// Numbas version: finer_feedback_settings
{"name": "Transpose linear formula 3 variables", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Transpose linear formula 3 variables", "tags": [], "metadata": {"description": "<p>Rearrange a linear formula au + bv + cw = d to make one of u,v,w the subject.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Transpose the formula \\(\\simplify{{formula}}\\) to make \\(\\var{selected_variable}\\) the subject.</p>", "advice": "<p><span data-jme-visible=\"sel_variable=0\">$\\begin{align}\\var{simplify(expression(a+\"*u+\"+b+\"*v+\"+c+\"*w\"),\"basic\")}=\\var{d}\\\\ \\var{a}u&amp;=\\var{simplify(expression(d+\"-\"+b+\"*v-\"+c+\"*w\"),\"basic\")}\\\\u&amp;= \\var[fractionNumbers]{simplify(expression(\"(\"+d+\"-\"+b+\"*v-\"+c+\"*w)/\"+a),\"all\")}\\\\ u &amp;= \\var{simplify(expression({d}+\"/\"+{a}+\"-\"+{b}+\"/\"+{a}+\"*v-\"+{c}+\"/\"+{a}+\"*w\"),\"all\")} \\end{align}$</span></p>\n<p><span data-jme-visible=\"sel_variable=1\">$\\begin{align}\\var{simplify(expression(a+\"*u+\"+b+\"*v+\"+c+\"*w\"),\"basic\")}=\\var{d}\\\\ \\var{b}v&amp;=\\var{simplify(expression(d+\"-\"+a+\"*u-\"+c+\"*w\"),\"basic\")}\\\\v&amp;= \\var[fractionNumbers]{simplify(expression(\"(\"+d+\"-\"+a+\"*u-\"+c+\"*w)/\"+b),\"all\")}\\\\ v &amp;= \\var{simplify(expression({d}+\"/\"+{b}+\"-\"+{a}+\"/\"+{b}+\"*u-\"+{c}+\"/\"+{b}+\"*w\"),\"all\")} \\end{align}$</span></p>\n<p><span data-jme-visible=\"sel_variable=2\">$\\begin{align}\\var{simplify(expression(a+\"*u+\"+b+\"*v+\"+c+\"*w\"),\"basic\")}=\\var{d}\\\\ \\var{c}w&amp;=\\var{simplify(expression(d+\"-\"+a+\"*u-\"+b+\"*v\"),\"basic\")}\\\\w&amp;= \\var[fractionNumbers]{simplify(expression(\"(\"+d+\"-\"+a+\"*u-\"+b+\"*v)/\"+c),\"basic\")}\\\\ w &amp;= \\var{simplify(expression({d}+\"/\"+{c}+\"-\"+{a}+\"/\"+{c}+\"*u-\"+{b}+\"/\"+{c}+\"*v\"),\"all\")} \\end{align}$</span></p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(1..9)*random(1,-1)", "description": "", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(1..9)*random(1,-1)", "description": "", "templateType": "anything", "can_override": false}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "random(1..9)*random(1,-1)", "description": "", "templateType": "anything", "can_override": false}, "formula": {"name": "formula", "group": "Ungrouped variables", "definition": "substitute([\"a\":a,\"b\":b,\"c\":c, \"d\":d],expression(\"a*u+b*v+c*w=d\"))\n  ", "description": "", "templateType": "anything", "can_override": false}, "variables": {"name": "variables", "group": "Ungrouped variables", "definition": "[latex(\"u\"),latex(\"v\"), latex(\"w\")]", "description": "", "templateType": "anything", "can_override": false}, "sel_variable": {"name": "sel_variable", "group": "Ungrouped variables", "definition": "random(0,1,2)", "description": "", "templateType": "anything", "can_override": false}, "selected_variable": {"name": "selected_variable", "group": "Ungrouped variables", "definition": "variables[sel_variable]", "description": "", "templateType": "anything", "can_override": false}, "answer": {"name": "answer", "group": "Ungrouped variables", "definition": "if(sel_variable=0,substitute([\"a\":a,\"b\":b,\"c\":c,\"d\":d],expression(\"1/a*(d-b*v-c*w)\")),\n  if(sel_variable=1, substitute([\"a\":a,\"b\":b,\"c\":c,\"d\":d],expression(\"1/b*(d-a*u-c*w)\")),\n    substitute([\"a\":a,\"b\":b,\"c\":c,\"d\":d],expression(\"1/c*(d-a*u-b*v)\"))))", "description": "", "templateType": "anything", "can_override": false}, "d": {"name": "d", "group": "Ungrouped variables", "definition": "random(-9..9)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "b", "c", "formula", "variables", "sel_variable", "selected_variable", "answer", "d"], "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>\\(\\var{selected_variable}=\\)[[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": "{answer}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "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/"}]}