy Free March!\r\n# Happy Free 15th Day of a Month!\r\n# \u003chttps://www.mathworks.com/matlabcentral/cody/problems/44518 Good Morning :)\u003e\r\n# Good Night :)\r\n# Leap Year","description_html":"\u003cp\u003eJust submit your solution on any Wednesday.\u003c/p\u003e\u003cp\u003e\u003cb\u003eRelated Challenges:\u003c/b\u003e\u003c/p\u003e\u003col\u003e\u003cli\u003eHappy Free Wednesday!\u003c/li\u003e\u003cli\u003eHappy Free 2019!\u003c/li\u003e\u003cli\u003eHappy Free March!\u003c/li\u003e\u003cli\u003eHappy Free 15th Day of a Month!\u003c/li\u003e\u003cli\u003e\u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/44518\"\u003eGood Morning :)\u003c/a\u003e\u003c/li\u003e\u003cli\u003eGood Night :)\u003c/li\u003e\u003cli\u003eLeap Year\u003c/li\u003e\u003c/ol\u003e","function_template":"function str = freeWednesday(x)\r\n    % If you're not sure how many days it's been to Wednesday, just click submit button\r\n    if weekday(datetime('today'))==4\r\n        disp('Congrats! It is a happy free Wednesday!')\r\n    else\r\n        daysTill = [3 2 1 0 6 5 4];\r\n        str =  sprintf('You have to wait %d days to solve this problem',daysTill(weekday(datetime('today'))));\r\n    end\r\nend","test_suite":"%%\r\nx = 1;\r\nfreeWednesday(x)\r\nassert(weekday(datetime('today'))==4)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":8703,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":44,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2018-02-07T09:30:21.000Z","updated_at":"2026-02-11T11:57:28.000Z","published_at":"2018-02-07T09:30:21.000Z","restored_at":"2018-03-07T18:37:01.000Z","restored_by":null,"spam":false,"simulink":false,"admin_reviewed":true,"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\u003eJust submit your solution on any Wednesday.\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:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eRelated Challenges:\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=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHappy Free Wednesday!\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=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHappy Free 2019!\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=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHappy Free March!\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=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHappy Free 15th Day of a Month!\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=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/44518\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eGood Morning :)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGood Night :)\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=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eLeap Year\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\\\" 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datetime('today');\r\nassert(isequal(generate_datetime(),y_correct))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":171559,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":135,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2018-05-29T14:59:26.000Z","updated_at":"2026-03-02T09:12:44.000Z","published_at":"2018-05-29T14:59:26.000Z","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\u003eGenerate the datetime scalar representing the current date\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":58588,"title":"How many revolutions 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","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: 51px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 25.5px; transform-origin: 407px 25.5px; 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: 219.5px 8px; transform-origin: 219.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCalculate how many revolutions you will around the earth till 1/1/2100.\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: 204.5px 8px; transform-origin: 204.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven the birhdate find your age in number of days on 1/1/2100. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function numdays = ageinDays(birthdate)\r\n   numdays = 0;\r\nend\r\n","test_suite":"%%\r\nx = '20-jan-1395';\r\ny_correct = 257477;\r\nassert(isequal( ageinDays(x),y_correct))\r\n\r\n%%\r\nx = '20-jan-1995';\r\ny_correct = 38332;\r\nassert(isequal( ageinDays(x),y_correct))\r\n\r\n%%\r\nx = '20-jan-2005';\r\ny_correct = 34679;\r\nassert(isequal( ageinDays(x),y_correct))\r\n\r\n%%\r\nx = '31-jul-2023';\r\ny_correct = 27913;\r\nassert(isequal( ageinDays(x),y_correct))\r\n\r\n%%\r\nx = '1-nov-2016';\r\ny_correct = 30376;\r\nassert(isequal( ageinDays(x),y_correct))\r\n\r\n%%\r\nx = '14-mar-2050';\r\ny_correct = 18190;\r\nassert(isequal( ageinDays(x),y_correct))\r\n\r\n%Test cases 4-6 added by Dyuman Joshi\r\n%18-07-2023","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":3494818,"edited_by":223089,"edited_at":"2023-07-18T10:59:24.000Z","deleted_by":null,"deleted_at":null,"solvers_count":12,"test_suite_updated_at":"2023-07-18T10:59:24.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2023-07-17T22:34:21.000Z","updated_at":"2024-11-06T13:55:31.000Z","published_at":"2023-07-17T22:34:21.000Z","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\u003eCalculate how many revolutions you will around the earth till 1/1/2100.\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 the birhdate find your age in number of days on 1/1/2100. \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":45848,"title":"What is the current time in Darwin, Australia?","description":"Traders need to track exchange calendars and trading hours in detail, and account for time zone differences and daylight savings offsets. These can be tricky in cities with half-hour and quarter-hour offset to UTC. \u003chttps://en.wikipedia.org/wiki/List_of_stock_exchange_trading_hours\u003e\r\n\r\nMATLAB comes to rescue!\r\n\u003chttps://www.mathworks.com/help/matlab/ref/datetime.html\u003e\r\n\r\nYou are given an array with UTC date and time as *[year, month, day, hour, minute]* and a char array with the name of the time zone.\r\nReturn a char array with the current date and time in the specified time zone, in the format *'MMM-dd-yyyy HH:mm'*.\r\n\r\nFor example, for inputs *[2020 6 9 21 50 0]* and *'Australia/Dawin'*, you should get *'Jun-10-2020 07:20'* in return.","description_html":"\u003cp\u003eTraders need to track exchange calendars and trading hours in detail, and account for time zone differences and daylight savings offsets. These can be tricky in cities with half-hour and quarter-hour offset to UTC. \u003ca href = \"https://en.wikipedia.org/wiki/List_of_stock_exchange_trading_hours\"\u003ehttps://en.wikipedia.org/wiki/List_of_stock_exchange_trading_hours\u003c/a\u003e\u003c/p\u003e\u003cp\u003eMATLAB comes to rescue! \u003ca href = \"https://www.mathworks.com/help/matlab/ref/datetime.html\"\u003ehttps://www.mathworks.com/help/matlab/ref/datetime.html\u003c/a\u003e\u003c/p\u003e\u003cp\u003eYou are given an array with UTC date and time as \u003cb\u003e[year, month, day, hour, minute]\u003c/b\u003e and a char array with the name of the time zone.\r\nReturn a char array with the current date and time in the specified time zone, in the format \u003cb\u003e'MMM-dd-yyyy HH:mm'\u003c/b\u003e.\u003c/p\u003e\u003cp\u003eFor example, for inputs \u003cb\u003e[2020 6 9 21 50 0]\u003c/b\u003e and \u003cb\u003e'Australia/Dawin'\u003c/b\u003e, you should get \u003cb\u003e'Jun-10-2020 07:20'\u003c/b\u003e in return.\u003c/p\u003e","function_template":"function [dateTime] = world_time(td,tz)\r\n  dateTime = now;\r\n  offset = 0;\r\nend","test_suite":"%%\r\ntz = 'Australia/Darwin';\r\ntd = [2020 6 9 21 50 0];\r\ny_correct = 'Jun-10-2020 07:20';\r\nassert(isequal(world_time(td,tz),y_correct))\r\n%%\r\ntz = 'America/St_Johns';\r\ntd = [2000 1 1 10 05 0];\r\ny_correct = 'Jan-01-2000 06:35';\r\nassert(isequal(world_time(td,tz),y_correct))\r\n%%\r\ntz = 'Asia/Calcutta';\r\ntd = [1999 9 9 9 9 9];\r\ny_correct = 'Sep-09-1999 14:39';\r\nassert(isequal(world_time(td,tz),y_correct))\r\n%%\r\ntz = 'Asia/Katmandu';\r\ntd = [2029 12 31 11 59 00];\r\ny_correct = 'Dec-31-2029 17:44';\r\nassert(isequal(world_time(td,tz),y_correct))\r\n%%\r\ntz = 'Atlantic/Bermuda';\r\ntd = [1945 12 05 10 04 00];\r\ny_correct = 'Dec-05-1945 06:04';\r\nassert(isequal(world_time(td,tz),y_correct))","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":452188,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":13,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-06-10T02:51:35.000Z","updated_at":"2025-11-26T20:54:03.000Z","published_at":"2020-06-10T02:51:35.000Z","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\u003eTraders need to track exchange calendars and trading hours in detail, and account for time zone differences and daylight savings offsets. These can be tricky in cities with half-hour and quarter-hour offset to UTC.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/List_of_stock_exchange_trading_hours\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026lt;https://en.wikipedia.org/wiki/List_of_stock_exchange_trading_hours\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\u003eMATLAB comes to rescue!\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/help/matlab/ref/datetime.html\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026lt;https://www.mathworks.com/help/matlab/ref/datetime.html\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\u003eYou are given an array with UTC date and time as\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[year, month, day, hour, minute]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and a char array with the name of the time zone. Return a char array with the current date and time in the specified time zone, in the format\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'MMM-dd-yyyy HH:mm'\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:r\u003e\u003cw:t\u003eFor example, for inputs\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[2020 6 9 21 50 0]\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\u003e'Australia/Dawin'\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, you should get\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'Jun-10-2020 07:20'\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e in return.\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":42352,"title":"Days until next NewYear ball drop","description":"Given a date string in the form 'yyyy-mm-dd' or 'yyyy-mm-dd hh:mm:ss', calculate the number of *days* until the dropping of the NewYear ball at Times Square (i.e., Dec 31st at midnight) of that year. Examples:\r\n\r\n    y = Days2NYE('2014-05-26') = 220 or\r\n    y = Days2NYE('2014-05-26 10:15:45') = 219","description_html":"\u003cp\u003eGiven a date string in the form 'yyyy-mm-dd' or 'yyyy-mm-dd hh:mm:ss', calculate the number of \u003cb\u003edays\u003c/b\u003e until the dropping of the NewYear ball at Times Square (i.e., Dec 31st at midnight) of that year. Examples:\u003c/p\u003e\u003cpre\u003e    y = Days2NYE('2014-05-26') = 220 or\r\n    y = Days2NYE('2014-05-26 10:15:45') = 219\u003c/pre\u003e","function_template":"function y = Days2NYE(x)\r\n  y = ??;\r\nend","test_suite":"%%\r\nx= '2015-05-26';\r\ny_correct = 220;\r\nassert(isequal(Days2NYE(x),y_correct))\r\n\r\n%%\r\nx = '2015-12-30';\r\ny_correct = 2;\r\nassert(isequal(Days2NYE(x),y_correct))\r\n\r\n%%\r\nx = '2014-05-26 10:15:45';\r\ny_correct = 219;\r\nassert(isequal(Days2NYE(x),y_correct))\r\n\r\n%%\r\nx = '2014-12-31 10:15:45';\r\ny_correct = 0;\r\nassert(isequal(Days2NYE(x),y_correct))","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":44306,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":78,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2015-06-02T18:07:53.000Z","updated_at":"2026-03-22T08:23:49.000Z","published_at":"2015-06-02T18:09:23.000Z","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 a date string in the form 'yyyy-mm-dd' or 'yyyy-mm-dd hh:mm:ss', calculate the number of\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\u003edays\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e until the dropping of the NewYear ball at Times Square (i.e., Dec 31st at midnight) of that year. Examples:\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[    y = Days2NYE('2014-05-26') = 220 or\\n    y = Days2NYE('2014-05-26 10:15:45') = 219]]\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":60406,"title":"Alert a city about a spill","description":"Problem statement\r\nCody Problem 54750 involved determining the length of a stream affected by a spill of a contaminant. Any municipalities within that reach would want to know when water from the river would be safe to drink—for example, below the U.S. Environmental Protection Agency’s maximum contaminant level (MCL). As in CP 54750, the spill of mass  will be assumed instantaneous at position  and time  and mixed over the cross section (with area ). Then if the flow is steady and the geometry of the flow does not change downstream, the concentration can be computed with  \r\n\r\nwhere  is the mean velocity of the river,  is the discharge or volumetric flow rate, and  is a dispersion coefficient, which describes spreading by several mechanisms. \r\nWrite a function that returns the dates and times (given as datetimes) between which the water is unsafe to drink (i.e., the concentration exceeds the MCL) at position  downstream of the spill. Round the times to the nearest second. If the concentration does not exceed the MCL, return 'The MCL is not exceeded.' Please note that the MCL is given in mg/L, whereas other variables are given in SI units. \r\nDetails\r\nMany empirical formulas are available for the dispersion coefficient. For this problem, use the formula of Seo and Cheong (1998):\r\n\r\nwhere  is the width of the channel (assumed rectangular here),  is the water depth, and  is the shear velocity, which is related to the shear stress on the wetted perimeter of the channel. In steady uniform flow, the component of the fluid’s weight down the slope will balance the friction on the channel bed, and the shear velocity can be computed as\r\n\r\nwhere  is the gravitational acceleration,  is the longitudinal slope of the channel,  is the hydraulic radius, and  is the wetted perimeter. For a rectangular channel, . \r\nIn addition to assuming steady uniform flow and an unchanging channel, ignore any reaction, decay, or loss of the chemical; this assumption provides a conservative estimate of the time range. In practice, one would include a factor of safety that accounts for uncertainty in the parameters. Nevertheless, the calculations here would form a basis for the advice to the city.  ","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: 690.033px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 345.017px; transform-origin: 407px 345.017px; 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-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: 63.0083px 7.79167px; transform-origin: 63.0083px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eProblem statement\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 105px; 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 52.5px; text-align: left; transform-origin: 384px 52.5px; 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/54750\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eCody Problem 54750\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: 307.167px 7.79167px; transform-origin: 307.167px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e involved determining the length of a stream affected by a spill of a contaminant. Any municipalities within that reach would want to know when water from the river would be safe to drink—for example, below the U.S. Environmental Protection Agency’s \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.epa.gov/ground-water-and-drinking-water/national-primary-drinking-water-regulations\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003emaximum contaminant level\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: 129.9px 7.79167px; transform-origin: 129.9px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (MCL). As in CP 54750, the spill of mass \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);\"\u003eM\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 23.3417px 7.79167px; transform-origin: 23.3417px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e will be assumed instantaneous at position \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"36.5\" height=\"18\" alt=\"x = 0\" style=\"width: 36.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 30.725px 7.79167px; transform-origin: 30.725px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and time \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"33.5\" height=\"18\" alt=\"t = 0\" style=\"width: 33.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 34.2333px 7.79167px; transform-origin: 34.2333px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and mixed\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 104.625px 7.79167px; transform-origin: 104.625px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e over the cross section (with 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: 62.6083px 7.79167px; transform-origin: 62.6083px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e). Then if the flow is steady and the geometry of the flow does not change downstream, the concentration can be computed 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: 1.94167px 7.79167px; transform-origin: 1.94167px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 40px; 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 20px; text-align: left; transform-origin: 384px 20px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"204.5\" height=\"40\" alt=\"C = (M/(A sqrt(4 pi K t)) exp(-(x-Ut)^2/(4Kt))\" style=\"width: 204.5px; height: 40px;\"\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-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: 21.0083px 7.79167px; transform-origin: 21.0083px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"61.5\" height=\"18.5\" alt=\"U = Q/A\" style=\"width: 61.5px; height: 18.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 101.892px 7.79167px; transform-origin: 101.892px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the mean velocity of the river, \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: 138.858px 7.79167px; transform-origin: 138.858px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the discharge or volumetric flow rate, and \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);\"\u003eK\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 48.625px 7.79167px; transform-origin: 48.625px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is a dispersion coefficient, which describes spreading by several mechanisms. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84.45px; 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 42.225px; text-align: left; transform-origin: 384px 42.225px; 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: 376.758px 7.79167px; transform-origin: 376.758px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that returns the dates and times (given as datetimes) between which the water is unsafe to drink (i.e., the concentration exceeds the MCL) at position \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);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 218.967px 7.79167px; transform-origin: 218.967px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e downstream of the spill. Round the times to the nearest second. If the concentration does not exceed the MCL, 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: 103.95px 7.79167px; transform-origin: 103.95px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 103.95px 8.25px; transform-origin: 103.95px 8.25px; \"\u003e'The MCL is not exceeded.' \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 132.242px 7.79167px; transform-origin: 132.242px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ePlease note that the MCL is given in mg/L, whereas other variables are given in SI units. \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-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: 22.95px 7.79167px; transform-origin: 22.95px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eDetails\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-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: 322.725px 7.79167px; transform-origin: 322.725px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eMany empirical formulas are available for the dispersion coefficient. For this problem, use the formula of \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://ascelibrary.org/doi/10.1061/%28ASCE%290733-9429%281998%29124%3A1%2825%29\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eSeo and Cheong (1998)\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: 1.94167px 7.79167px; transform-origin: 1.94167px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 44.1333px; 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 22.0667px; text-align: left; transform-origin: 384px 22.0667px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"190.5\" height=\"44\" alt=\"K = 5.915u*H(B/H)^0.62(U/u*)^1.428\" style=\"width: 190.5px; height: 44px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63.8167px; 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 31.9083px; text-align: left; transform-origin: 384px 31.9083px; 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: 21.0083px 7.79167px; transform-origin: 21.0083px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \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: 174.65px 7.79167px; transform-origin: 174.65px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the width of the channel (assumed rectangular here), \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);\"\u003eH\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 74.675px 7.79167px; transform-origin: 74.675px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the water depth, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"15.5\" height=\"20\" alt=\"u*\" style=\"width: 15.5px; 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: 86.6083px 7.79167px; transform-origin: 86.6083px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the shear velocity, which is related to the shear stress on the wetted perimeter of the channel. In steady uniform flow, the component of the fluid’s weight down the slope will balance the friction on the channel bed, and the shear velocity can be computed as\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.8167px; 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 10.9083px; text-align: left; transform-origin: 384px 10.9083px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"90\" height=\"21\" alt=\"u* = sqrt(gRS0)\" style=\"width: 90px; height: 21px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42.8167px; 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 21.4083px; text-align: left; transform-origin: 384px 21.4083px; 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: 21.0083px 7.79167px; transform-origin: 21.0083px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"87.5\" height=\"19.5\" alt=\"g = 9.81 m/s^2\" style=\"width: 87.5px; height: 19.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 101.917px 7.79167px; transform-origin: 101.917px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the gravitational acceleration, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"15.5\" height=\"20\" alt=\"S0\" style=\"width: 15.5px; 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: 124.483px 7.79167px; transform-origin: 124.483px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the longitudinal slope of the channel, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"59\" height=\"18.5\" alt=\"R = A/P\" style=\"width: 59px; height: 18.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 50.5667px 7.79167px; transform-origin: 50.5667px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the hydraulic radius, and \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: 159.858px 7.79167px; transform-origin: 159.858px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the wetted perimeter. For a rectangular channel, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"78\" height=\"18\" alt=\"P = B + 2H\" style=\"width: 78px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 7.79167px; transform-origin: 3.88333px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\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: 384px 7.79167px; transform-origin: 384px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn addition to assuming steady uniform flow and an unchanging channel, ignore any reaction, decay, or loss of the chemical; this assumption provides a conservative estimate of the time range. In practice, one would include a factor of safety that accounts for uncertainty in the parameters. Nevertheless, the calculations here would form a basis for the advice to the city. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.00833px 7.79167px; transform-origin: 1.00833px 7.79167px; 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 t = spillAlert(x,t0,M,Q,B,H,S0,MCL)\r\n% See the tests for the definitions of the variables and note that the MCL is given in mg/L.\r\n  t = datetime(x*B*H/Q);\r\nend","test_suite":"%% Benzene\r\nx = 80000;                          %  Distance from spill to water intake (m)\r\nt0 = datetime(2018,5,26,10,0,0);    %  Datetime for spill\r\nM = 26000;                          %  Mass of spill (kg)\r\nQ = 5.1;                            %  Discharge (m3/s)\r\nB = 10;                             %  Width of channel (m)\r\nH = 0.8;                            %  Depth of channel (m)\r\nS0 = 1.5e-4;                        %  Longitudinal slope of channel\r\nMCL = 0.005;                        %  Maximum contaminant level (mg/L) \r\nt = spillAlert(x,t0,M,Q,B,H,S0,MCL);\r\nt_correct = datetime([2018 05 27 14 08 05; 2018 05 28 05 06 05])';\r\nassert(isequal(t,t_correct))\r\n\r\n%% Chlorobenzene\r\nx = 79500;                          %  Distance from spill to water intake (m)\r\nt0 = datetime(2018,5,26,10,0,0);    %  Datetime for spill\r\nM = 34000;                          %  Mass of spill (kg)\r\nQ = 5.1;                            %  Discharge (m3/s)\r\nB = 10;                             %  Width of channel (m)\r\nH = 0.8;                            %  Depth of channel (m)\r\nS0 = 1.5e-4;                        %  Longitudinal slope of channel\r\nMCL = 0.1;                          %  Maximum contaminant level (mg/L) \r\nt = spillAlert(x,t0,M,Q,B,H,S0,MCL);\r\nt_correct = datetime([2018 05 27 14 43 39; 2018 05 28 03 41 07])';\r\nassert(isequal(t,t_correct))\r\n\r\n%% Atrazine\r\nx = 14300;                          %  Distance from spill to water intake (m)\r\nt0 = datetime(2020,7,3,16,35,0);    %  Datetime for spill\r\nM = 5600;                           %  Mass of spill (kg)\r\nQ = 3.8;                            %  Discharge (m3/s)\r\nB = 32;                             %  Width of channel (m)\r\nH = 0.4;                            %  Depth of channel (m)\r\nS0 = 6e-4;                          %  Longitudinal slope of channel\r\nMCL = 0.003;                        %  Maximum contaminant level (mg/L) \r\nt = spillAlert(x,t0,M,Q,B,H,S0,MCL);\r\nt_correct = datetime([2020 07 04 00 51 03; 2020 07 04 14 00 39])';\r\nassert(isequal(t,t_correct))\r\n\r\n%% Dalapon\r\nx = 4200;                           %  Distance from spill to water intake (m)\r\nt0 = datetime(2019,6,13,14,23,0);   %  Datetime for spill\r\nM = 3000;                           %  Mass of spill (kg)\r\nQ = 3.8;                            %  Discharge (m3/s)\r\nB = 15;                             %  Width of channel (m)\r\nH = 0.6;                            %  Depth of channel (m)\r\nS0 = 3.2e-4;                        %  Longitudinal slope of channel\r\nMCL = 0.2;                          %  Maximum contaminant level (mg/L) \r\nt = spillAlert(x,t0,M,Q,B,H,S0,MCL);\r\nt_correct = datetime([2019 06 13 15 47 17; 2019 06 13 19 39 06])';\r\nassert(isequal(t,t_correct))\r\n\r\n%% Glyphosate 1\r\nx = 9400;                           %  Distance from spill to water intake (m)\r\nt0 = datetime(2015,5,11,20,12,00);  %  Datetime for spill\r\nM = 300;                            %  Mass of spill (kg)\r\nQ = 23;                             %  Discharge (m3/s)\r\nB = 28;                             %  Width of channel (m)\r\nH = 1.1;                            %  Depth of channel (m)\r\nS0 = 3.2e-4;                        %  Longitudinal slope of channel\r\nMCL = 0.7;                          %  Maximum contaminant level (mg/L) \r\nt = spillAlert(x,t0,M,Q,B,H,S0,MCL);\r\nt_correct = datetime([2015 5 11 22 49 08; 2015 5 12 0 43 38])';\r\nassert(isequal(t,t_correct))\r\n\r\n%% Glyphosate 1\r\nx = 9400;                           %  Distance from spill to water intake (m)\r\nt0 = datetime(2015,5,11,20,12,00);  %  Datetime for spill\r\nM = 300;                            %  Mass of spill (kg)\r\nQ = 23;                             %  Discharge (m3/s)\r\nB = 28;                             %  Width of channel (m)\r\nH = 1.1;                            %  Depth of channel (m)\r\nS0 = 3.2e-4;                        %  Longitudinal slope of channel\r\nMCL = 0.7;                          %  Maximum contaminant level (mg/L) \r\nt = spillAlert(x,t0,M,Q,B,H,S0,MCL);\r\nt_correct = datetime([2015 5 11 22 49 08; 2015 5 12 0 43 38])';\r\nassert(isequal(t,t_correct))\r\n\r\n%% Glyphosate 2\r\nx = 9400;                           %  Distance from spill to water intake (m)\r\nt0 = datetime(2015,5,11,20,12,00);  %  Datetime for spill\r\nM = 80;                             %  Mass of spill (kg)\r\nQ = 23;                             %  Discharge (m3/s)\r\nB = 28;                             %  Width of channel (m)\r\nH = 1.1;                            %  Depth of channel (m)\r\nS0 = 3.2e-4;                        %  Longitudinal slope of channel\r\nMCL = 0.7;                          %  Maximum contaminant level (mg/L) \r\nt = spillAlert(x,t0,M,Q,B,H,S0,MCL);\r\nt_correct = 'The MCL is not exceeded.';\r\nassert(isequal(t,t_correct))\r\n\r\n%% Glyphosate 3\r\nx = 94000;                          %  Distance from spill to water intake (m)\r\nt0 = datetime(2015,5,11,20,12,00);  %  Datetime for spill\r\nM = 300;                            %  Mass of spill (kg)\r\nQ = 37;                             %  Discharge (m3/s)\r\nB = 28;                             %  Width of channel (m)\r\nH = 1.1;                            %  Depth of channel (m)\r\nS0 = 3.2e-4;                        %  Longitudinal slope of channel\r\nMCL = 0.7;                          %  Maximum contaminant level (mg/L) \r\nt = spillAlert(x,t0,M,Q,B,H,S0,MCL);\r\nt_correct = 'The MCL is not exceeded.';\r\nassert(isequal(t,t_correct))\r\n\r\n%% Nitrate \r\nx = 1600;                           %  Distance from spill to water intake (m)\r\nt0 = datetime(2024,4,30,15,20,00);  %  Datetime for spill\r\nM = 140;                            %  Mass of spill (kg)\r\nQ = 14;                             %  Discharge (m3/s)\r\nB = 14;                             %  Width of channel (m)\r\nH = 0.6;                            %  Depth of channel (m)\r\nS0 = 5e-4;                          %  Longitudinal slope of channel\r\nMCL = 10;                           %  Maximum contaminant level (mg/L) \r\nt = spillAlert(x,t0,M,Q,B,H,S0,MCL);\r\nt_correct = datetime([2024 4 30 15 32 22; 2024 4 30 15 38 03])';\r\nassert(isequal(t,t_correct))","published":true,"deleted":false,"likes_count":2,"comments_count":1,"created_by":46909,"edited_by":46909,"edited_at":"2024-05-28T15:13:28.000Z","deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-05-27T17:17:23.000Z","updated_at":"2026-01-25T17:02:57.000Z","published_at":"2024-05-27T17:22:34.000Z","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:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eProblem statement\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:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/54750\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 54750\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e involved determining the length of a stream affected by a spill of a contaminant. Any municipalities within that reach would want to know when water from the river would be safe to drink—for example, below the U.S. Environmental Protection Agency’s \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.epa.gov/ground-water-and-drinking-water/national-primary-drinking-water-regulations\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003emaximum contaminant level\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e (MCL). As in CP 54750, the spill of mass \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\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eM\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e will be assumed instantaneous at position \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=\\\"x = 0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and 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 = 0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003et = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and mixed\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e over the cross section (with 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). Then if the flow is steady and the geometry of the flow does not change downstream, the concentration can be computed with \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=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"C = (M/(A sqrt(4 pi K t)) exp(-(x-Ut)^2/(4Kt))\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC = \\\\frac{M}{A\\\\sqrt{4\\\\pi K t}} \\\\exp\\\\left(-\\\\frac{(x-U t)^2}{4 K t}\\\\right)\u003c/w:t\u003e\u003c/w:r\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\u003ewhere \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=\\\"U = Q/A\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eU = Q/A\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the mean velocity of the river, \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 is the discharge or volumetric flow rate, 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\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is a dispersion coefficient, which describes spreading by several mechanisms. \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 that returns the dates and times (given as datetimes) between which the water is unsafe to drink (i.e., the concentration exceeds the MCL) at position \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\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e downstream of the spill. Round the times to the nearest second. If the concentration does not exceed the MCL, return \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e'The MCL is not exceeded.' \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003ePlease note that the MCL is given in mg/L, whereas other variables are given in SI units. \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\u003eDetails\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\u003eMany empirical formulas are available for the dispersion coefficient. For this problem, use the formula of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://ascelibrary.org/doi/10.1061/%28ASCE%290733-9429%281998%29124%3A1%2825%29\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eSeo and Cheong (1998)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\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=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K = 5.915u*H(B/H)^0.62(U/u*)^1.428\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK = 5.915u_*H\\\\left(\\\\frac{B}{H}\\\\right)^{\\\\!\\\\!0.62}\\\\left(\\\\frac{U}{u_*}\\\\right)^{\\\\!\\\\!1.428}\u003c/w:t\u003e\u003c/w:r\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\u003ewhere \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=\\\"B\\\"/\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 is the width of the channel (assumed rectangular here), \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=\\\"H\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eH\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the water depth, 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\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"u*\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eu_*\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the shear velocity, which is related to the shear stress on the wetted perimeter of the channel. In steady uniform flow, the component of the fluid’s weight down the slope will balance the friction on the channel bed, and the shear velocity can be computed as\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=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"u* = sqrt(gRS0)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eu_* = (g R S_0)^{1/2}\u003c/w:t\u003e\u003c/w:r\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\u003ewhere \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=\\\"g = 9.81 m/s^2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eg = 9.81\\\\,\\\\rm{m/s^2}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the gravitational acceleration, \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=\\\"S0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eS_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the longitudinal slope of the channel, \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=\\\"R = A/P\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eR = A/P\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the hydraulic radius, 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\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 is the wetted perimeter. For a rectangular channel, \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 = B + 2H\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eP = B + 2H\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\u003eIn addition to assuming steady uniform flow and an unchanging channel, ignore any reaction, decay, or loss of the chemical; this assumption provides a conservative estimate of the time range. In practice, one would include a factor of safety that accounts for uncertainty in the parameters. Nevertheless, the calculations here would form a basis for the advice to the city. \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\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":51830,"title":"Find the number of days in a given year","description":"Given a year number (eg. 2000) as input, find how many days are there in the given year.","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: 331.5px 10.4px; transform-origin: 331.5px 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: 308.5px 10.4px; text-align: left; transform-origin: 308.5px 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=\"\"\u003eGiven a year number (eg. 2000) as input, find how many days are there in the given year.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = daysInTheYear(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = 2000;\r\ny_correct = 366;\r\nassert(isequal(daysInTheYear(x),y_correct))\r\n\r\n%%\r\nx = 1000;\r\ny_correct = 365;\r\nassert(isequal(daysInTheYear(x),y_correct))\r\n\r\n%%\r\nx = 2021;\r\ny_correct = 365;\r\nassert(isequal(daysInTheYear(x),y_correct))\r\n\r\n\r\n%%\r\nx = 2020;\r\ny_correct = 366;\r\nassert(isequal(daysInTheYear(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":14038,"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":"2021-06-02T07:51:08.000Z","updated_at":"2026-03-02T14:04:40.000Z","published_at":"2021-06-02T07:51:08.000Z","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 a year number (eg. 2000) as input, find how many days are there in the given year.\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":44514,"title":"Happy Free Wednesday!","description":"Just submit your solution on any Wednesday. \r\n\r\n*Related Challenges:*\r\n\r\n# Happy Free Wednesday!\r\n# Happy Free 2019!\r\n# Happy Free March!\r\n# Happy Free 15th Day of a Month!\r\n# \u003chttps://www.mathworks.com/matlabcentral/cody/problems/44518 Good Morning :)\u003e\r\n# Good Night :)\r\n# Leap Year","description_html":"\u003cp\u003eJust submit your solution on any Wednesday.\u003c/p\u003e\u003cp\u003e\u003cb\u003eRelated Challenges:\u003c/b\u003e\u003c/p\u003e\u003col\u003e\u003cli\u003eHappy Free Wednesday!\u003c/li\u003e\u003cli\u003eHappy Free 2019!\u003c/li\u003e\u003cli\u003eHappy Free March!\u003c/li\u003e\u003cli\u003eHappy Free 15th Day of a Month!\u003c/li\u003e\u003cli\u003e\u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/44518\"\u003eGood Morning :)\u003c/a\u003e\u003c/li\u003e\u003cli\u003eGood Night :)\u003c/li\u003e\u003cli\u003eLeap Year\u003c/li\u003e\u003c/ol\u003e","function_template":"function str = freeWednesday(x)\r\n    % If you're not sure how many days it's been to Wednesday, just click submit button\r\n    if weekday(datetime('today'))==4\r\n        disp('Congrats! It is a happy free Wednesday!')\r\n    else\r\n        daysTill = [3 2 1 0 6 5 4];\r\n        str =  sprintf('You have to wait %d days to solve this problem',daysTill(weekday(datetime('today'))));\r\n    end\r\nend","test_suite":"%%\r\nx = 1;\r\nfreeWednesday(x)\r\nassert(weekday(datetime('today'))==4)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":8703,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":44,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2018-02-07T09:30:21.000Z","updated_at":"2026-02-11T11:57:28.000Z","published_at":"2018-02-07T09:30:21.000Z","restored_at":"2018-03-07T18:37:01.000Z","restored_by":null,"spam":false,"simulink":false,"admin_reviewed":true,"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\u003eJust submit your solution on any Wednesday.\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:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eRelated Challenges:\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=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHappy Free Wednesday!\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=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHappy Free 2019!\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=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHappy Free March!\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=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHappy Free 15th Day of a Month!\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=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/44518\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eGood Morning :)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGood Night :)\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=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eLeap Year\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":44663,"title":"Datetime basics","description":"Generate the datetime scalar representing the current date","description_html":"\u003cp\u003eGenerate the datetime scalar representing the current date\u003c/p\u003e","function_template":"function y = generate_datetime()\r\n  \r\nend","test_suite":"%%\r\ny_correct = datetime('today');\r\nassert(isequal(generate_datetime(),y_correct))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":171559,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":135,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2018-05-29T14:59:26.000Z","updated_at":"2026-03-02T09:12:44.000Z","published_at":"2018-05-29T14:59:26.000Z","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\u003eGenerate the datetime scalar representing the current date\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":58588,"title":"How many revolutions around the earth","description":"Calculate how many revolutions you will around the earth till 1/1/2100.\r\nGiven the birhdate find your age in number of days on 1/1/2100. ","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: 51px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 25.5px; transform-origin: 407px 25.5px; 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: 219.5px 8px; transform-origin: 219.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCalculate how many revolutions you will around the earth till 1/1/2100.\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: 204.5px 8px; transform-origin: 204.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven the birhdate find your age in number of days on 1/1/2100. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function numdays = ageinDays(birthdate)\r\n   numdays = 0;\r\nend\r\n","test_suite":"%%\r\nx = '20-jan-1395';\r\ny_correct = 257477;\r\nassert(isequal( ageinDays(x),y_correct))\r\n\r\n%%\r\nx = '20-jan-1995';\r\ny_correct = 38332;\r\nassert(isequal( ageinDays(x),y_correct))\r\n\r\n%%\r\nx = '20-jan-2005';\r\ny_correct = 34679;\r\nassert(isequal( ageinDays(x),y_correct))\r\n\r\n%%\r\nx = '31-jul-2023';\r\ny_correct = 27913;\r\nassert(isequal( ageinDays(x),y_correct))\r\n\r\n%%\r\nx = '1-nov-2016';\r\ny_correct = 30376;\r\nassert(isequal( ageinDays(x),y_correct))\r\n\r\n%%\r\nx = '14-mar-2050';\r\ny_correct = 18190;\r\nassert(isequal( ageinDays(x),y_correct))\r\n\r\n%Test cases 4-6 added by Dyuman Joshi\r\n%18-07-2023","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":3494818,"edited_by":223089,"edited_at":"2023-07-18T10:59:24.000Z","deleted_by":null,"deleted_at":null,"solvers_count":12,"test_suite_updated_at":"2023-07-18T10:59:24.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2023-07-17T22:34:21.000Z","updated_at":"2024-11-06T13:55:31.000Z","published_at":"2023-07-17T22:34:21.000Z","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\u003eCalculate how many revolutions you will around the earth till 1/1/2100.\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 the birhdate find your age in number of days on 1/1/2100. \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":45848,"title":"What is the current time in Darwin, Australia?","description":"Traders need to track exchange calendars and trading hours in detail, and account for time zone differences and daylight savings offsets. These can be tricky in cities with half-hour and quarter-hour offset to UTC. \u003chttps://en.wikipedia.org/wiki/List_of_stock_exchange_trading_hours\u003e\r\n\r\nMATLAB comes to rescue!\r\n\u003chttps://www.mathworks.com/help/matlab/ref/datetime.html\u003e\r\n\r\nYou are given an array with UTC date and time as *[year, month, day, hour, minute]* and a char array with the name of the time zone.\r\nReturn a char array with the current date and time in the specified time zone, in the format *'MMM-dd-yyyy HH:mm'*.\r\n\r\nFor example, for inputs *[2020 6 9 21 50 0]* and *'Australia/Dawin'*, you should get *'Jun-10-2020 07:20'* in return.","description_html":"\u003cp\u003eTraders need to track exchange calendars and trading hours in detail, and account for time zone differences and daylight savings offsets. These can be tricky in cities with half-hour and quarter-hour offset to UTC. \u003ca href = \"https://en.wikipedia.org/wiki/List_of_stock_exchange_trading_hours\"\u003ehttps://en.wikipedia.org/wiki/List_of_stock_exchange_trading_hours\u003c/a\u003e\u003c/p\u003e\u003cp\u003eMATLAB comes to rescue! \u003ca href = \"https://www.mathworks.com/help/matlab/ref/datetime.html\"\u003ehttps://www.mathworks.com/help/matlab/ref/datetime.html\u003c/a\u003e\u003c/p\u003e\u003cp\u003eYou are given an array with UTC date and time as \u003cb\u003e[year, month, day, hour, minute]\u003c/b\u003e and a char array with the name of the time zone.\r\nReturn a char array with the current date and time in the specified time zone, in the format \u003cb\u003e'MMM-dd-yyyy HH:mm'\u003c/b\u003e.\u003c/p\u003e\u003cp\u003eFor example, for inputs \u003cb\u003e[2020 6 9 21 50 0]\u003c/b\u003e and \u003cb\u003e'Australia/Dawin'\u003c/b\u003e, you should get \u003cb\u003e'Jun-10-2020 07:20'\u003c/b\u003e in return.\u003c/p\u003e","function_template":"function [dateTime] = world_time(td,tz)\r\n  dateTime = now;\r\n  offset = 0;\r\nend","test_suite":"%%\r\ntz = 'Australia/Darwin';\r\ntd = [2020 6 9 21 50 0];\r\ny_correct = 'Jun-10-2020 07:20';\r\nassert(isequal(world_time(td,tz),y_correct))\r\n%%\r\ntz = 'America/St_Johns';\r\ntd = [2000 1 1 10 05 0];\r\ny_correct = 'Jan-01-2000 06:35';\r\nassert(isequal(world_time(td,tz),y_correct))\r\n%%\r\ntz = 'Asia/Calcutta';\r\ntd = [1999 9 9 9 9 9];\r\ny_correct = 'Sep-09-1999 14:39';\r\nassert(isequal(world_time(td,tz),y_correct))\r\n%%\r\ntz = 'Asia/Katmandu';\r\ntd = [2029 12 31 11 59 00];\r\ny_correct = 'Dec-31-2029 17:44';\r\nassert(isequal(world_time(td,tz),y_correct))\r\n%%\r\ntz = 'Atlantic/Bermuda';\r\ntd = [1945 12 05 10 04 00];\r\ny_correct = 'Dec-05-1945 06:04';\r\nassert(isequal(world_time(td,tz),y_correct))","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":452188,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":13,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-06-10T02:51:35.000Z","updated_at":"2025-11-26T20:54:03.000Z","published_at":"2020-06-10T02:51:35.000Z","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\u003eTraders need to track exchange calendars and trading hours in detail, and account for time zone differences and daylight savings offsets. These can be tricky in cities with half-hour and quarter-hour offset to UTC.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/List_of_stock_exchange_trading_hours\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026lt;https://en.wikipedia.org/wiki/List_of_stock_exchange_trading_hours\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\u003eMATLAB comes to rescue!\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/help/matlab/ref/datetime.html\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026lt;https://www.mathworks.com/help/matlab/ref/datetime.html\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\u003eYou are given an array with UTC date and time as\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[year, month, day, hour, minute]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and a char array with the name of the time zone. Return a char array with the current date and time in the specified time zone, in the format\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'MMM-dd-yyyy HH:mm'\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:r\u003e\u003cw:t\u003eFor example, for inputs\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[2020 6 9 21 50 0]\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\u003e'Australia/Dawin'\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, you should get\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'Jun-10-2020 07:20'\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e in return.\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":42352,"title":"Days until next NewYear ball drop","description":"Given a date string in the form 'yyyy-mm-dd' or 'yyyy-mm-dd hh:mm:ss', calculate the number of *days* until the dropping of the NewYear ball at Times Square (i.e., Dec 31st at midnight) of that year. Examples:\r\n\r\n    y = Days2NYE('2014-05-26') = 220 or\r\n    y = Days2NYE('2014-05-26 10:15:45') = 219","description_html":"\u003cp\u003eGiven a date string in the form 'yyyy-mm-dd' or 'yyyy-mm-dd hh:mm:ss', calculate the number of \u003cb\u003edays\u003c/b\u003e until the dropping of the NewYear ball at Times Square (i.e., Dec 31st at midnight) of that year. Examples:\u003c/p\u003e\u003cpre\u003e    y = Days2NYE('2014-05-26') = 220 or\r\n    y = Days2NYE('2014-05-26 10:15:45') = 219\u003c/pre\u003e","function_template":"function y = Days2NYE(x)\r\n  y = ??;\r\nend","test_suite":"%%\r\nx= '2015-05-26';\r\ny_correct = 220;\r\nassert(isequal(Days2NYE(x),y_correct))\r\n\r\n%%\r\nx = '2015-12-30';\r\ny_correct = 2;\r\nassert(isequal(Days2NYE(x),y_correct))\r\n\r\n%%\r\nx = '2014-05-26 10:15:45';\r\ny_correct = 219;\r\nassert(isequal(Days2NYE(x),y_correct))\r\n\r\n%%\r\nx = '2014-12-31 10:15:45';\r\ny_correct = 0;\r\nassert(isequal(Days2NYE(x),y_correct))","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":44306,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":78,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2015-06-02T18:07:53.000Z","updated_at":"2026-03-22T08:23:49.000Z","published_at":"2015-06-02T18:09:23.000Z","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 a date string in the form 'yyyy-mm-dd' or 'yyyy-mm-dd hh:mm:ss', calculate the number of\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\u003edays\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e until the dropping of the NewYear ball at Times Square (i.e., Dec 31st at midnight) of that year. Examples:\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[    y = Days2NYE('2014-05-26') = 220 or\\n    y = Days2NYE('2014-05-26 10:15:45') = 219]]\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":60406,"title":"Alert a city about a spill","description":"Problem statement\r\nCody Problem 54750 involved determining the length of a stream affected by a spill of a contaminant. Any municipalities within that reach would want to know when water from the river would be safe to drink—for example, below the U.S. Environmental Protection Agency’s maximum contaminant level (MCL). As in CP 54750, the spill of mass  will be assumed instantaneous at position  and time  and mixed over the cross section (with area ). Then if the flow is steady and the geometry of the flow does not change downstream, the concentration can be computed with  \r\n\r\nwhere  is the mean velocity of the river,  is the discharge or volumetric flow rate, and  is a dispersion coefficient, which describes spreading by several mechanisms. \r\nWrite a function that returns the dates and times (given as datetimes) between which the water is unsafe to drink (i.e., the concentration exceeds the MCL) at position  downstream of the spill. Round the times to the nearest second. If the concentration does not exceed the MCL, return 'The MCL is not exceeded.' Please note that the MCL is given in mg/L, whereas other variables are given in SI units. \r\nDetails\r\nMany empirical formulas are available for the dispersion coefficient. For this problem, use the formula of Seo and Cheong (1998):\r\n\r\nwhere  is the width of the channel (assumed rectangular here),  is the water depth, and  is the shear velocity, which is related to the shear stress on the wetted perimeter of the channel. In steady uniform flow, the component of the fluid’s weight down the slope will balance the friction on the channel bed, and the shear velocity can be computed as\r\n\r\nwhere  is the gravitational acceleration,  is the longitudinal slope of the channel,  is the hydraulic radius, and  is the wetted perimeter. For a rectangular channel, . \r\nIn addition to assuming steady uniform flow and an unchanging channel, ignore any reaction, decay, or loss of the chemical; this assumption provides a conservative estimate of the time range. In practice, one would include a factor of safety that accounts for uncertainty in the parameters. Nevertheless, the calculations here would form a basis for the advice to the city.  ","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: 690.033px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 345.017px; transform-origin: 407px 345.017px; 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-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: 63.0083px 7.79167px; transform-origin: 63.0083px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eProblem statement\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 105px; 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 52.5px; text-align: left; transform-origin: 384px 52.5px; 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/54750\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eCody Problem 54750\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: 307.167px 7.79167px; transform-origin: 307.167px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e involved determining the length of a stream affected by a spill of a contaminant. Any municipalities within that reach would want to know when water from the river would be safe to drink—for example, below the U.S. Environmental Protection Agency’s \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.epa.gov/ground-water-and-drinking-water/national-primary-drinking-water-regulations\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003emaximum contaminant level\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: 129.9px 7.79167px; transform-origin: 129.9px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (MCL). As in CP 54750, the spill of mass \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);\"\u003eM\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 23.3417px 7.79167px; transform-origin: 23.3417px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e will be assumed instantaneous at position \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"36.5\" height=\"18\" alt=\"x = 0\" style=\"width: 36.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 30.725px 7.79167px; transform-origin: 30.725px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and time \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEMAAAAkCAYAAADSO4eRAAACtklEQVRoQ+1YPUsdQRT1/QAJif6CGLuAKZSAaKuStAG1SyH4QZogKGqtYMoUxuQPJAEtExTBRhs/igQskxSpo6J/QM+RO8+7+2Z2Z7Lre/qchcuws/fenXvmzL0zU2mJTxWBSsTiGoEIhmJDBCOCYU8OkRn3iBl9iLVX4v2Ldgty7CoazcqMFwj4PeQU8laCf4N2ADIH+WgDpBnBGEGgnyGHkKEUEzbwPghZgiykAWk2MB4LCA/RvoR8TwXM77+l7xnan/q7LxiLYlSDpmv9Nah/Bf+dlOXR6cgPB+jvFtB6QsEwtBuF4ZcGBenz2zYo/RPFTVkiNjtO7Lx86ED7xyjlMWMGisui3O5A2meg9dAxk8Z/WXOCDELrTaCvmkxdYNBgWuhEH1xnn8TZmkazHlF6/kNPXCLIlD3L7Y70fUXLWK8eGxhMMq8gDyCGTqTdtti8Cxicp6pTjXsD36VpKgWd+YLBSX6SBYb5xlr9TV760e4GRnYRqG9TT8xcjj8NRlZ+64KfH+KL+5BHPmCYREMDV2bOGh9pW/Q5goN0eXT51GDUlM2UkZkobzB+wQGzbcjsFA2+iL0Gw7bHML71XsMLDG2Qtf6KDL5sW+aWYXFaas7Q5SePcmUH9b/+bqSacDBmJ5fItoGjLCNnhFQTnfBnMVZX1XPqufYZJ3DG/f0HyFQgCEa93tVE70Cz8pxmUKJK2sDQpceUKPYlDjUeAJXBjJBqohmdVQGDzibj8LoqwbKatEK4Jedx+LY/IafWmr2TjRkmK/M+YAyyDnkOcd4Q3TKEsu4zTGze9xm6XjOBvoaE7j4bjQ8BYRHYh/DG6xzCmy6WXmdydeUM3gadQXgouyuMSE8AEyoZ/VQ+MP/sZcWTd4Rv9AzX9f8RDAV3BCOCYV99kRmRGZEZuZUpLpO4TOwkuQRnmo0l4jm74gAAAABJRU5ErkJggg==\" width=\"33.5\" height=\"18\" alt=\"t = 0\" style=\"width: 33.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 34.2333px 7.79167px; transform-origin: 34.2333px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and mixed\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 104.625px 7.79167px; transform-origin: 104.625px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e over the cross section (with 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: 62.6083px 7.79167px; transform-origin: 62.6083px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e). Then if the flow is steady and the geometry of the flow does not change downstream, the concentration can be computed 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: 1.94167px 7.79167px; transform-origin: 1.94167px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 40px; 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 20px; text-align: left; transform-origin: 384px 20px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"204.5\" height=\"40\" alt=\"C = (M/(A sqrt(4 pi K t)) exp(-(x-Ut)^2/(4Kt))\" style=\"width: 204.5px; height: 40px;\"\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-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: 21.0083px 7.79167px; transform-origin: 21.0083px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"61.5\" height=\"18.5\" alt=\"U = Q/A\" style=\"width: 61.5px; height: 18.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 101.892px 7.79167px; transform-origin: 101.892px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the mean velocity of the river, \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: 138.858px 7.79167px; transform-origin: 138.858px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the discharge or volumetric flow rate, and \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);\"\u003eK\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 48.625px 7.79167px; transform-origin: 48.625px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is a dispersion coefficient, which describes spreading by several mechanisms. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84.45px; 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 42.225px; text-align: left; transform-origin: 384px 42.225px; 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: 376.758px 7.79167px; transform-origin: 376.758px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that returns the dates and times (given as datetimes) between which the water is unsafe to drink (i.e., the concentration exceeds the MCL) at position \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);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 218.967px 7.79167px; transform-origin: 218.967px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e downstream of the spill. Round the times to the nearest second. If the concentration does not exceed the MCL, 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: 103.95px 7.79167px; transform-origin: 103.95px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 103.95px 8.25px; transform-origin: 103.95px 8.25px; \"\u003e'The MCL is not exceeded.' \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 132.242px 7.79167px; transform-origin: 132.242px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ePlease note that the MCL is given in mg/L, whereas other variables are given in SI units. \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-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: 22.95px 7.79167px; transform-origin: 22.95px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eDetails\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-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: 322.725px 7.79167px; transform-origin: 322.725px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eMany empirical formulas are available for the dispersion coefficient. For this problem, use the formula of \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://ascelibrary.org/doi/10.1061/%28ASCE%290733-9429%281998%29124%3A1%2825%29\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eSeo and Cheong (1998)\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: 1.94167px 7.79167px; transform-origin: 1.94167px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 44.1333px; 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 22.0667px; text-align: left; transform-origin: 384px 22.0667px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"190.5\" height=\"44\" alt=\"K = 5.915u*H(B/H)^0.62(U/u*)^1.428\" style=\"width: 190.5px; height: 44px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63.8167px; 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 31.9083px; text-align: left; transform-origin: 384px 31.9083px; 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: 21.0083px 7.79167px; transform-origin: 21.0083px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \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: 174.65px 7.79167px; transform-origin: 174.65px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the width of the channel (assumed rectangular here), \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);\"\u003eH\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 74.675px 7.79167px; transform-origin: 74.675px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the water depth, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"15.5\" height=\"20\" alt=\"u*\" style=\"width: 15.5px; 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: 86.6083px 7.79167px; transform-origin: 86.6083px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the shear velocity, which is related to the shear stress on the wetted perimeter of the channel. In steady uniform flow, the component of the fluid’s weight down the slope will balance the friction on the channel bed, and the shear velocity can be computed as\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.8167px; 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 10.9083px; text-align: left; transform-origin: 384px 10.9083px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAALQAAAAqCAYAAAAaoXEBAAAJaklEQVR4Xu2cR4ttRRDH530AMS5VxLAQBcW8UEHBDKIoz4gMKOat+bkziwhiBkHECC5EzIKCujGiuHBhQFy4MuIH0Po9zv9ZU7dPh7lz5947dEMxM+d0qK7+d3WFPrNtpZcugS0kgW1baC59Kl0CKx3QHQRbSgId0FtqOftkOqA7BmYtgb1tgH2NvmkY6HGr+6LRJ6HNEfb3bka/Gv2U6q8DukHKvWqzBK6xFvcaPWF0R0PrH6zuwa7+xfY7IN/TPbvHfn8mArsDukHKvWq1BE60mmcZnW50jBHgqwU04N3f6IFhtLPt5yNGFxih5fn7+QHcbJTrPVcd0NVrtFNDfGT0cn2TLVMTEF1hdIPR7w2zutnq3t8I6HcGkMqk+Nz+vmoAs4aGnzeN/jQ6xPPUAV23OrMEs+zCEifRnizVx3Y91FXy7dGg3zWCkzYPG53Z0K4V0Ada38iaMVToQ9raz/nf4Y99OqBLUFj7HgGjCWqPzLbeV1YA9Haj20NDxvzMCFvyoIEHToenjHIOFsDbYXTG0IY+KPTzitHRw7v1KDPMgVUjD7jcfFsBTf+UmlMQQP84zGsXD+uZVG4CW+0dAr7L6HijlqN2PXLgqAWElC+MjnWd4Fw9OfwN0M81Smls+H1pqHet/QT8KmycD41wrN41qgVlnAt8fmCU0pqxbiug6buGL+bytdGEbd4BPQ49juzvjXA6ajTGeE91bzygb0kAhpPiuqErAHmZkd9k4hfAooml7fzoAnyLkxa5xyxAMx5pVArFtQA6ZW6MSY5+bzVaYz9TuQN6HGwI7WojHz6qg2Z7LcD4m2t2kv0eNbAcIVVbYzvaQ/9+DLAa5xyr/1Y7m7tasMH3MCpp0xZAU/cXo5Ly0Ma9PDWHDuj0qkpot9lrf2xPgYFsUw9GTIq9ErWxjT92z7GrfXJB4KHKRDjLtcP2jG1b5yV+S/20ADrGnsd4AvCYTsl16YBOi01Hc82x2gqGVP277aGcwjFzIdrREfTefmZTEP9NZdPGogat82BjlEyXWkCzWS81WhNTTjBEfwfk6tUAGtuGdGO0lzDM5cS8OiK8ViEtSn20AEmBlKas4ZEFovyTkFuqPbFWAEiJzhzPODE+NUIjUlI2trehqYNj2RJiq5mXr4PNz5jeeY191AJ6LNXt+2PDnmcUfQPw+bfRTn8iBWiYvNLoVCMBtuSk1GyMVoHVxmdL/bbGb+nvDyPCXSUb0Y8Nv5goFxmhZb8ywganPD38RPDxqJSTpb7iMc56AB4BfkyD095rcf7G9LjTaBYRGp0qubWvBXTJ3FC0KfozyOYFv045ZvwxGI/eGo+6BLTSe+/1l+qOvR+zR3P9yXHK2aGxvT/uvay8bYzGfM8oxrOjqUBIjsKFnpONeK87DCnFEnnx0RDesQFaM3w18hZYUw6s2ouXnCxjqjuOLd8B+cWNeZw9W+Pn5AAtQKVAkYt31gijpg4biiTANOWvARAtfUiANeChX69hYxvvyI1FFjwAlUxhoQRiAPmcUUtUIoJ6FppaGEgBGpmcZnT+IHjW4TUjTr1o18dUt18rlMtjRkRUxsqa8GUO0By7YzFNrz03y3FqAeU0dVsB7U+yaC74jT8GaMkZngUOD8iWk8LPO4K6doPWyq5VTmP91iZTqvgaA7QyMXRyiZGPDXqts54jvYqxOVZqXSht7pjdYwoeVKkQl5cz9bUe/vnEBZwG2USzLad85MjW+hytckqx3ZLqrpr2GKC9cxEXwgsp56BUMbCAlVoXis2OIxgBXeNneDnHdDSOkqIaUanUii1GR1JhNt1ZJlFxuBGO7KpRCdiSUyoqU8tfztyo7WNNvTFAa5Hi5Y8Y3F+voGuYnVeUoxXQMiuQlb/zIVMkPvdzl5x5Fk2CHNh9H4AipsH9++iYpu6IeHNIaeVTrJNcalv85ZzC3Dq3pLpr8LKzzhigZdf5HS2NwyLoTkEpU1TNSKLivKIcsELSoMV2FXhpw6dDNxqhtVN3LvxUdQWSZxEYpXAebRSRiWnwKE6N408RrSd1fbxd45ZOX0U51utD1aa6mzCUArS33/zOVcoRz5X49MTVvaaRy5XnFeWAM457qDYOra8qCMv9bES8+X2j5Hdvw9RrfBGvwVNHu/oogUqA9ptUJ0vq5p0UWk5hyT+YRQ6ijI6RGilm/FGn9zzjCEIIUThM7A2jGFZSooGUbm5h1838DBu2LJaO9NbMXE2620dJUv3X3J7zJodXUBo/ZVfrdMxdYiK7SVy4dtPPcLn+7zoFaC2mjifAfJMR9iHBfu6hUpjsfkYAN5WD18aY9mbXpggiDCIQlDQfzbxphLZ71oivQUpXK326O3cnwof1Ij/+QlLKlvVZxmhCiO8coMf4klkyjUM4k3VNAdovEGYFRc6OPyb1zqcjATEmCZfiuccA+LHvCLKvGvGxY0uCYCaTruwUINV8rRwdZXUPuJFD6SI+9XP2ug/9RZtca8VaYB7IhqfPw4xQRDxP2cPTAFonQ8l2rxT1xlUbs6FJJ1LI7sT7qQiYHcpXC3xG7tORsiVxMkjh8g3aQ0Z8RYHQufCzLOaHvP3cBSV9gcxc2cDbjXAGFW5Dhj4ShNy4J5PKgH5pz982Sv0vCj40VUF++p8VrIXuanBSnmCEaajMGms0dnFsGkBzukCl23GO7c35dVYGvexnAHyfUQT+5sxuulEUw33QukndvZXmTJklaDDek2nNhe2m43C61uI/Z3KksoucSK8bTXwtMh07G9N6owENCC4ctAQcckOMaAFaBceRK5CzuPm1MdKY7GVs8WRm5EwFb4os3NFsU5WPkwK07Ptol2uT77D2pS9LZrUm2X43GtByUrDZiG7gWAJq/ubnMjqIaNtVo/hpfc3/m0h+mTyXlZ4cVOHZVMpekayID7Q6ZeFMDU1vowHNDiYSgocvx0FHMhqrlE5dkLWeYIONeoBbSEVBcokTacBZZlOnlZfsaB9v1tyi5mY9uc66sGBGGBsNaC/g3PXCaRdiHu2Zz+5Gsqdlg3L6POo2K44fZhcafNFPJHhFQ2M+4FxSADnFp8gBOfc8av51wTzWZteYswT0XCe2SYPrM7SjbDxFFohWfGtEpnAZ/AV9ocRmpcD7QtrHNWvaAV0jpV5naSTQAb00S9UZrZFAB3SNlHqdpZFAB/TSLFVntEYCHdA1Uup1lkYCHdBLs1Sd0RoJdEDXSKnXWRoJ/Acoa1NJ6a/jDwAAAABJRU5ErkJggg==\" width=\"90\" height=\"21\" alt=\"u* = sqrt(gRS0)\" style=\"width: 90px; height: 21px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42.8167px; 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 21.4083px; text-align: left; transform-origin: 384px 21.4083px; 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: 21.0083px 7.79167px; transform-origin: 21.0083px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"87.5\" height=\"19.5\" alt=\"g = 9.81 m/s^2\" style=\"width: 87.5px; height: 19.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 101.917px 7.79167px; transform-origin: 101.917px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the gravitational acceleration, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"15.5\" height=\"20\" alt=\"S0\" style=\"width: 15.5px; 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: 124.483px 7.79167px; transform-origin: 124.483px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the longitudinal slope of the channel, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"59\" height=\"18.5\" alt=\"R = A/P\" style=\"width: 59px; height: 18.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 50.5667px 7.79167px; transform-origin: 50.5667px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the hydraulic radius, and \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: 159.858px 7.79167px; transform-origin: 159.858px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the wetted perimeter. For a rectangular channel, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"78\" height=\"18\" alt=\"P = B + 2H\" style=\"width: 78px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 7.79167px; transform-origin: 3.88333px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\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: 384px 7.79167px; transform-origin: 384px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn addition to assuming steady uniform flow and an unchanging channel, ignore any reaction, decay, or loss of the chemical; this assumption provides a conservative estimate of the time range. In practice, one would include a factor of safety that accounts for uncertainty in the parameters. Nevertheless, the calculations here would form a basis for the advice to the city. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.00833px 7.79167px; transform-origin: 1.00833px 7.79167px; 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 t = spillAlert(x,t0,M,Q,B,H,S0,MCL)\r\n% See the tests for the definitions of the variables and note that the MCL is given in mg/L.\r\n  t = datetime(x*B*H/Q);\r\nend","test_suite":"%% Benzene\r\nx = 80000;                          %  Distance from spill to water intake (m)\r\nt0 = datetime(2018,5,26,10,0,0);    %  Datetime for spill\r\nM = 26000;                          %  Mass of spill (kg)\r\nQ = 5.1;                            %  Discharge (m3/s)\r\nB = 10;                             %  Width of channel (m)\r\nH = 0.8;                            %  Depth of channel (m)\r\nS0 = 1.5e-4;                        %  Longitudinal slope of channel\r\nMCL = 0.005;                        %  Maximum contaminant level (mg/L) \r\nt = spillAlert(x,t0,M,Q,B,H,S0,MCL);\r\nt_correct = datetime([2018 05 27 14 08 05; 2018 05 28 05 06 05])';\r\nassert(isequal(t,t_correct))\r\n\r\n%% Chlorobenzene\r\nx = 79500;                          %  Distance from spill to water intake (m)\r\nt0 = datetime(2018,5,26,10,0,0);    %  Datetime for spill\r\nM = 34000;                          %  Mass of spill (kg)\r\nQ = 5.1;                            %  Discharge (m3/s)\r\nB = 10;                             %  Width of channel (m)\r\nH = 0.8;                            %  Depth of channel (m)\r\nS0 = 1.5e-4;                        %  Longitudinal slope of channel\r\nMCL = 0.1;                          %  Maximum contaminant level (mg/L) \r\nt = spillAlert(x,t0,M,Q,B,H,S0,MCL);\r\nt_correct = datetime([2018 05 27 14 43 39; 2018 05 28 03 41 07])';\r\nassert(isequal(t,t_correct))\r\n\r\n%% Atrazine\r\nx = 14300;                          %  Distance from spill to water intake (m)\r\nt0 = datetime(2020,7,3,16,35,0);    %  Datetime for spill\r\nM = 5600;                           %  Mass of spill (kg)\r\nQ = 3.8;                            %  Discharge (m3/s)\r\nB = 32;                             %  Width of channel (m)\r\nH = 0.4;                            %  Depth of channel (m)\r\nS0 = 6e-4;                          %  Longitudinal slope of channel\r\nMCL = 0.003;                        %  Maximum contaminant level (mg/L) \r\nt = spillAlert(x,t0,M,Q,B,H,S0,MCL);\r\nt_correct = datetime([2020 07 04 00 51 03; 2020 07 04 14 00 39])';\r\nassert(isequal(t,t_correct))\r\n\r\n%% Dalapon\r\nx = 4200;                           %  Distance from spill to water intake (m)\r\nt0 = datetime(2019,6,13,14,23,0);   %  Datetime for spill\r\nM = 3000;                           %  Mass of spill (kg)\r\nQ = 3.8;                            %  Discharge (m3/s)\r\nB = 15;                             %  Width of channel (m)\r\nH = 0.6;                            %  Depth of channel (m)\r\nS0 = 3.2e-4;                        %  Longitudinal slope of channel\r\nMCL = 0.2;                          %  Maximum contaminant level (mg/L) \r\nt = spillAlert(x,t0,M,Q,B,H,S0,MCL);\r\nt_correct = datetime([2019 06 13 15 47 17; 2019 06 13 19 39 06])';\r\nassert(isequal(t,t_correct))\r\n\r\n%% Glyphosate 1\r\nx = 9400;                           %  Distance from spill to water intake (m)\r\nt0 = datetime(2015,5,11,20,12,00);  %  Datetime for spill\r\nM = 300;                            %  Mass of spill (kg)\r\nQ = 23;                             %  Discharge (m3/s)\r\nB = 28;                             %  Width of channel (m)\r\nH = 1.1;                            %  Depth of channel (m)\r\nS0 = 3.2e-4;                        %  Longitudinal slope of channel\r\nMCL = 0.7;                          %  Maximum contaminant level (mg/L) \r\nt = spillAlert(x,t0,M,Q,B,H,S0,MCL);\r\nt_correct = datetime([2015 5 11 22 49 08; 2015 5 12 0 43 38])';\r\nassert(isequal(t,t_correct))\r\n\r\n%% Glyphosate 1\r\nx = 9400;                           %  Distance from spill to water intake (m)\r\nt0 = datetime(2015,5,11,20,12,00);  %  Datetime for spill\r\nM = 300;                            %  Mass of spill (kg)\r\nQ = 23;                             %  Discharge (m3/s)\r\nB = 28;                             %  Width of channel (m)\r\nH = 1.1;                            %  Depth of channel (m)\r\nS0 = 3.2e-4;                        %  Longitudinal slope of channel\r\nMCL = 0.7;                          %  Maximum contaminant level (mg/L) \r\nt = spillAlert(x,t0,M,Q,B,H,S0,MCL);\r\nt_correct = datetime([2015 5 11 22 49 08; 2015 5 12 0 43 38])';\r\nassert(isequal(t,t_correct))\r\n\r\n%% Glyphosate 2\r\nx = 9400;                           %  Distance from spill to water intake (m)\r\nt0 = datetime(2015,5,11,20,12,00);  %  Datetime for spill\r\nM = 80;                             %  Mass of spill (kg)\r\nQ = 23;                             %  Discharge (m3/s)\r\nB = 28;                             %  Width of channel (m)\r\nH = 1.1;                            %  Depth of channel (m)\r\nS0 = 3.2e-4;                        %  Longitudinal slope of channel\r\nMCL = 0.7;                          %  Maximum contaminant level (mg/L) \r\nt = spillAlert(x,t0,M,Q,B,H,S0,MCL);\r\nt_correct = 'The MCL is not exceeded.';\r\nassert(isequal(t,t_correct))\r\n\r\n%% Glyphosate 3\r\nx = 94000;                          %  Distance from spill to water intake (m)\r\nt0 = datetime(2015,5,11,20,12,00);  %  Datetime for spill\r\nM = 300;                            %  Mass of spill (kg)\r\nQ = 37;                             %  Discharge (m3/s)\r\nB = 28;                             %  Width of channel (m)\r\nH = 1.1;                            %  Depth of channel (m)\r\nS0 = 3.2e-4;                        %  Longitudinal slope of channel\r\nMCL = 0.7;                          %  Maximum contaminant level (mg/L) \r\nt = spillAlert(x,t0,M,Q,B,H,S0,MCL);\r\nt_correct = 'The MCL is not exceeded.';\r\nassert(isequal(t,t_correct))\r\n\r\n%% Nitrate \r\nx = 1600;                           %  Distance from spill to water intake (m)\r\nt0 = datetime(2024,4,30,15,20,00);  %  Datetime for spill\r\nM = 140;                            %  Mass of spill (kg)\r\nQ = 14;                             %  Discharge (m3/s)\r\nB = 14;                             %  Width of channel (m)\r\nH = 0.6;                            %  Depth of channel (m)\r\nS0 = 5e-4;                          %  Longitudinal slope of channel\r\nMCL = 10;                           %  Maximum contaminant level (mg/L) \r\nt = spillAlert(x,t0,M,Q,B,H,S0,MCL);\r\nt_correct = datetime([2024 4 30 15 32 22; 2024 4 30 15 38 03])';\r\nassert(isequal(t,t_correct))","published":true,"deleted":false,"likes_count":2,"comments_count":1,"created_by":46909,"edited_by":46909,"edited_at":"2024-05-28T15:13:28.000Z","deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-05-27T17:17:23.000Z","updated_at":"2026-01-25T17:02:57.000Z","published_at":"2024-05-27T17:22:34.000Z","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:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eProblem statement\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:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/54750\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 54750\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e involved determining the length of a stream affected by a spill of a contaminant. Any municipalities within that reach would want to know when water from the river would be safe to drink—for example, below the U.S. Environmental Protection Agency’s \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.epa.gov/ground-water-and-drinking-water/national-primary-drinking-water-regulations\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003emaximum contaminant level\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e (MCL). As in CP 54750, the spill of mass \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\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eM\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e will be assumed instantaneous at position \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=\\\"x = 0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and 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 = 0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003et = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and mixed\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e over the cross section (with 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). Then if the flow is steady and the geometry of the flow does not change downstream, the concentration can be computed with \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=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"C = (M/(A sqrt(4 pi K t)) exp(-(x-Ut)^2/(4Kt))\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC = \\\\frac{M}{A\\\\sqrt{4\\\\pi K t}} \\\\exp\\\\left(-\\\\frac{(x-U t)^2}{4 K t}\\\\right)\u003c/w:t\u003e\u003c/w:r\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\u003ewhere \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=\\\"U = Q/A\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eU = Q/A\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the mean velocity of the river, \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 is the discharge or volumetric flow rate, 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\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is a dispersion coefficient, which describes spreading by several mechanisms. \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 that returns the dates and times (given as datetimes) between which the water is unsafe to drink (i.e., the concentration exceeds the MCL) at position \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\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e downstream of the spill. Round the times to the nearest second. If the concentration does not exceed the MCL, return \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e'The MCL is not exceeded.' \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003ePlease note that the MCL is given in mg/L, whereas other variables are given in SI units. \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\u003eDetails\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\u003eMany empirical formulas are available for the dispersion coefficient. For this problem, use the formula of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://ascelibrary.org/doi/10.1061/%28ASCE%290733-9429%281998%29124%3A1%2825%29\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eSeo and Cheong (1998)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\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=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K = 5.915u*H(B/H)^0.62(U/u*)^1.428\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK = 5.915u_*H\\\\left(\\\\frac{B}{H}\\\\right)^{\\\\!\\\\!0.62}\\\\left(\\\\frac{U}{u_*}\\\\right)^{\\\\!\\\\!1.428}\u003c/w:t\u003e\u003c/w:r\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\u003ewhere \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=\\\"B\\\"/\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 is the width of the channel (assumed rectangular here), \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=\\\"H\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eH\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the water depth, 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\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"u*\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eu_*\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the shear velocity, which is related to the shear stress on the wetted perimeter of the channel. In steady uniform flow, the component of the fluid’s weight down the slope will balance the friction on the channel bed, and the shear velocity can be computed as\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=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"u* = sqrt(gRS0)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eu_* = (g R S_0)^{1/2}\u003c/w:t\u003e\u003c/w:r\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\u003ewhere \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=\\\"g = 9.81 m/s^2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eg = 9.81\\\\,\\\\rm{m/s^2}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the gravitational acceleration, \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=\\\"S0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eS_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the longitudinal slope of the channel, \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=\\\"R = A/P\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eR = A/P\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the hydraulic radius, 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\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 is the wetted perimeter. For a rectangular channel, \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 = B + 2H\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eP = B + 2H\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\u003eIn addition to assuming steady uniform flow and an unchanging channel, ignore any reaction, decay, or loss of the chemical; this assumption provides a conservative estimate of the time range. In practice, one would include a factor of safety that accounts for uncertainty in the parameters. Nevertheless, the calculations here would form a basis for the advice to the city. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e 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