// Numbas version: finer_feedback_settings
{"name": "Trigonometry: Right angled: Find approx side lengths", "extensions": ["jsxgraph"], "custom_part_types": [], "resources": [["question-resources/undefined_YwBJcjH", "/srv/numbas/media/question-resources/undefined_YwBJcjH"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Trigonometry: Right angled: Find approx side lengths", "tags": ["epphys", "JSXgraph", "Jsxgraph", "jsxgraph", "Triangle", "triangle", "trig", "trigonometry", "Trigonometry"], "metadata": {"description": "<p>A right-angled triangle is displayed either pointing left or right with one of the other angles and one of the sides given. Use&nbsp;SOH CAH TOA to find the side indicated with an x.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "", "advice": "<p>Based on the sides that we have and are interested in we use</p>\n<p><span data-jme-visible=\"(anglelist[1]=3 and h='') or (anglelist[1]=4 and v='')\">$\\sin \\theta = \\dfrac{\\text{opposite}}{\\text{hypotenuse}}$</span> <span data-jme-visible=\"(anglelist[1]=4 and h='') or (anglelist[1]=3 and v='')\">$\\cos \\theta = \\dfrac{\\text{adjacent}}{\\text{hypotenuse}}$</span> <span data-jme-visible=\"d=''\">$\\tan \\theta = \\dfrac{\\text{opposite}}{\\text{adjacent}}$</span></p>\n<p>and substitute in the values that we have</p>\n<p><span data-jme-visible=\"anglelist[1]=3 and h=''\">$\\sin \\var{anglelist[0]}^\\circ = \\dfrac{\\var{v}}{\\var{d}}$.</span> <span data-jme-visible=\"anglelist[1]=3 and v=''\">$\\cos \\var{anglelist[0]}^\\circ = \\dfrac{\\var{h}}{\\var{d}}$.</span> <span data-jme-visible=\"anglelist[1]=3 and d=''\">$\\tan \\var{anglelist[0]}^\\circ= \\dfrac{\\var{v}}{\\var{h}}$.</span> <span data-jme-visible=\"anglelist[1]=4 and v=''\">$\\sin \\var{anglelist[0]}^\\circ = \\dfrac{\\var{h}}{\\var{d}}$.</span> <span data-jme-visible=\"anglelist[1]=4 and h=''\">$\\cos \\var{anglelist[0]}^\\circ = \\dfrac{\\var{v}}{\\var{d}}$.</span> <span data-jme-visible=\"anglelist[1]=4 and d=''\">$\\tan \\var{anglelist[0]}^\\circ= \\dfrac{\\var{h}}{\\var{v}}$.</span></p>\n<p><span data-jme-visible=\"(anglelist[1]=3 and (vec1=[0,2,1] or vec1=[2,0,1] or vec1=[2,1,0])) or (anglelist[1]=4 and (vec1=[0,2,1] or vec1=[1,2,0] or vec1=[2,0,1]))\">To solve this equation for $x$ we multiply both sides of the equation by the denominator.</span> <span data-jme-visible=\"not((anglelist[1]=3 and (vec1=[0,2,1] or vec1=[2,0,1] or vec1=[2,1,0])) or (anglelist[1]=4 and (vec1=[0,2,1] or vec1=[1,2,0] or vec1=[2,0,1])))\">To solve this equation for $x$ we multiply both sides of the equation by the denominator and then divide both sides of the equation by the trig term.</span></p>\n<p><span data-jme-visible=\"anglelist[1]=3 and vec1=[0,1,2]\">$x=\\dfrac{\\var{h}}{\\cos \\var{anglelist[0]}^\\circ}$</span> <span data-jme-visible=\"anglelist[1]=3 and vec1=[0,2,1]\">$x=\\var{d}\\cos \\var{anglelist[0]}^\\circ$</span> <span data-jme-visible=\"anglelist[1]=3 and vec1=[1,0,2]\">$x=\\dfrac{\\var{v}}{\\sin \\var{anglelist[0]}^\\circ}$</span> <span data-jme-visible=\"anglelist[1]=3 and vec1=[1,2,0]\">$x=\\dfrac{\\var{v}}{\\tan \\var{anglelist[0]}^\\circ}$</span> <span data-jme-visible=\"anglelist[1]=3 and vec1=[2,0,1]\">$x=\\var{d}\\sin \\var{anglelist[0]}^\\circ$</span> <span data-jme-visible=\"anglelist[1]=3 and vec1=[2,1,0]\">$x=\\var{h}\\tan \\var{anglelist[0]}^\\circ$</span></p>\n<p><span data-jme-visible=\"anglelist[1]=4 and vec1=[0,1,2]\">$x=\\dfrac{\\var{h}}{\\sin \\var{anglelist[0]}^\\circ}$</span> <span data-jme-visible=\"anglelist[1]=4 and vec1=[0,2,1]\">$x=\\var{d}\\sin \\var{anglelist[0]}^\\circ$</span> <span data-jme-visible=\"anglelist[1]=4 and vec1=[1,0,2]\">$x=\\dfrac{\\var{v}}{\\cos \\var{anglelist[0]}^\\circ}$</span> <span data-jme-visible=\"anglelist[1]=4 and vec1=[1,2,0]\">$x=\\var{v}\\tan \\var{anglelist[0]}^\\circ$</span> <span data-jme-visible=\"anglelist[1]=4 and vec1=[2,0,1]\">$x=\\var{d}\\cos \\var{anglelist[0]}^\\circ$</span> <span data-jme-visible=\"anglelist[1]=4 and vec1=[2,1,0]\">$x=\\dfrac{\\var{h}}{\\tan \\var{anglelist[0]}^\\circ}$</span></p>\n<p>A calculator (in degrees mode) evaluates this as $\\var{ans}\\ldots$ <span data-jme-visible=\"ans&lt;&gt;precround(ans,0)\">which we round to one decimal place as $\\var{precround(ans,1)}$</span></p>", "rulesets": {}, "extensions": ["jsxgraph"], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"deltax": {"name": "deltax", "group": "Ungrouped variables", "definition": "precround(-12+2*triples[1]/triples[0],4)", "description": "", "templateType": "anything", "can_override": false}, "thetaans": {"name": "thetaans", "group": "Ungrouped variables", "definition": "if(vec1=[0,1,2], h/cos(rsang),\nif(vec1=[0,2,1], d*cos(rsang),\nif(vec1=[1,0,2], v/sin(rsang),\nif(vec1=[1,2,0], v/tan(rsang),\nif(vec1=[2,0,1], d*sin(rsang),\nif(vec1=[2,1,0], h*tan(rsang),\n'error'))))))", "description": "<p>answer using theta (lower angle in diagram)</p>", "templateType": "anything", "can_override": false}, "ans": {"name": "ans", "group": "Ungrouped variables", "definition": "if(anglelist[1]=3, thetaans, phians)", "description": "<p>I think I just calculated the answer two different ways</p>", "templateType": "anything", "can_override": false}, "display_angles1": {"name": "display_angles1", "group": "Ungrouped variables", "definition": "display_angles[1]", "description": "", "templateType": "anything", "can_override": false}, "rsang": {"name": "rsang", "group": "Ungrouped variables", "definition": "smallest_angle*pi/180", "description": "<p>radians smallest angle</p>", "templateType": "anything", "can_override": false}, "display_angles": {"name": "display_angles", "group": "Ungrouped variables", "definition": "if(anglelist[1]=3,[smallest_angle,''],['',complement])", "description": "<p>used in jsxgraph</p>", "templateType": "anything", "can_override": false}, "display_angles0": {"name": "display_angles0", "group": "Ungrouped variables", "definition": "display_angles[0]", "description": "", "templateType": "anything", "can_override": false}, "vec1": {"name": "vec1", "group": "Ungrouped variables", "definition": "shuffle([0,1,2])", "description": "<p>shuffles which edge is shortest</p>", "templateType": "anything", "can_override": false}, "triples": {"name": "triples", "group": "Ungrouped variables", "definition": "random([[3, 4, 5], [5, 12, 13], [7, 24, 25], [8, 15, 17], [9, 40, 41], [11, 60, 61], [12, 35, 37], [16, 63, 65], [20, 21, 29], [20, 99, 101], [24, 143, 145], [28, 45, 53], [33, 56, 65], [36, 77, 85], [39, 80, 89], [44, 117, 125], [48, 55, 73], [51, 140, 149], [52, 165, 173], [57, 176, 185], [60, 91, 109], [60, 221, 229], [65, 72, 97], [68, 285, 293], [69, 260, 269], [75, 308, 317], [76, 357, 365], [84, 187, 205], [84, 437, 445], [85, 132, 157], [87, 416, 425], [88, 105, 137], [92, 525, 533], [93, 476, 485], [95, 168, 193], [96, 247, 265], [100, 621, 629], [104, 153, 185], [105, 208, 233], [105, 608, 617], [111, 680, 689], [115, 252, 277], [119, 120, 169], [120, 209, 241], [120, 391, 409], [132, 475, 493], [133, 156, 205], [135, 352, 377], [136, 273, 305], [140, 171, 221], [145, 408, 433], [152, 345, 377], [155, 468, 493], [156, 667, 685], [160, 231, 281], [161, 240, 289], [165, 532, 557], [168, 425, 457], [168, 775, 793], [175, 288, 337], [180, 299, 349], [184, 513, 545], [185, 672, 697], [189, 340, 389], [195, 748, 773], [200, 609, 641], [203, 396, 445], [204, 253, 325], [205, 828, 853], [207, 224, 305], [215, 912, 937], [216, 713, 745], [217, 456, 505], [220, 459, 509], [225, 272, 353], [228, 325, 397], [231, 520, 569], [232, 825, 857], [240, 551, 601], [248, 945, 977], [252, 275, 373], [259, 660, 709], [260, 651, 701], [261, 380, 461], [273, 736, 785], [276, 493, 565], [279, 440, 521], [280, 351, 449], [280, 759, 809], [287, 816, 865], [297, 304, 425], [300, 589, 661], [301, 900, 949], [308, 435, 533], [315, 572, 653], [319, 360, 481], [333, 644, 725], [336, 377, 505], [336, 527, 625], [341, 420, 541], [348, 805, 877], [364, 627, 725], [368, 465, 593], [369, 800, 881], [372, 925, 997], [385, 552, 673], [387, 884, 965], [396, 403, 565], [400, 561, 689], [407, 624, 745], [420, 851, 949], [429, 460, 629], [429, 700, 821], [432, 665, 793], [451, 780, 901], [455, 528, 697], [464, 777, 905], [468, 595, 757], [473, 864, 985], [481, 600, 769], [504, 703, 865], [533, 756, 925], [540, 629, 829], [555, 572, 797], [580, 741, 941], [615, 728, 953], [616, 663, 905], [696, 697, 985]])\n", "description": "<p>Some the following were too skinny and so were removed.<br /><br />use&nbsp;https://www.mathsisfun.com/numbers/pythagorean-triples.html</p>\n<p><br />random([[3,4,5], [5,12,13], [7,24,25], [8,15,17], [9,40,41],<br />[11,60,61], [12,35,37], [13,84,85], [15,112,113], [16,63,65],<br />[19,180,181], [20,21,29], [20,99,101],<br />[23,264,265], [24,143,145], [25,312,313], [27,364,365], [28,45,53],<br />[28,195,197], [31,480,481], [32,255,257], [33,56,65],<br />[33,544,545], [35,612,613], [36,77,85], [36,323,325], [37,684,685],<br />[39,80,89], [40,399,401], [41,840,841], [43,924,925],<br />[44,117,125], [44,483,485], [48,55,73], [48,575,577], [51,140,149],<br />[52,165,173], [52,675,677], [56,783,785], [57,176,185], [60,91,109],<br />[60,221,229], [60,899,901], [65,72,97], [68,285,293], [69,260,269],<br />[75,308,317], [76,357,365], [84,187,205], [84,437,445], [85,132,157],<br />[87,416,425], [88,105,137], [92,525,533], [93,476,485], [95,168,193],<br />[96,247,265], [100,621,629], [104,153,185], [105,208,233], [105,608,617],<br />[108,725,733], [111,680,689], [115,252,277], [116,837,845], [119,120,169],<br />[120,209,241], [120,391,409], [123,836,845], [129,920,929],<br />[132,475,493], [133,156,205], [135,352,377], [136,273,305], [140,171,221],<br />[145,408,433], [152,345,377], [155,468,493], [156,667,685], [160,231,281],<br />[161,240,289], [165,532,557], [168,425,457], [168,775,793], [175,288,337],<br />[180,299,349], [184,513,545], [185,672,697], [189,340,389], [195,748,773],<br />[200,609,641], [203,396,445], [204,253,325], [205,828,853], [207,224,305],<br />[215,912,937], [216,713,745], [217,456,505], [220,459,509], [225,272,353],<br />[228,325,397], [231,520,569], [232,825,857], [240,551,601], [248,945,977],<br />[252,275,373], [259,660,709], [260,651,701], [261,380,461], [273,736,785],<br />[276,493,565], [279,440,521], [280,351,449], [280,759,809], [287,816,865],<br />[297,304,425], [300,589,661], [301,900,949], [308,435,533], [315,572,653],<br />[319,360,481], [333,644,725], [336,377,505], [336,527,625], [341,420,541],<br />[348,805,877], [364,627,725], [368,465,593], [369,800,881], [372,925,997],<br />[385,552,673], [387,884,965], [396,403,565], [400,561,689], [407,624,745],<br />[420,851,949], [429,460,629], [429,700,821], [432,665,793], [451,780,901],<br />[455,528,697], [464,777,905], [468,595,757], [473,864,985], [481,600,769],<br />[504,703,865], [533,756,925], [540,629,829], [555,572,797], [580,741,941],<br />[615,728,953], [616,663,905], [696,697,985]])</p>", "templateType": "anything", "can_override": false}, "tritop": {"name": "tritop", "group": "Ungrouped variables", "definition": "precround(triples[0]*scale,4)/2", "description": "<p>top of triangle for jsxgraph, keeping same ratios.</p>", "templateType": "anything", "can_override": false}, "d": {"name": "d", "group": "Ungrouped variables", "definition": "if(vec1[2]=1,triples[2],if(vec1[2]=0,'','$x$'))", "description": "<p>diagonal length in triangle</p>\n<p></p>\n<p></p>\n<p>so always integer and scale by k for more randomness.</p>", "templateType": "anything", "can_override": false}, "anglelist": {"name": "anglelist", "group": "Ungrouped variables", "definition": "random([smallest_angle,3,'$\\\\theta$'],[complement,4,'$\\\\phi$'])", "description": "<p>[precround(180*arctan(triples[0]/triples[1])/pi,0),90-precround(180*arctan(triples[0]/triples[1])/pi,0)]</p>", "templateType": "anything", "can_override": false}, "smallest_angle": {"name": "smallest_angle", "group": "Ungrouped variables", "definition": "precround(180*arctan(triples[0]/triples[1])/pi,0)", "description": "", "templateType": "anything", "can_override": false}, "phians": {"name": "phians", "group": "Ungrouped variables", "definition": "if(vec1=[0,1,2], h/sin(rcang),\nif(vec1=[0,2,1], d*sin(rcang),\nif(vec1=[1,0,2], v/cos(rcang),\nif(vec1=[1,2,0], v*tan(rcang),\nif(vec1=[2,0,1], d*cos(rcang),\nif(vec1=[2,1,0], h/tan(rcang),\n'error'))))))", "description": "<p>ans using phi (upper angle in diagram)</p>", "templateType": "anything", "can_override": false}, "scale": {"name": "scale", "group": "Ungrouped variables", "definition": "24/triples[1]", "description": "", "templateType": "anything", "can_override": false}, "rcang": {"name": "rcang", "group": "Ungrouped variables", "definition": "complement*pi/180", "description": "<p>radians complement angle</p>", "templateType": "anything", "can_override": false}, "switcharoo": {"name": "switcharoo", "group": "Ungrouped variables", "definition": "random(0,1)", "description": "<p>determines which orientation the triangle is displayed as</p>", "templateType": "anything", "can_override": false}, "h": {"name": "h", "group": "Ungrouped variables", "definition": "if(vec1[1]=1,triples[1],if(vec1[1]=0,'','$x$'))", "description": "<p>horizontal length in triangle</p>", "templateType": "anything", "can_override": false}, "complement": {"name": "complement", "group": "Ungrouped variables", "definition": "90-smallest_angle", "description": "", "templateType": "anything", "can_override": false}, "v": {"name": "v", "group": "Ungrouped variables", "definition": "if(vec1[0]=1,triples[0],if(vec1[0]=0,'','$x$'))", "description": "<p>vertical length in triangle</p>", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["triples", "vec1", "v", "h", "d", "scale", "tritop", "deltax", "switcharoo", "smallest_angle", "complement", "anglelist", "display_angles", "display_angles0", "display_angles1", "rsang", "rcang", "ans", "thetaans", "phians"], "variable_groups": [], "functions": {"otherway": {"parameters": [], "type": "html", "language": "javascript", "definition": "var div = Numbas.extensions.jsxgraph.makeBoard('500px','500px',{boundingBox:[-17,17,14,-14],grid:false,axis:false});\nvar board = div.board;\n\n//Doesn't look like you need this\nJXG.Options.text.useMathJax = true;\n\n// get the height of the triangle\nTT = Numbas.jme.unwrapValue(scope.variables.tritop);\ndx = Numbas.jme.unwrapValue(scope.variables.deltax);\nh = Numbas.jme.unwrapValue(scope.variables.h);\nv = Numbas.jme.unwrapValue(scope.variables.v);\nd = Numbas.jme.unwrapValue(scope.variables.d);\ntheta = Numbas.jme.unwrapValue(scope.variables.display_angles0);\nphi = Numbas.jme.unwrapValue(scope.variables.display_angles1);\n\n// create the horizontal line\nvar hor = board.create('line',[[-12,-TT],[12,-TT]], { straightFirst:false, straightLast:false, strokeColor: 'black', fixed: true});\n\n//create the vertical line\nvar vert = board.create('line',[[-12,-TT],[-12,TT/1]], { straightFirst:false, straightLast:false, strokeColor: 'black', fixed: true});\n\n//create the diagonal line\nvar vert = board.create('line',[[12,-TT],[-12,TT/1]], { straightFirst:false, straightLast:false, strokeColor: 'black', fixed: true});\n\n//create the box for right angle\nboard.create('line',[[(-12+0.1*TT),-TT],[(-12+0.1*TT),-TT*0.9]], { straightFirst:false, straightLast:false, strokeColor: 'black', fixed: true});\nboard.create('line',[[(-12+0.1*TT),-TT*0.9],[-12,-TT*0.9]], { straightFirst:false, straightLast:false, strokeColor: 'black', fixed: true});\n\n//label the angle theta\nif (theta == '') {\n} else {\nboard.create('text',[5.5,-4*TT/5,\n  function() { \n    return theta + \"\\u00B0\";\n  }], {fontSize:20,fixed: true});\n}\n\n//label the angle phi\nif (phi == '') {\n} else {\nboard.create('text',[-11.5,3*TT/5,\n  function() { \n    return phi + \"\\u00B0\";\n  }], {fontSize:20,fixed: true});\n}\n\n//display the side lengths\nvar vtext= board.create('text',[-15,0,v], {fontSize:20,fixed: true});\nvar htext= board.create('text',[-2,-TT-1,h], {fontSize:20,fixed: true});\nvar dtext= board.create('text',[-2,TT/2+0.3,d], {fontSize:20,fixed: true});\n\n//can't figure out how to rotate text. http://jsxgraph.uni-bayreuth.de/wiki/index.php/Texts_and_Transformations suggests the following\n//var tRot = board.create('transform', [Math.PI/2, 13,0], {type:'rotate'}); \n//tRot.bindTo(vtext);\n\n\n\n\nreturn div;\n\n"}, "triangle": {"parameters": [], "type": "html", "language": "javascript", "definition": "var div = Numbas.extensions.jsxgraph.makeBoard('500px','500px',{boundingBox:[-13,13,17,-17],grid:false,axis:false});\nvar board = div.board;\n\n//Doesn't look like you need this\nJXG.Options.text.useMathJax = true;\n\n// get the height of the triangle\nTT = Numbas.jme.unwrapValue(scope.variables.tritop);\ndx = Numbas.jme.unwrapValue(scope.variables.deltax);\nh = Numbas.jme.unwrapValue(scope.variables.h);\nv = Numbas.jme.unwrapValue(scope.variables.v);\nd = Numbas.jme.unwrapValue(scope.variables.d);\ntheta = Numbas.jme.unwrapValue(scope.variables.display_angles0);\nphi = Numbas.jme.unwrapValue(scope.variables.display_angles1);\n\n// create the horizontal line\nvar hor = board.create('line',[[-12,-TT],[12,-TT]], { straightFirst:false, straightLast:false, strokeColor: 'black', fixed: true});\n\n//create the vertical line\nvar vert = board.create('line',[[12,-TT],[12,TT/1]], { straightFirst:false, straightLast:false, strokeColor: 'black', fixed: true});\n\n//create the diagonal line\nvar vert = board.create('line',[[-12,-TT],[12,TT/1]], { straightFirst:false, straightLast:false, strokeColor: 'black', fixed: true});\n\n//create the box for right angle\nboard.create('line',[[(12-0.1*TT),-TT],[(12-0.1*TT),-TT*0.9]], { straightFirst:false, straightLast:false, strokeColor: 'black', fixed: true});\nboard.create('line',[[(12-0.1*TT),-TT*0.9],[12,-TT*0.9]], { straightFirst:false, straightLast:false, strokeColor: 'black', fixed: true});\n\n//label the angle theta\nif (theta == '') {\n} else {\nboard.create('text',[-7.2,-4*TT/5,\n  function() { \n    return theta + \"\\u00B0\";\n  }], {fontSize:20,fixed: true});\n}\n\n//label the angle phi\nif (phi == ''){\n} else {\n  board.create('text',[9.6,3*TT/5,\n  function() { \n    return phi + \"\\u00B0\";\n  }], {fontSize:20,fixed: true});\n}\n  \n//display the side lengths\nvar vtext= board.create('text',[12.5,0,v], {fontSize:20,fixed: true});\nvar htext= board.create('text',[0,-TT-1,h], {fontSize:20,fixed: true});\nvar dtext= board.create('text',[0,TT/2+0.3,d], {fontSize:20,fixed: true});\n\n//can't figure out how to rotate text. http://jsxgraph.uni-bayreuth.de/wiki/index.php/Texts_and_Transformations suggests the following\n//var tRot = board.create('transform', [Math.PI/2, 13,0], {type:'rotate'}); \n//tRot.bindTo(vtext);\n\n\n\n\nreturn div;\n\n"}}, "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>Given the triangle described below, the value of $x$ is [[0]] to&nbsp;1 decimal place.</p>\n<p>{if(switcharoo=0,triangle(),otherway())}</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "ans", "maxValue": "ans", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "1", "precisionPartialCredit": "50", "precisionMessage": "<p>You have not given your answer to the correct precision.</p>", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question", "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}]}]}], "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}]}