// Numbas version: finer_feedback_settings
{"name": "PreCal Application of Polynomials Cubic Max Box Volume", "extensions": [], "custom_part_types": [], "resources": [["question-resources/boxCutSquares.png", "/srv/numbas/media/question-resources/boxCutSquares.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"tags": [], "metadata": {"licence": "All rights reserved", "description": ""}, "ungrouped_variables": ["L", "W", "aCut", "bCut", "cCut", "xCut1", "xCut2", "volMax"], "rulesets": {}, "name": "PreCal Application of Polynomials Cubic Max Box Volume", "advice": "", "parts": [{"showFeedbackIcon": true, "useCustomName": false, "adaptiveMarkingPenalty": 0, "customName": "", "showCorrectAnswer": true, "customMarkingAlgorithm": "", "scripts": {}, "gaps": [{"showFeedbackIcon": true, "mustBeReduced": false, "precision": "3", "adaptiveMarkingPenalty": 0, "correctAnswerStyle": "plain", "notationStyles": ["plain", "en", "si-en"], "precisionType": "dp", "unitTests": [], "type": "numberentry", "strictPrecision": true, "useCustomName": false, "allowFractions": false, "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": "75", "mustBeReducedPC": 0, "customName": "", "showCorrectAnswer": true, "maxValue": "xCut1", "minValue": "xCut1", "customMarkingAlgorithm": "", "scripts": {}, "variableReplacements": [], "correctAnswerFraction": false, "extendBaseMarkingAlgorithm": true, "precisionMessage": "You have not given your answer to the correct precision.", "showPrecisionHint": true, "marks": 1}, {"showFeedbackIcon": true, "mustBeReduced": false, "precision": "3", "adaptiveMarkingPenalty": 0, "correctAnswerStyle": "plain", "notationStyles": ["plain", "en", "si-en"], "precisionType": "dp", "unitTests": [], "type": "numberentry", "strictPrecision": true, "useCustomName": false, "allowFractions": false, "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": "75", "mustBeReducedPC": 0, "customName": "", "showCorrectAnswer": true, "maxValue": "volMax", "minValue": "volMax", "customMarkingAlgorithm": "", "scripts": {}, "variableReplacements": [], "correctAnswerFraction": false, "extendBaseMarkingAlgorithm": true, "precisionMessage": "You have not given your answer to the correct precision.", "showPrecisionHint": true, "marks": 1}], "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "unitTests": [], "type": "gapfill", "variableReplacementStrategy": "originalfirst", "sortAnswers": false, "prompt": "<p>Cornercut dimension (meters): [[0]]</p>\n<p>Maximum Volume of the box (cu. meters): [[1]]</p>", "marks": 0}], "variablesTest": {"condition": "", "maxRuns": 100}, "variable_groups": [], "extensions": [], "statement": "<p><img src=\"resources/question-resources/boxCutSquares.png\"/></p>\n<p>Given a sheet of cardboard that is $\\var{L}$ meters by $\\var{W}$ meters,&nbsp;what is the side dimension of the square corners that must be removed to form an open top box of maximum volume? What is the maximum volume?</p>", "variables": {"xCut1": {"name": "xCut1", "group": "Ungrouped variables", "definition": "precround((-bCut-sqrt(bCut^2-4*aCut*cCut))/(2*aCut),3)", "description": "", "templateType": "anything"}, "W": {"name": "W", "group": "Ungrouped variables", "definition": "random(10..22#0.25)", "description": "", "templateType": "anything"}, "aCut": {"name": "aCut", "group": "Ungrouped variables", "definition": "12", "description": "", "templateType": "anything"}, "volMax": {"name": "volMax", "group": "Ungrouped variables", "definition": "precround((L-2*xCut1)*(W-2*xCut1)*xCut1,3)", "description": "", "templateType": "anything"}, "L": {"name": "L", "group": "Ungrouped variables", "definition": "random(25..50#0.25)", "description": "", "templateType": "anything"}, "bCut": {"name": "bCut", "group": "Ungrouped variables", "definition": "-(4W+4L)", "description": "", "templateType": "anything"}, "cCut": {"name": "cCut", "group": "Ungrouped variables", "definition": "L*W", "description": "", "templateType": "anything"}, "xCut2": {"name": "xCut2", "group": "Ungrouped variables", "definition": "precround((-bCut+sqrt(bCut^2-4*aCut*cCut))/(2*aCut),3)", "description": "", "templateType": "anything"}}, "preamble": {"css": "", "js": ""}, "functions": {}, "type": "question", "contributors": [{"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}]}]}], "contributors": [{"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}]}