// Numbas version: finer_feedback_settings
{"name": "PreCal Application of Polynomials Volume Problem", "extensions": [], "custom_part_types": [], "resources": [["question-resources/Apex-Sand-and-Gravel-51.jpg", "/srv/numbas/media/question-resources/Apex-Sand-and-Gravel-51.jpg"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"rulesets": {}, "preamble": {"js": "", "css": ""}, "variable_groups": [], "tags": [], "ungrouped_variables": ["varBase", "rateSand", "tConveyor", "ratePerHour", "V", "pie", "a", "b", "c", "d", "p", "q", "r", "R1", "height"], "functions": {}, "name": "PreCal Application of Polynomials Volume Problem", "advice": "", "metadata": {"licence": "All rights reserved", "description": ""}, "extensions": [], "variables": {"c": {"group": "Ungrouped variables", "templateType": "anything", "definition": "varBase^2", "name": "c", "description": ""}, "p": {"group": "Ungrouped variables", "templateType": "anything", "definition": "-b/(3a)", "name": "p", "description": ""}, "r": {"group": "Ungrouped variables", "templateType": "anything", "definition": "c/(3*a)", "name": "r", "description": ""}, "q": {"group": "Ungrouped variables", "templateType": "anything", "definition": "p^3+(b*c-3*a*d)/(6a^2)", "name": "q", "description": ""}, "d": {"group": "Ungrouped variables", "templateType": "anything", "definition": "-3*V/pie", "name": "d", "description": ""}, "varBase": {"group": "Ungrouped variables", "templateType": "anything", "definition": "random(3..10)", "name": "varBase", "description": ""}, "a": {"group": "Ungrouped variables", "templateType": "anything", "definition": "1", "name": "a", "description": ""}, "height": {"group": "Ungrouped variables", "templateType": "anything", "definition": "precround(R1,1)", "name": "height", "description": ""}, "tConveyor": {"group": "Ungrouped variables", "templateType": "anything", "definition": "random(1.25..3#0.05)", "name": "tConveyor", "description": ""}, "rateSand": {"group": "Ungrouped variables", "templateType": "anything", "definition": "random(50..100#0.2)", "name": "rateSand", "description": ""}, "pie": {"group": "Ungrouped variables", "templateType": "anything", "definition": "decimal(pi)", "name": "pie", "description": ""}, "b": {"group": "Ungrouped variables", "templateType": "anything", "definition": "2*varBase", "name": "b", "description": ""}, "V": {"group": "Ungrouped variables", "templateType": "anything", "definition": "ratePerHour*tConveyor", "name": "V", "description": ""}, "ratePerHour": {"group": "Ungrouped variables", "templateType": "anything", "definition": "rateSand*60", "name": "ratePerHour", "description": ""}, "R1": {"group": "Ungrouped variables", "templateType": "anything", "definition": "(q + (q^2 + (r-p^2)^3)^(1/2))^(1/3)   +   (q - (q^2 + (r-p^2)^3)^(1/2))^(1/3)   +   p", "name": "R1", "description": ""}}, "parts": [{"showFeedbackIcon": true, "type": "numberentry", "correctAnswerStyle": "plain", "precisionPartialCredit": "75", "adaptiveMarkingPenalty": 0, "allowFractions": false, "notationStyles": ["plain", "en", "si-en"], "precision": "1", "mustBeReduced": false, "customMarkingAlgorithm": "", "correctAnswerFraction": false, "showCorrectAnswer": true, "unitTests": [], "precisionType": "dp", "showPrecisionHint": true, "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "precisionMessage": "You have not given your answer to the correct precision.", "useCustomName": false, "mustBeReducedPC": 0, "strictPrecision": true, "variableReplacements": [], "minValue": "height", "maxValue": "height", "marks": 1, "customName": "", "scripts": {}}], "statement": "<p><img src=\"resources/question-resources/Apex-Sand-and-Gravel-51.jpg\"/></p>\n<p>The Sands of Time Company has received loads from work crews and is currently piling them by use of a conveyor belt.&nbsp; The pile formed such that the cone shape had a base radius that was $\\var{varBase}$ feet longer than the height of the pile.&nbsp; If the conveyor delievers sand at a rate of $\\var{rateSand}$ cubic feet per minute and had ran a total of $\\var{tConveyor}$ hours, then determine the height of the newly formed pile assuming the pile's initial height was zero feet.</p>", "variablesTest": {"condition": "", "maxRuns": 100}, "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/"}]}