// Numbas version: finer_feedback_settings
{"name": "Transpose complex formula", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Transpose complex formula", "tags": [], "metadata": {"description": "<p>Rearrange a complex formula involving squares, square roots, fractions and additions. This is a fixed question with no randomisation.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Transpose \\(\\displaystyle{q=A_1\\sqrt{\\frac{2gh}{\\left(A_1/A_2\\right)^2-1}}}\\) for \\(A_2\\).</p>\n<p>(Note: to enter the variable name \\(A_1\\) type <code>A_1</code>, for&nbsp; \\(\\sqrt{a/b}\\)&nbsp; type <code>sqrt(a/b)</code>.)</p>", "advice": "<p>$\\begin{align} q&amp;=A_1\\sqrt{\\frac{2gh}{\\left(A_1/A_2\\right)^2-1}}\\\\ \\frac{q}{A_1}&amp;=\\sqrt{\\frac{2gh}{\\left(A_1/A_2\\right)^2-1}}\\qquad\\textrm{divide by }A_1\\\\ \\left(\\frac{q}{A_1}\\right)^2&amp;=\\frac{2gh}{\\left(A_1/A_2\\right)^2-1}\\qquad\\textrm{square}\\\\\\left(\\frac{q}{A_1}\\right)^2\\left(\\left(\\frac{A_1}{A_2}\\right)^2-1\\right)&amp;=2gh\\qquad\\textrm{multiply by the LH denominator}\\\\\\left(\\left(\\frac{A_1}{A_2}\\right)^2-1\\right)&amp;=2gh\\left(\\frac{A_1}{q}\\right)^2\\qquad\\textrm{divide by }\\left(\\frac{q}{A_1}\\right)^2\\\\&nbsp; \\left(\\frac{A_1}{A_2}\\right)^2&amp;=2gh\\left(\\frac{A_1}{q}\\right)^2+1\\qquad\\textrm{add 1 to both sides}\\\\ A_1^2 &amp;= \\left[ 2gh\\left(\\frac{A_1}{q}\\right)^2+1 \\right]A_2^2\\qquad\\textrm{multiply by }A_2^2\\\\A_2^2&amp;=\\frac{A_1^2}{2gh\\left(\\frac{A_1}{q}\\right)^2+1}\\qquad\\textrm{divide by term on RHS}\\\\ A_2 &amp;= \\frac{A_1}{\\sqrt{2gh\\left(\\frac{A_1}{q}\\right)^2+1}}\\qquad\\textrm{take the square root}\\end{align}$</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>\\(A_2=\\)[[0]]</p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "sqrt((A_1^2*q^2)/(2*A_1^2*g*h+q^2))", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": true, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "a_1", "value": ""}, {"name": "g", "value": ""}, {"name": "h", "value": ""}, {"name": "q", "value": ""}]}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question", "contributors": [{"name": "Don Shearman", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/680/"}, {"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}]}]}], "contributors": [{"name": "Don Shearman", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/680/"}, {"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}]}