// Numbas version: exam_results_page_options
{"name": "Harry's copy of Differentiation 18 - Applications", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"question_groups": [{"pickQuestions": 0, "name": "", "pickingStrategy": "all-ordered", "questions": []}], "variablesTest": {"maxRuns": 100, "condition": ""}, "name": "Harry's copy of Differentiation 18 - Applications", "parts": [{"type": "gapfill", "variableReplacementStrategy": "originalfirst", "marks": 0, "variableReplacements": [], "gaps": [{"showpreview": true, "variableReplacementStrategy": "originalfirst", "expectedvariablenames": ["x"], "variableReplacements": [], "checkingaccuracy": 0.001, "vsetrangepoints": 5, "showCorrectAnswer": true, "type": "jme", "marks": "2", "checkingtype": "absdiff", "scripts": {}, "answer": "{v}/x^2", "vsetrange": [0, 1], "checkvariablenames": true, "answersimplification": "all"}], "prompt": "<p>The height of the tank</p>\n<p>$h=$&nbsp;[[0]] m</p>\n<p></p>", "showCorrectAnswer": true, "scripts": {}}, {"type": "gapfill", "variableReplacementStrategy": "originalfirst", "marks": 0, "variableReplacements": [], "gaps": [{"showpreview": true, "variableReplacementStrategy": "originalfirst", "expectedvariablenames": ["x"], "variableReplacements": [], "checkingaccuracy": 0.001, "vsetrangepoints": 5, "showCorrectAnswer": true, "type": "jme", "marks": "2", "checkingtype": "absdiff", "scripts": {}, "answer": "x^2+4{v}/x", "vsetrange": [0, 1], "checkvariablenames": true, "answersimplification": "all"}], "prompt": "<p>The surface area of the tank</p>\n<p>$S=$ [[0]]&nbsp;$\\text{m}^2$</p>", "showCorrectAnswer": true, "scripts": {}}, {"type": "gapfill", "stepsPenalty": "1", "variableReplacementStrategy": "originalfirst", "marks": 0, "variableReplacements": [], "gaps": [{"allowFractions": false, "variableReplacementStrategy": "originalfirst", "precisionMessage": "You have not given your answer to the correct precision.", "variableReplacements": [], "precision": "2", "showCorrectAnswer": true, "type": "numberentry", "precisionType": "dp", "showPrecisionHint": false, "correctAnswerFraction": false, "precisionPartialCredit": "50", "minValue": "{a}", "strictPrecision": false, "scripts": {}, "maxValue": "{a}", "marks": "2"}, {"showpreview": true, "variableReplacementStrategy": "originalfirst", "expectedvariablenames": ["x"], "variableReplacements": [], "checkingaccuracy": 0.001, "vsetrangepoints": 5, "showCorrectAnswer": true, "type": "jme", "marks": 1, "checkingtype": "absdiff", "scripts": {}, "answer": "2x-4{v}/x^2", "vsetrange": [0, 1], "checkvariablenames": true, "answersimplification": "all"}, {"showpreview": true, "variableReplacementStrategy": "originalfirst", "expectedvariablenames": ["x"], "variableReplacements": [], "checkingaccuracy": 0.001, "vsetrangepoints": 5, "showCorrectAnswer": true, "type": "jme", "marks": 1, "checkingtype": "absdiff", "scripts": {}, "answer": "2+8{v}/x^3", "vsetrange": [0, 1], "checkvariablenames": true, "answersimplification": "all"}, {"showpreview": false, "variableReplacementStrategy": "originalfirst", "expectedvariablenames": ["Y", "N", "U"], "variableReplacements": [], "checkingaccuracy": 0.001, "vsetrangepoints": 5, "showCorrectAnswer": true, "type": "jme", "marks": 1, "checkingtype": "absdiff", "scripts": {}, "answer": "Y", "vsetrange": [0, 1], "checkvariablenames": true, "answersimplification": "all"}, {"allowFractions": false, "variableReplacementStrategy": "originalfirst", "precisionMessage": "You have not given your answer to the correct precision.", "variableReplacements": [], "precision": "2", "showCorrectAnswer": true, "type": "numberentry", "precisionType": "dp", "showPrecisionHint": false, "correctAnswerFraction": false, "precisionPartialCredit": "50", "minValue": "{a}^2+4({v}/{a})", "strictPrecision": false, "scripts": {}, "maxValue": "{a}^2+4({v}/{a})", "marks": "1"}], "prompt": "<p>Given that the surface area is a minimum, find the value of $x$.</p>\n<p>$S'(x)=$&nbsp;[[1]]</p>\n<p>Therefore,</p>\n<p>$x=$&nbsp;[[0]] &nbsp; &nbsp;&nbsp;(give your answer to 2 decimal places)</p>\n<p>Check this is a minimum.</p>\n<p>$S''(x)=$&nbsp;[[2]]</p>\n<p>Substitute your value for $x$ into $S''(x)$ and determine whether is it a minimum.</p>\n<p>Type '$Y$' for yes, '$N$' for no, or '$U$' for undefined.</p>\n<p>[[3]]</p>\n<p></p>\n<p>Hence, the minimum area of metal used is</p>\n<p>$A_{min}=$&nbsp;[[4]] &nbsp; &nbsp;&nbsp;(give your answer to 2 decimal places)</p>", "showCorrectAnswer": true, "steps": [{"type": "information", "variableReplacementStrategy": "originalfirst", "marks": 0, "variableReplacements": [], "prompt": "<p><em>Hint:</em> find $x$ at stationary point</p>", "showCorrectAnswer": true, "scripts": {}}], "scripts": {}}], "rulesets": {}, "tags": [], "ungrouped_variables": ["v", "a"], "variable_groups": [], "statement": "<p>An&nbsp;<em>open</em> metal tank of square base has a volume of $\\var{v}\\text{ m}^3$</p>\n<p><strong>Given that the square base has sides of length $x$ metres, find expressions, in terms of $x$, for the following.</strong></p>", "functions": {}, "type": "question", "showQuestionGroupNames": false, "metadata": {"notes": "", "licence": "Creative Commons Attribution 4.0 International", "description": "<p>Another practical application of differentiation</p>"}, "variables": {"v": {"group": "Ungrouped variables", "definition": "random(100..200)", "name": "v", "templateType": "anything", "description": ""}, "a": {"group": "Ungrouped variables", "definition": "siground((2v)^(1/3),3)", "name": "a", "templateType": "anything", "description": ""}}, "preamble": {"js": "", "css": ""}, "advice": "<p>This section draws on the skills learnt the previous parts of the&nbsp;<em>'Differentiation'</em> series of questions, and some geometry knowledge.</p>\n<p>The hint&nbsp;under the steps should be all the extra information you need.</p>", "contributors": [{"name": "Harry Flynn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/976/"}]}]}], "contributors": [{"name": "Harry Flynn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/976/"}]}