// Numbas version: exam_results_page_options
{"name": "19. Centroids by Composite Area", "metadata": {"description": "<p>Homework set. &nbsp;Find centroids of shapes by dividing them into simple subshapes.</p>", "licence": "Creative Commons Attribution-ShareAlike 4.0 International"}, "duration": 0, "percentPass": 0, "showQuestionGroupNames": false, "shuffleQuestionGroups": false, "showstudentname": true, "question_groups": [{"name": "Group", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": ["", "", ""], "variable_overrides": [[], [], []], "questions": [{"name": "Centroid of parts", "extensions": ["geogebra", "quantities"], "custom_part_types": [{"source": {"pk": 19, "author": {"name": "William Haynes", "pk": 2530}, "edit_page": "/part_type/19/edit"}, "name": "Engineering Accuracy with units", "short_name": "engineering-answer", "description": "<p>A value with units marked right if within an adjustable % error of the correct value. &nbsp;Marked close if within a wider margin of error.</p>", "help_url": "", "input_widget": "string", "input_options": {"correctAnswer": "siground(settings['correctAnswer'],4)", "hint": {"static": true, "value": ""}, "allowEmpty": {"static": true, "value": true}}, "can_be_gap": true, "can_be_step": true, "marking_script": "mark:\nswitch( \n  right and good_units and right_sign, add_credit(1.0,'Correct.'),\n  right and good_units and not right_sign, add_credit(settings['C2'],'Wrong sign.'),\n  right and right_sign and not good_units, add_credit(settings['C2'],'Correct value, but wrong or missing units.'),\n  close and good_units, add_credit(settings['C1'],'Close.'),\n  close and not good_units, add_credit(settings['C3'],'Answer is close, but wrong or missing units.'),\n  incorrect('Wrong answer.')\n)\n\n\ninterpreted_answer:\nqty(student_scalar, student_units)\n\n\n\ncorrect_quantity:\nsettings[\"correctAnswer\"]\n\n\n\ncorrect_units:\nunits(correct_quantity)\n\n\nallowed_notation_styles:\n[\"plain\",\"en\"]\n\nmatch_student_number:\nmatchnumber(studentAnswer,allowed_notation_styles)\n\nstudent_scalar:\nmatch_student_number[1]\n\nstudent_units:\nreplace_regex('ohms','ohm',\n  replace_regex('\u00b0', ' deg',\n    replace_regex('-', ' ' ,\n      studentAnswer[len(match_student_number[0])..len(studentAnswer)])),\"i\")\n\ngood_units:\ntry(\ncompatible(quantity(1, student_units),correct_units),\nmsg,\nfeedback(msg);false)\n\n\nstudent_quantity:\nswitch(not good_units, \n       student_scalar * correct_units, \n       not right_sign,\n       -quantity(student_scalar, student_units),\n       quantity(student_scalar,student_units)\n)\n  \n\n\npercent_error:\ntry(\nscalar(abs((correct_quantity - student_quantity)/correct_quantity))*100  \n,msg,\nif(student_quantity=correct_quantity,0,100))\n   \n\nright:\npercent_error <= settings['right']\n\n\nclose:\nright_sign and percent_error <= settings['close']\n\nright_sign:\nsign(student_scalar) = sign(correct_quantity)", "marking_notes": [{"name": "mark", "description": "This is the main marking note. It should award credit and provide feedback based on the student's answer.", "definition": "switch( \n  right and good_units and right_sign, add_credit(1.0,'Correct.'),\n  right and good_units and not right_sign, add_credit(settings['C2'],'Wrong sign.'),\n  right and right_sign and not good_units, add_credit(settings['C2'],'Correct value, but wrong or missing units.'),\n  close and good_units, add_credit(settings['C1'],'Close.'),\n  close and not good_units, add_credit(settings['C3'],'Answer is close, but wrong or missing units.'),\n  incorrect('Wrong answer.')\n)\n"}, {"name": "interpreted_answer", "description": "A value representing the student's answer to this part.", "definition": "qty(student_scalar, student_units)\n\n"}, {"name": "correct_quantity", "description": "", "definition": "settings[\"correctAnswer\"]\n\n"}, {"name": "correct_units", "description": "", "definition": "units(correct_quantity)\n"}, {"name": "allowed_notation_styles", "description": "", "definition": "[\"plain\",\"en\"]"}, {"name": "match_student_number", "description": "", "definition": "matchnumber(studentAnswer,allowed_notation_styles)"}, {"name": "student_scalar", "description": "", "definition": "match_student_number[1]"}, {"name": "student_units", "description": "<p>Modify&nbsp;the&nbsp;unit portion of&nbsp;the student's answer by</p>\n<p>1. replacing \"ohms\" with \"ohm\" &nbsp;case insensitive</p>\n<p>2.&nbsp;replacing '-'&nbsp;with ' '&nbsp;</p>\n<p>3. replacing '&deg;' with ' deg'&nbsp;</p>\n<p>to allow answers like 10 ft-lb and 30&deg;</p>", "definition": "replace_regex('ohms','ohm',\n  replace_regex('\u00b0', ' deg',\n    replace_regex('-', ' ' ,\n      studentAnswer[len(match_student_number[0])..len(studentAnswer)])),\"i\")"}, {"name": "good_units", "description": "", "definition": "try(\ncompatible(quantity(1, student_units),correct_units),\nmsg,\nfeedback(msg);false)\n"}, {"name": "student_quantity", "description": "<p>This fixes the student answer for two common errors. &nbsp;</p>\n<p>If student_units are wrong&nbsp;&nbsp;- replace with correct units</p>\n<p>If student_scalar has the wrong sign - replace with right sign</p>\n<p>If student makes both errors, only one gets fixed.</p>", "definition": "switch(not good_units, \n       student_scalar * correct_units, \n       not right_sign,\n       -quantity(student_scalar, student_units),\n       quantity(student_scalar,student_units)\n)\n  \n"}, {"name": "percent_error", "description": "", "definition": "try(\nscalar(abs((correct_quantity - student_quantity)/correct_quantity))*100  \n,msg,\nif(student_quantity=correct_quantity,0,100))\n   "}, {"name": "right", "description": "", "definition": "percent_error <= settings['right']\n"}, {"name": "close", "description": "<p>Only marked close if the student actually has the right sign.</p>", "definition": "right_sign and percent_error <= settings['close']"}, {"name": "right_sign", "description": "", "definition": "sign(student_scalar) = sign(correct_quantity) "}], "settings": [{"name": "correctAnswer", "label": "Correct Quantity.", "help_url": "", "hint": "The correct answer given as a JME quantity.", "input_type": "code", "default_value": "", "evaluate": true}, {"name": "right", "label": "% Accuracy for right.", "help_url": "", "hint": "Question will be considered correct if the scalar part of the student's answer is within this % of correct value.", "input_type": "code", "default_value": "0.2", "evaluate": true}, {"name": "close", "label": "% Accuracy for close.", "help_url": "", "hint": "Question will be considered close if the scalar part of the student's answer is within this % of correct value.", "input_type": "code", "default_value": "1.0", "evaluate": true}, {"name": "C1", "label": "Close with units.", "help_url": "", "hint": "Partial Credit for close value with appropriate units. &nbsp;if correct answer is 100 N and close is &plusmn;1%,<br />99 &nbsp;N is accepted.", "input_type": "percent", "default_value": "75"}, {"name": "C2", "label": "No units or wrong sign", "help_url": "", "hint": "Partial credit for forgetting units or using wrong sign.<br />If the correct answer is 100 N, both 100 and -100 N are accepted.", "input_type": "percent", "default_value": "50"}, {"name": "C3", "label": "Close, no units.", "help_url": "", "hint": "Partial Credit for close value but forgotten units.<br />This value would be close&nbsp;if the expected units were provided. &nbsp;If the correct answer is 100 N, and close is &plusmn;1%,<br />99 is accepted.", "input_type": "percent", "default_value": "25"}], "public_availability": "always", "published": true, "extensions": ["quantities"]}], "resources": [["question-resources/centroids.png", "/srv/numbas/media/question-resources/centroids.png"], ["question-resources/centroids_3A0rXlj.png", "/srv/numbas/media/question-resources/centroids_3A0rXlj.png"], ["question-resources/centroids_zSOgoBb.png", "/srv/numbas/media/question-resources/centroids_zSOgoBb.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}], "tags": [], "metadata": {"description": "<p>Locate the centroid of a rectangle, triangle, and semi-circle on a coordinate grid.</p>", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "<p>Determine the coordinates of the centroids of the three shapes. &nbsp;Grid units are [<em>{units}</em>].</p>\n<p>{geogebra_applet('xjjm7qqr',[['R_1',R1],['R_2',R2],['T_1',T1],['T_2',T2],['C_1',C1],['C_2',C2]])}</p>\n<p></p>\n<p></p>", "advice": "<p>For a rectangle, the centroid is at the geometric center.</p>\n<p>For a right triangle, divide the base and height into thirds. &nbsp;The centroid is located at the intersection point nearest to the right angle.</p>\n<p>For a semicircle, the centroid is located on the axis of symmetry, a distance of $\\frac{4r}{3\\pi}$ from the straight edge.</p>\n<p></p>\n<p><img src=\"resources/question-resources/centroids_zSOgoBb.png\" width=\"778\" height=\"250\"/></p>", "rulesets": {}, "variables": {"CC": {"name": "CC", "group": "Ungrouped variables", "definition": "C1 + (C2-C1) 4 / 3 / 3.14159", "description": "", "templateType": "anything"}, "C2": {"name": "C2", "group": "inputs", "definition": "random(\n  vector(C1[0],c1[1]+random(-6..6)),\n  vector(C1[0]+random(-6..6),C1[1]))\n  \n  \n  \n  ", "description": "", "templateType": "anything"}, "TC": {"name": "TC", "group": "Ungrouped variables", "definition": "T1 + (T2-T1)/3", "description": "", "templateType": "anything"}, "T1": {"name": "T1", "group": "inputs", "definition": "vector(random(-10..10),random(-8..8))", "description": "", "templateType": "anything"}, "T2": {"name": "T2", "group": "inputs", "definition": "vector(random(-10..10),random(-8..8))", "description": "", "templateType": "anything"}, "C1": {"name": "C1", "group": "inputs", "definition": "vector(random(-10..10),random(-8..8))\n", "description": "", "templateType": "anything"}, "debug": {"name": "debug", "group": "Ungrouped variables", "definition": "false", "description": "", "templateType": "anything"}, "R1": {"name": "R1", "group": "inputs", "definition": "vector(random(-10..10),random(-8..8))", "description": "", "templateType": "anything"}, "R2": {"name": "R2", "group": "inputs", "definition": "vector(random(-10..10),random(-8..8))", "description": "", "templateType": "anything"}, "units": {"name": "units", "group": "Ungrouped variables", "definition": "random('in','cm','mm','ft')", "description": "", "templateType": "anything"}, "RC": {"name": "RC", "group": "Ungrouped variables", "definition": "R1 + (R2-R1)/2", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "(R1-R2)[0] >= 2 and (R1-R2)[1] >= 2 and  \n(T1-T2)[0] >= 2 and (T1-T2)[1] >= 2 and \nC1<>C2 and abs(C1-C2) > 2\n\n", "maxRuns": "200"}, "ungrouped_variables": ["units", "RC", "TC", "CC", "debug"], "variable_groups": [{"name": "inputs", "variables": ["R1", "R2", "T1", "T2", "C1", "C2"]}], "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": "<table border=\"1\" style=\"float: left;\">\n<tbody>\n<tr>\n<th>Part</th>\n<td style=\"text-align: center;\">$\\bar{x}$</td>\n<td style=\"text-align: center;\">$\\bar{y}$</td>\n</tr>\n<tr>\n<th span=\"\" style=\"color: blue;\">Rectangle</th>\n<td>[[0]]</td>\n<td>[[1]]</td>\n</tr>\n<tr>\n<th span=\"\" style=\"color: red;\">Triangle</th>\n<td>[[2]]</td>\n<td>[[3]]</td>\n</tr>\n<tr>\n<th style=\"color: green;\">Semicircle:</th>\n<td>[[4]]</td>\n<td>[[5]]</td>\n</tr>\n</tbody>\n</table>\n<p><span data-jme-visible=\"debug\"> {RC} {units}</span></p>\n<p><span data-jme-visible=\"debug\">{TC} {units}</span></p>\n<p><span data-jme-visible=\"debug\">{CC} {units}</span></p>", "gaps": [{"type": "engineering-answer", "useCustomName": true, "customName": "$R_x$", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(rc[0],units)", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "$R_y$", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(rc[1],units)", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "$T_x$", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(tc[0],units)", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "$T_y$", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(tc[1],units)", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "$C_x$", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(cc[0],units)", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "$C_y$", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(cc[1],units)", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Centroid of a composite area: shape with hole", "extensions": ["geogebra"], "custom_part_types": [{"source": {"pk": 19, "author": {"name": "William Haynes", "pk": 2530}, "edit_page": "/part_type/19/edit"}, "name": "Engineering Accuracy with units", "short_name": "engineering-answer", "description": "<p>A value with units marked right if within an adjustable % error of the correct value. &nbsp;Marked close if within a wider margin of error.</p>", "help_url": "", "input_widget": "string", "input_options": {"correctAnswer": "siground(settings['correctAnswer'],4)", "hint": {"static": true, "value": ""}, "allowEmpty": {"static": true, "value": true}}, "can_be_gap": true, "can_be_step": true, "marking_script": "mark:\nswitch( \n  right and good_units and right_sign, add_credit(1.0,'Correct.'),\n  right and good_units and not right_sign, add_credit(settings['C2'],'Wrong sign.'),\n  right and right_sign and not good_units, add_credit(settings['C2'],'Correct value, but wrong or missing units.'),\n  close and good_units, add_credit(settings['C1'],'Close.'),\n  close and not good_units, add_credit(settings['C3'],'Answer is close, but wrong or missing units.'),\n  incorrect('Wrong answer.')\n)\n\n\ninterpreted_answer:\nqty(student_scalar, student_units)\n\n\n\ncorrect_quantity:\nsettings[\"correctAnswer\"]\n\n\n\ncorrect_units:\nunits(correct_quantity)\n\n\nallowed_notation_styles:\n[\"plain\",\"en\"]\n\nmatch_student_number:\nmatchnumber(studentAnswer,allowed_notation_styles)\n\nstudent_scalar:\nmatch_student_number[1]\n\nstudent_units:\nreplace_regex('ohms','ohm',\n  replace_regex('\u00b0', ' deg',\n    replace_regex('-', ' ' ,\n      studentAnswer[len(match_student_number[0])..len(studentAnswer)])),\"i\")\n\ngood_units:\ntry(\ncompatible(quantity(1, student_units),correct_units),\nmsg,\nfeedback(msg);false)\n\n\nstudent_quantity:\nswitch(not good_units, \n       student_scalar * correct_units, \n       not right_sign,\n       -quantity(student_scalar, student_units),\n       quantity(student_scalar,student_units)\n)\n  \n\n\npercent_error:\ntry(\nscalar(abs((correct_quantity - student_quantity)/correct_quantity))*100  \n,msg,\nif(student_quantity=correct_quantity,0,100))\n   \n\nright:\npercent_error <= settings['right']\n\n\nclose:\nright_sign and percent_error <= settings['close']\n\nright_sign:\nsign(student_scalar) = sign(correct_quantity)", "marking_notes": [{"name": "mark", "description": "This is the main marking note. It should award credit and provide feedback based on the student's answer.", "definition": "switch( \n  right and good_units and right_sign, add_credit(1.0,'Correct.'),\n  right and good_units and not right_sign, add_credit(settings['C2'],'Wrong sign.'),\n  right and right_sign and not good_units, add_credit(settings['C2'],'Correct value, but wrong or missing units.'),\n  close and good_units, add_credit(settings['C1'],'Close.'),\n  close and not good_units, add_credit(settings['C3'],'Answer is close, but wrong or missing units.'),\n  incorrect('Wrong answer.')\n)\n"}, {"name": "interpreted_answer", "description": "A value representing the student's answer to this part.", "definition": "qty(student_scalar, student_units)\n\n"}, {"name": "correct_quantity", "description": "", "definition": "settings[\"correctAnswer\"]\n\n"}, {"name": "correct_units", "description": "", "definition": "units(correct_quantity)\n"}, {"name": "allowed_notation_styles", "description": "", "definition": "[\"plain\",\"en\"]"}, {"name": "match_student_number", "description": "", "definition": "matchnumber(studentAnswer,allowed_notation_styles)"}, {"name": "student_scalar", "description": "", "definition": "match_student_number[1]"}, {"name": "student_units", "description": "<p>Modify&nbsp;the&nbsp;unit portion of&nbsp;the student's answer by</p>\n<p>1. replacing \"ohms\" with \"ohm\" &nbsp;case insensitive</p>\n<p>2.&nbsp;replacing '-'&nbsp;with ' '&nbsp;</p>\n<p>3. replacing '&deg;' with ' deg'&nbsp;</p>\n<p>to allow answers like 10 ft-lb and 30&deg;</p>", "definition": "replace_regex('ohms','ohm',\n  replace_regex('\u00b0', ' deg',\n    replace_regex('-', ' ' ,\n      studentAnswer[len(match_student_number[0])..len(studentAnswer)])),\"i\")"}, {"name": "good_units", "description": "", "definition": "try(\ncompatible(quantity(1, student_units),correct_units),\nmsg,\nfeedback(msg);false)\n"}, {"name": "student_quantity", "description": "<p>This fixes the student answer for two common errors. &nbsp;</p>\n<p>If student_units are wrong&nbsp;&nbsp;- replace with correct units</p>\n<p>If student_scalar has the wrong sign - replace with right sign</p>\n<p>If student makes both errors, only one gets fixed.</p>", "definition": "switch(not good_units, \n       student_scalar * correct_units, \n       not right_sign,\n       -quantity(student_scalar, student_units),\n       quantity(student_scalar,student_units)\n)\n  \n"}, {"name": "percent_error", "description": "", "definition": "try(\nscalar(abs((correct_quantity - student_quantity)/correct_quantity))*100  \n,msg,\nif(student_quantity=correct_quantity,0,100))\n   "}, {"name": "right", "description": "", "definition": "percent_error <= settings['right']\n"}, {"name": "close", "description": "<p>Only marked close if the student actually has the right sign.</p>", "definition": "right_sign and percent_error <= settings['close']"}, {"name": "right_sign", "description": "", "definition": "sign(student_scalar) = sign(correct_quantity) "}], "settings": [{"name": "correctAnswer", "label": "Correct Quantity.", "help_url": "", "hint": "The correct answer given as a JME quantity.", "input_type": "code", "default_value": "", "evaluate": true}, {"name": "right", "label": "% Accuracy for right.", "help_url": "", "hint": "Question will be considered correct if the scalar part of the student's answer is within this % of correct value.", "input_type": "code", "default_value": "0.2", "evaluate": true}, {"name": "close", "label": "% Accuracy for close.", "help_url": "", "hint": "Question will be considered close if the scalar part of the student's answer is within this % of correct value.", "input_type": "code", "default_value": "1.0", "evaluate": true}, {"name": "C1", "label": "Close with units.", "help_url": "", "hint": "Partial Credit for close value with appropriate units. &nbsp;if correct answer is 100 N and close is &plusmn;1%,<br />99 &nbsp;N is accepted.", "input_type": "percent", "default_value": "75"}, {"name": "C2", "label": "No units or wrong sign", "help_url": "", "hint": "Partial credit for forgetting units or using wrong sign.<br />If the correct answer is 100 N, both 100 and -100 N are accepted.", "input_type": "percent", "default_value": "50"}, {"name": "C3", "label": "Close, no units.", "help_url": "", "hint": "Partial Credit for close value but forgotten units.<br />This value would be close&nbsp;if the expected units were provided. &nbsp;If the correct answer is 100 N, and close is &plusmn;1%,<br />99 is accepted.", "input_type": "percent", "default_value": "25"}], "public_availability": "always", "published": true, "extensions": ["quantities"]}], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}], "tags": ["centroids", "composite area method", "Mechanics", "mechanics", "Statics", "statics"], "metadata": {"description": "<p>Find the centroid of&nbsp;a shape made from&nbsp;a rectangle, triangle, and circle.</p>", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "<p>{geogebra_applet('fcfsjuv9',[ ['A',A],['b_1',b1],['h_1',h1],['h_t',ht],['n',n],['Center',center],['radius',radius]])}</p>\n<p><strong></strong>Complete the table below and detemine the coordinates of the centroid of the composite shape.</p>\n<p>Consider the shape to be made up of a {if (m=1,'large','')} rectangle {if (m=0,'and a triangle with a circle','with a triangle and circle')} removed.&nbsp;The circular hole has a {if(random(true,false), 'radius of '+ radius , 'diameter of '+ 2*radius)} {units}, centered at ({(center+A)[0]}, {(center+A)[1]}).</p>", "advice": "<p>{geogebra_applet('fcfsjuv9',[ ['A',A],['b_1',b1],['h_1',h1],['h_t',ht],['n',n],['Center',center],['radius',radius],['visibility',m]])}</p>\n<p></p>\n<p>1. Divide the shape into three subshapes as described in the problem statement.&nbsp;</p>\n<p>2. You should be able to set up a table to gather the required information like the one provided in this problem.</p>\n<p>3. Determine and enter&nbsp;the area and centroidal coordinates for each subshape into the table</p>\n<p style=\"padding-left: 30px;\">$\\qquad A_i, \\bar{x}_i,\\bar{y}_i$</p>\n<p>4. Multiply area by the centroidal coordinates to&nbsp;get the moment of areas for the pieces.</p>\n<p style=\"padding-left: 30px;\">$\\qquad (Q_x)_i = A_i\\bar{y}_i ,\\quad(Q_y)_i=A_i\\bar{x}_i$.</p>\n<p>5. Sum columns 1, 4, and 5&nbsp;to find the total area and moments of area.</p>\n<p style=\"padding-left: 30px;\">$\\qquad A, Q_x, Q_y$</p>\n<p></p>\n<table class=\"centroid\">\n<tbody>\n<tr class=\"underline\">\n<td><strong> Part </strong></td>\n<td>$A_i$ [{units}<sup>2</sup>]</td>\n<td>$\\bar{x}_i$ [{units}]</td>\n<td>$\\bar{y}_i$ [{units}]</td>\n<td>$A_i\\bar{x}_i$ [{units}<sup>3</sup>]</td>\n<td>$A_i\\bar{y}_i$ [{units}<sup>3</sup>]</td>\n</tr>\n<tr>\n<td><strong> rectangle </strong></td>\n<td>{area_rect[m]}</td>\n<td>{C_rect[m][0]}</td>\n<td>{C_rect[m][1]}</td>\n<td>{Q_rect[1]}</td>\n<td>{Q_rect[0]}</td>\n</tr>\n<tr>\n<td><strong> triangle </strong></td>\n<td>{area_tri[m]}</td>\n<td>{siground(C_tri[m][0],3)}</td>\n<td>{siground(C_tri[m][1],3)}</td>\n<td>{Q_tri[1]}</td>\n<td>{Q_tri[0]}</td>\n</tr>\n<tr>\n<td><strong> circle </strong></td>\n<td class=\"underline\">{siground(area_circ[m],3)}</td>\n<td>{C_circ[m][0]}</td>\n<td>{C_circ[m][1]}</td>\n<td class=\"underline\">{siground(Q_circ[1],3)}</td>\n<td class=\"underline\">{siground(Q_circ[0],3)}</td>\n</tr>\n<tr>\n<td><strong> $\\Sigma$ </strong></td>\n<td>{siground(area_total,3)}</td>\n<td></td>\n<td></td>\n<td>{siground(Q_total[1],3)}</td>\n<td>{siground(Q_total[0],3)}</td>\n</tr>\n</tbody>\n</table>\n<p>6. Find answers&nbsp;with&nbsp;&nbsp;</p>\n<p></p>\n<p style=\"padding-left: 30px;\">$\\qquad &nbsp;\\bar{x} = \\dfrac{Q_y}{A} =\\dfrac{\\Sigma A_i \\bar{x}_i}{\\Sigma A_i} = \\dfrac{\\var{siground(Q_total[1],3)}}{\\var{siground(area_total,3)}} = &nbsp;\\var{siground(centroid[0],3)}\\, \\var{units}$</p>\n<p style=\"padding-left: 30px;\">$\\qquad &nbsp;\\bar{y} &nbsp;= \\dfrac{Q_x}{A} = \\dfrac{\\Sigma A_i \\bar{y}_i}{\\Sigma A_i}= \\dfrac{\\var{siground(Q_total[0],3)}}{\\var{siground(area_total,3)}}= \\var{siground(centroid[1],3)}\\, \\var{units} $</p>", "rulesets": {}, "variables": {"ht": {"name": "ht", "group": "Input values", "definition": "random(3..9#3)", "description": "<p>\"height\" of triangle &nbsp;</p>\n<p>horizontal for n = 4,5,6,10,11,12</p>\n<p>vertical for n = 1,2,3,7,8,9</p>", "templateType": "anything"}, "C_rect": {"name": "C_rect", "group": "centroids", "definition": "[vector(b1/2,h1/2) + A,\n if(n in [1,2,3], vector(b1/2,(h1-ht)/2)+A,\n if(n in [4,5,6], vector((b1+ht)/2,h1/2)+A,\n if(n in [7,8,9], vector(b1/2,(h1+ht)/2)+A,\n vector((b1-ht)/2,h1/2)+A)))] ", "description": "", "templateType": "anything"}, "C_circ": {"name": "C_circ", "group": "centroids", "definition": "[center +A ,center +A]", "description": "", "templateType": "anything"}, "units": {"name": "units", "group": "Input values", "definition": "random('in', 'cm', 'ft' )", "description": "<p>Offset of bottom right corner from originl</p>", "templateType": "anything"}, "area_circ": {"name": "area_circ", "group": "Calculated areas", "definition": "[- pi * radius^2, - pi* radius^2]", "description": "", "templateType": "anything"}, "area_total": {"name": "area_total", "group": "Calculated areas", "definition": "area_rect[0]+area_tri[0]+area_circ[0]", "description": "", "templateType": "anything"}, "area_tri": {"name": "area_tri", "group": "Calculated areas", "definition": "[if(n in [1,2,3,7,8,9], b1*ht/2,h1*ht/2),\n-if(n in [1,2,3,7,8,9], b1*ht/2,h1*ht/2)]", "description": "", "templateType": "anything"}, "center": {"name": "center", "group": "Input values", "definition": "vector(b1/2,h1/2) + random(0..3) *\nvector(if(n<=3,[0,-1],\nif(n<=6,[1,0],\nif(n<=9,[0,1],\n[-1,0]))))\n\n\n\n\n", "description": "<p>center of the circle measured from bottom left of the rectangle</p>", "templateType": "anything"}, "Q_circ": {"name": "Q_circ", "group": "moments of area", "definition": "area_circ[m] * vector(C_circ[m][1],C_circ[m][0])", "description": "", "templateType": "anything"}, "radius": {"name": "radius", "group": "Input values", "definition": "random(1..(min(h1-1,b1-1)/2)#0.5)", "description": "<p>radius of the circle</p>", "templateType": "anything"}, "A": {"name": "A", "group": "Input values", "definition": "-vector(random([0,0],[b1,0],[b1,h1],[0,h1],[b1/2,h1/2],[0,h1/2],[center[0],center[1]]))", "description": "<p>This offsets the shape to one of the corners of the rect, the center of the rect, or the center of the circle.</p>", "templateType": "anything"}, "h1": {"name": "h1", "group": "Input values", "definition": "random(4..12#2)", "description": "<p>vertical height of rectangle</p>", "templateType": "anything"}, "b1": {"name": "b1", "group": "Input values", "definition": "random(4..12#2)", "description": "<p>horizontal base of rectangle</p>", "templateType": "anything"}, "n": {"name": "n", "group": "Input values", "definition": "random(1 .. 12#1)", "description": "<p>Selects the position of the triangle, index gives vertex location</p>\n<table>\n<tbody>\n<tr>\n<td style=\"text-align: center;\"></td>\n<td style=\"text-align: center;\">9</td>\n<td style=\"text-align: center;\">8</td>\n<td style=\"text-align: center;\">7</td>\n<td style=\"text-align: center;\"></td>\n</tr>\n<tr>\n<td style=\"text-align: center;\">10</td>\n<td style=\"text-align: center;\"></td>\n<td style=\"text-align: center;\"></td>\n<td style=\"text-align: center;\"></td>\n<td style=\"text-align: center;\">6</td>\n</tr>\n<tr>\n<td style=\"text-align: center;\">11</td>\n<td style=\"text-align: center;\"></td>\n<td style=\"text-align: center;\">rectangle</td>\n<td style=\"text-align: center;\"></td>\n<td style=\"text-align: center;\">5</td>\n</tr>\n<tr>\n<td style=\"text-align: center;\">12</td>\n<td style=\"text-align: center;\"></td>\n<td style=\"text-align: center;\"></td>\n<td style=\"text-align: center;\"></td>\n<td style=\"text-align: center;\">4</td>\n</tr>\n<tr>\n<td style=\"text-align: center;\"></td>\n<td style=\"text-align: center;\">1</td>\n<td style=\"text-align: center;\">2</td>\n<td style=\"text-align: center;\">3</td>\n<td style=\"text-align: center;\"></td>\n</tr>\n</tbody>\n</table>", "templateType": "randrange"}, "C_tri": {"name": "C_tri", "group": "centroids", "definition": "// determines location of centroid\n// returns array of centroid coordinates, first term for m=0 \n[\nswitch(\n  n=1, vector(b1/3,-ht/3),\n  n=2, vector(b1/2,-ht/3),\n  n=3, vector(2*b1/3,-ht/3),\n  n=4, vector(b1+ht/3,h1/3),\n  n=5, vector(b1+ht/3,h1/2),\n  n=6, vector(b1+ht/3,2*h1/3),\n  n=7, vector(2 * b1/3, h1+ht/3),\n  n=8, vector(b1/2, h1+ht/3),\n  n=9, vector(b1/3, h1+ht/3),\n  n=10, vector(-ht/3,2*h1/3),\n  n=11, vector(-ht/3,h1/2),\n  n=12, vector(-ht/3,h1/3)\n  ) + A\n  ,\n  switch(\n  n=3, vector(b1/3,-2*ht/3),\n  n=2, vector(b1/2,-2*ht/3),\n  n=1, vector(2*b1/3,-2*ht/3),\n  n=6, vector(b1+2*ht/3,h1/3),\n  n=5, vector(b1+2*ht/3,h1/2),\n  n=4, vector(b1+2*ht/3,2*h1/3),\n  n=9, vector(2 * b1/3, h1+2*ht/3),\n  n=8, vector(b1/2, h1+2*ht/3),\n  n=7, vector(b1/3, h1+2*ht/3),\n  n=12, vector(-2*ht/3,2*h1/3),\n  n=11, vector(-2*ht/3,h1/2),\n  n=10, vector(-2*ht/3,h1/3)\n  ) + A\n  ]", "description": "<p>determines location of centroid of triangle based on location and method<br />returns array of centroid coordinates, first term for m=0 <br /><br /></p>", "templateType": "anything"}, "m": {"name": "m", "group": "Input values", "definition": "if(n in [2,5,8,11],0,random(0..1))\n", "description": "<p>This is the method used to solve the problem:&nbsp;</p>\n<p>m=0: small rectangle + triangle - circle</p>\n<p>m=1: big rectangle - triangle - circle</p>\n<p>when n is in [2,5,8,11], use method 0, becauses otherwise it would require 2 negative triangles.</p>", "templateType": "anything"}, "Q_rect": {"name": "Q_rect", "group": "moments of area", "definition": "area_rect[m] * vector(C_rect[m][1],C_rect[m][0])", "description": "<p>[Q_x,Q_y]</p>", "templateType": "anything"}, "area_rect": {"name": "area_rect", "group": "Calculated areas", "definition": "[b1*h1,if(n in [1,2,3,7,8,9],b1*(h1+ht),h1*(b1+ht))]", "description": "", "templateType": "anything"}, "centroid": {"name": "centroid", "group": "moments of area", "definition": "vector(Q_total[1]/area_total,Q_total[0]/area_total)", "description": "", "templateType": "anything"}, "Q_tri": {"name": "Q_tri", "group": "moments of area", "definition": "area_tri[m] * vector(C_tri[m][1],C_tri[m][0])", "description": "", "templateType": "anything"}, "Q_total": {"name": "Q_total", "group": "moments of area", "definition": "Q_rect+Q_tri+Q_circ", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "// tries to prevent the circle from extending beyond the perimiter.\n\nif (n<=3,  center[1]-2*radius   > -(h1+ht/2),\nif (n<=6, (center[0]+2*radius) <  (b1+ht/2),\nif (n<=9, (center[1]+2*radius) <  (h1+ht/2),\n          (center[0]-2*radius) > -(b1-ht/2))))\n", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [{"name": "Input values", "variables": ["A", "b1", "h1", "ht", "center", "units", "radius", "n", "m"]}, {"name": "Calculated areas", "variables": ["area_rect", "area_tri", "area_circ", "area_total"]}, {"name": "centroids", "variables": ["C_rect", "C_circ", "C_tri"]}, {"name": "moments of area", "variables": ["Q_rect", "Q_tri", "Q_circ", "Q_total", "centroid"]}], "functions": {}, "preamble": {"js": "\n", "css": "table.centroid{margin-left:0;}\n\ntable.centroid td {\n  width:6em; \n  vertical-align:center; \n  text-align:center;}\ntable.centroid *.underline {border-bottom: 2px solid black;}\n\n"}, "parts": [{"type": "gapfill", "useCustomName": true, "customName": "Table", "marks": 0, "scripts": {"mark": {"script": "//var method = Numbas.jme.unwrapValue(this.scope.variables.m);\n//numbasGGBApplet0.setValue('visibility',method)\n", "order": "after"}}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<table class=\"centroid &lt;/button&gt;\" tbody=\"\">\n<tbody>\n<tr class=\"underline\">\n<td><strong> Part </strong></td>\n<td>\n<p>$A_i$&nbsp;</p>\n</td>\n<td class=\"underline\">\n<p>$\\bar{x}_i$&nbsp;</p>\n</td>\n<td>\n<p>$\\bar{y}_i$&nbsp;</p>\n</td>\n<td>\n<p>$A_i\\bar{x}_i$&nbsp;</p>\n</td>\n<td>\n<p>$A_i\\bar{y}_i$&nbsp;</p>\n</td>\n</tr>\n<tr>\n<td><strong> rectangle </strong></td>\n<td>[[0]]</td>\n<td>[[4]]</td>\n<td>[[7]]</td>\n<td>[[10]]</td>\n<td>[[14]]</td>\n</tr>\n<tr>\n<td><strong> triangle </strong></td>\n<td>[[1]]</td>\n<td>[[5]]</td>\n<td>[[8]]</td>\n<td>[[11]]</td>\n<td>[[15]]</td>\n</tr>\n<tr>\n<td><strong> circle </strong></td>\n<td class=\"underline\">[[2]]</td>\n<td>[[6]]</td>\n<td>[[9]]</td>\n<td class=\"underline\">[[12]]</td>\n<td class=\"underline\">[[16]]</td>\n</tr>\n<tr>\n<td><strong> $\\Sigma$ </strong></td>\n<td>[[3]]</td>\n<td></td>\n<td></td>\n<td>[[13]]</td>\n<td>[[17]]</td>\n</tr>\n</tbody>\n</table>\n<p></p>", "gaps": [{"type": "engineering-answer", "useCustomName": true, "customName": "Ar", "marks": "0", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(area_rect[m],units)*qty(1,units)", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "At", "marks": "0", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(area_tri[m],units)*qty(1,units)", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "Ac", 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"C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "xr", "marks": "0", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(C_rect[m][0],units)", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "xt", "marks": "0", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(C_tri[m][0],units)", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "xc", "marks": "0", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(C_circ[m][0],units)", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "yr", "marks": "0", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(C_rect[m][1],units)", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "yt", "marks": "0", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(C_tri[m][1],units)", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "yc", "marks": "0", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(C_circ[m][1],units)", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "qyr", "marks": "0", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(Q_rect[1],units)*qty(1,units)*qty(1,units)", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "qyt", "marks": "0", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(Q_tri[1],units)*qty(1,units)*qty(1,units)", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "qyc", "marks": "0", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(Q_circ[1],units)*qty(1,units)*qty(1,units)", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "qy", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(Q_total[1],units)*qty(1,units)*qty(1,units)", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "qxr", "marks": "0", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(Q_rect[0],units)*qty(1,units)*qty(1,units)", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "qxt", "marks": "0", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(Q_tri[0],units)*qty(1,units)*qty(1,units)", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "qxr", "marks": "0", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(Q_circ[0],units)*qty(1,units)*qty(1,units)", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "qx", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(Q_total[0],units)*qty(1,units)*qty(1,units)", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "Centroid", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>$\\bar{x} =\\dfrac{Q_y}{A} =$ [[0]]&nbsp;$\\qquad \\bar{y} =\\dfrac{Q_x}{A} = $ [[1]]<br/><br/></p>", "gaps": [{"type": "engineering-answer", "useCustomName": true, "customName": "xbar", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "quantity(centroid[0],units)", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "ybar", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "quantity(centroid[1],units)", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Centroid of a composite area: rectangles and triangles", "extensions": ["geogebra", "quantities"], "custom_part_types": [{"source": {"pk": 19, "author": {"name": "William Haynes", "pk": 2530}, "edit_page": "/part_type/19/edit"}, "name": "Engineering Accuracy with units", "short_name": "engineering-answer", "description": "<p>A value with units marked right if within an adjustable % error of the correct value. &nbsp;Marked close if within a wider margin of error.</p>", "help_url": "", "input_widget": "string", "input_options": {"correctAnswer": "siground(settings['correctAnswer'],4)", "hint": {"static": true, "value": ""}, "allowEmpty": {"static": true, "value": true}}, "can_be_gap": true, "can_be_step": true, "marking_script": "mark:\nswitch( \n  right and good_units and right_sign, add_credit(1.0,'Correct.'),\n  right and good_units and not right_sign, add_credit(settings['C2'],'Wrong sign.'),\n  right and right_sign and not good_units, add_credit(settings['C2'],'Correct value, but wrong or missing units.'),\n  close and good_units, add_credit(settings['C1'],'Close.'),\n  close and not good_units, add_credit(settings['C3'],'Answer is close, but wrong or missing units.'),\n  incorrect('Wrong answer.')\n)\n\n\ninterpreted_answer:\nqty(student_scalar, student_units)\n\n\n\ncorrect_quantity:\nsettings[\"correctAnswer\"]\n\n\n\ncorrect_units:\nunits(correct_quantity)\n\n\nallowed_notation_styles:\n[\"plain\",\"en\"]\n\nmatch_student_number:\nmatchnumber(studentAnswer,allowed_notation_styles)\n\nstudent_scalar:\nmatch_student_number[1]\n\nstudent_units:\nreplace_regex('ohms','ohm',\n  replace_regex('\u00b0', ' deg',\n    replace_regex('-', ' ' ,\n      studentAnswer[len(match_student_number[0])..len(studentAnswer)])),\"i\")\n\ngood_units:\ntry(\ncompatible(quantity(1, student_units),correct_units),\nmsg,\nfeedback(msg);false)\n\n\nstudent_quantity:\nswitch(not good_units, \n       student_scalar * correct_units, \n       not right_sign,\n       -quantity(student_scalar, student_units),\n       quantity(student_scalar,student_units)\n)\n  \n\n\npercent_error:\ntry(\nscalar(abs((correct_quantity - student_quantity)/correct_quantity))*100  \n,msg,\nif(student_quantity=correct_quantity,0,100))\n   \n\nright:\npercent_error <= settings['right']\n\n\nclose:\nright_sign and percent_error <= settings['close']\n\nright_sign:\nsign(student_scalar) = sign(correct_quantity)", "marking_notes": [{"name": "mark", "description": "This is the main marking note. It should award credit and provide feedback based on the student's answer.", "definition": "switch( \n  right and good_units and right_sign, add_credit(1.0,'Correct.'),\n  right and good_units and not right_sign, add_credit(settings['C2'],'Wrong sign.'),\n  right and right_sign and not good_units, add_credit(settings['C2'],'Correct value, but wrong or missing units.'),\n  close and good_units, add_credit(settings['C1'],'Close.'),\n  close and not good_units, add_credit(settings['C3'],'Answer is close, but wrong or missing units.'),\n  incorrect('Wrong answer.')\n)\n"}, {"name": "interpreted_answer", "description": "A value representing the student's answer to this part.", "definition": "qty(student_scalar, student_units)\n\n"}, {"name": "correct_quantity", "description": "", "definition": "settings[\"correctAnswer\"]\n\n"}, {"name": "correct_units", "description": "", "definition": "units(correct_quantity)\n"}, {"name": "allowed_notation_styles", "description": "", "definition": "[\"plain\",\"en\"]"}, {"name": "match_student_number", "description": "", "definition": "matchnumber(studentAnswer,allowed_notation_styles)"}, {"name": "student_scalar", "description": "", "definition": "match_student_number[1]"}, {"name": "student_units", "description": "<p>Modify&nbsp;the&nbsp;unit portion of&nbsp;the student's answer by</p>\n<p>1. replacing \"ohms\" with \"ohm\" &nbsp;case insensitive</p>\n<p>2.&nbsp;replacing '-'&nbsp;with ' '&nbsp;</p>\n<p>3. replacing '&deg;' with ' deg'&nbsp;</p>\n<p>to allow answers like 10 ft-lb and 30&deg;</p>", "definition": "replace_regex('ohms','ohm',\n  replace_regex('\u00b0', ' deg',\n    replace_regex('-', ' ' ,\n      studentAnswer[len(match_student_number[0])..len(studentAnswer)])),\"i\")"}, {"name": "good_units", "description": "", "definition": "try(\ncompatible(quantity(1, student_units),correct_units),\nmsg,\nfeedback(msg);false)\n"}, {"name": "student_quantity", "description": "<p>This fixes the student answer for two common errors. &nbsp;</p>\n<p>If student_units are wrong&nbsp;&nbsp;- replace with correct units</p>\n<p>If student_scalar has the wrong sign - replace with right sign</p>\n<p>If student makes both errors, only one gets fixed.</p>", "definition": "switch(not good_units, \n       student_scalar * correct_units, \n       not right_sign,\n       -quantity(student_scalar, student_units),\n       quantity(student_scalar,student_units)\n)\n  \n"}, {"name": "percent_error", "description": "", "definition": "try(\nscalar(abs((correct_quantity - student_quantity)/correct_quantity))*100  \n,msg,\nif(student_quantity=correct_quantity,0,100))\n   "}, {"name": "right", "description": "", "definition": "percent_error <= settings['right']\n"}, {"name": "close", "description": "<p>Only marked close if the student actually has the right sign.</p>", "definition": "right_sign and percent_error <= settings['close']"}, {"name": "right_sign", "description": "", "definition": "sign(student_scalar) = sign(correct_quantity) "}], "settings": [{"name": "correctAnswer", "label": "Correct Quantity.", "help_url": "", "hint": "The correct answer given as a JME quantity.", "input_type": "code", "default_value": "", "evaluate": true}, {"name": "right", "label": "% Accuracy for right.", "help_url": "", "hint": "Question will be considered correct if the scalar part of the student's answer is within this % of correct value.", "input_type": "code", "default_value": "0.2", "evaluate": true}, {"name": "close", "label": "% Accuracy for close.", "help_url": "", "hint": "Question will be considered close if the scalar part of the student's answer is within this % of correct value.", "input_type": "code", "default_value": "1.0", "evaluate": true}, {"name": "C1", "label": "Close with units.", "help_url": "", "hint": "Partial Credit for close value with appropriate units. &nbsp;if correct answer is 100 N and close is &plusmn;1%,<br />99 &nbsp;N is accepted.", "input_type": "percent", "default_value": "75"}, {"name": "C2", "label": "No units or wrong sign", "help_url": "", "hint": "Partial credit for forgetting units or using wrong sign.<br />If the correct answer is 100 N, both 100 and -100 N are accepted.", "input_type": "percent", "default_value": "50"}, {"name": "C3", "label": "Close, no units.", "help_url": "", "hint": "Partial Credit for close value but forgotten units.<br />This value would be close&nbsp;if the expected units were provided. &nbsp;If the correct answer is 100 N, and close is &plusmn;1%,<br />99 is accepted.", "input_type": "percent", "default_value": "25"}], "public_availability": "always", "published": true, "extensions": ["quantities"]}], "resources": [["question-resources/centroid-t-r.ggb", "/srv/numbas/media/question-resources/centroid-t-r.ggb"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}], "tags": ["centroids", "first moment of area", "mechanics", "Mechanics", "statics", "Statics"], "metadata": {"description": "<p>Find the centroid of a shape made up of a rectangle and two triangles.</p>", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "<p>{applet()}</p>\n<p>Determine the coordinates of the centroid of the polygon shown. &nbsp;Grid units are [{units}].</p>\n<p>Consider the polygon to be made up of a ({b0} $\\times$&nbsp;{h0}) rectangle {sign1} a ({b1} $\\times$&nbsp;{h1}) triangle {sign2} a ({b2} $\\times$&nbsp;{h2}) triangle.</p>", "advice": "<div>\n<table border=\"1px\" style=\"float: left;\">\n<tbody>\n<tr>\n<td>Part</td>\n<td>$A_i$</td>\n<td>$\\bar{x}_i$</td>\n<td>$\\bar{y}_i$</td>\n<td>$A_i\\bar{x}_i$</td>\n<td>$A_i\\bar{y}_i$</td>\n</tr>\n<tr>\n<td>Rectangle</td>\n<td>{A0}</td>\n<td>{bar(C0[0])}</td>\n<td>{bar(C0[1])}</td>\n<td>{Q(a0, c0[0])}</td>\n<td>{Q(a0, c0[1])}</td>\n</tr>\n<tr>\n<td>Triangle 1</td>\n<td>{A1}</td>\n<td>{bar(C1[0])}</td>\n<td>{bar(C1[1])}</td>\n<td>{Q(a1, c1[0])}</td>\n<td>{Q(a1, c1[1])}</td>\n</tr>\n<tr>\n<td>Triangle 2</td>\n<td>{A2}</td>\n<td>{bar(C2[0])}</td>\n<td>{bar(C2[1])}</td>\n<td>{Q(a2, c2[0])}</td>\n<td>{Q(a2, c2[1])}</td>\n</tr>\n<tr>\n<td>$\\Sigma$</td>\n<td>{AT}</td>\n<td></td>\n<td></td>\n<td>{display(xbar AT)}</td>\n<td>{display(ybar AT)}</td>\n</tr>\n</tbody>\n</table>\n</div>\n<div>\n<p>$\\qquad\\bar{x} = \\dfrac{\\Sigma A_i\\bar{x}_i}{\\Sigma A_i} = &nbsp;\\var{display(xbar)}$</p>\n<p>$\\qquad \\bar{y} = &nbsp;\\dfrac{\\Sigma A_i\\bar{y}_i}{\\Sigma A_i} &nbsp;=\\var{display(ybar)}$</p>\n</div>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"A": {"name": "A", "group": "Ungrouped variables", "definition": "vector(0,random(2..12))", "description": "", "templateType": "anything", "can_override": false}, "C2": {"name": "C2", "group": "geometry", "definition": "vector(A[0],B[1])+(vector(B[0],A[1])-vector(A[0],B[1]))/3  ", "description": "", "templateType": "anything", "can_override": false}, "A0": {"name": "A0", "group": "geometry", "definition": "b0 h0", "description": "", "templateType": "anything", "can_override": false}, "A2": {"name": "A2", "group": "geometry", "definition": "b2 h2/2 if(sign2='+',1,-1)", "description": "", "templateType": "anything", "can_override": false}, "b0": {"name": "b0", "group": "geometry", "definition": "qty(B[0\n  ],units)", "description": "", "templateType": "anything", "can_override": false}, "C": {"name": "C", "group": "Ungrouped variables", "definition": "vector(random(2..12),0)", "description": "", "templateType": "anything", "can_override": false}, "b2": {"name": "b2", "group": "geometry", "definition": "b0", "description": "", "templateType": "anything", "can_override": false}, "C1": {"name": "C1", "group": "geometry", "definition": "vector(B[0],C[1])+(vector(C[0],B[1])-vector(B[0],C[1]))/3  ", "description": "", "templateType": "anything", "can_override": false}, "A1": {"name": "A1", "group": "geometry", "definition": "b1 h1 /2 if(sign1='+',1,-1)", "description": "", "templateType": "anything", "can_override": false}, "ybar": {"name": "ybar", "group": "Unnamed group", "definition": "(a0 c0[1] + a1 c1[1] + a2 c2[1])/AT qty(1,units)", "description": "", "templateType": "anything", "can_override": false}, "h1": {"name": "h1", "group": "geometry", "definition": "h0", "description": "", "templateType": "anything", "can_override": false}, "B": {"name": "B", "group": "Ungrouped variables", "definition": "vector(random(2..12),random(2..12))", "description": "", "templateType": "anything", "can_override": false}, "h0": {"name": "h0", "group": "geometry", "definition": "qty(B[1],units)", "description": "", "templateType": "anything", "can_override": false}, "sign2": {"name": "sign2", "group": "geometry", "definition": "if(b[1]<a[1],'+','\u2013')", "description": "", "templateType": "anything", "can_override": false}, "C0": {"name": "C0", "group": "geometry", "definition": "(B/2)", "description": "", "templateType": "anything", "can_override": false}, "AT": {"name": "AT", "group": "geometry", "definition": "A0+A1+A2", "description": "", "templateType": "anything", "can_override": false}, "h2": {"name": "h2", "group": "geometry", "definition": "qty(abs(b[1]-A[1]),units)", "description": "", "templateType": "anything", "can_override": false}, "xbar": {"name": "xbar", "group": "Unnamed group", "definition": "(a0 c0[0] + a1 c1[0] + a2 c2[0])/AT qty(1,units)", "description": "", "templateType": "anything", "can_override": false}, "b1": {"name": "b1", "group": "geometry", "definition": "qty(abs(b[0]-c[0]),units)", "description": "", "templateType": "anything", "can_override": false}, "units": {"name": "units", "group": "Ungrouped variables", "definition": "random('in','cm','ft','m')", "description": "", "templateType": "anything", "can_override": false}, "sign1": {"name": "sign1", "group": "geometry", "definition": "if(b[0]<c[0],'+','\u2013')", "description": "", "templateType": "anything", "can_override": false}, "debug": {"name": "debug", "group": "Ungrouped variables", "definition": "false", "description": "", "templateType": "anything", "can_override": false}, "D": {"name": "D", "group": "Ungrouped variables", "definition": "vector(0,0)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "B[1]<>A[1] and B[0]<>C[0]", "maxRuns": "100"}, "ungrouped_variables": ["A", "B", "C", "D", "units", "debug"], "variable_groups": [{"name": "geometry", "variables": ["b0", "h0", "b2", "h1", "b1", "h2", "sign1", "sign2", "A0", "A1", "A2", "AT", "C0", "C2", "C1"]}, {"name": "Unnamed group", "variables": ["xbar", "ybar"]}], "functions": {"Q": {"parameters": [["area", "quantity"], ["distance", "number"]], "type": "quantity", "language": "jme", "definition": "display(area*distance*qty(1,units))"}, "display": {"parameters": [["q", "quantity"]], "type": "quantity", "language": "jme", "definition": "string(siground(q,4))"}, "bar": {"parameters": [["coord", "number"]], "type": "quantity", "language": "jme", "definition": "display(quantity(coord,units))"}, "applet": {"parameters": [], "type": "ggbapplet", "language": "javascript", "definition": "\n// Create the worksheet. \n// This function returns an object with a container `element` and a `promise` resolving to a GeoGebra applet.\nvar params = {\n  material_id: 'ftkm8mfx',\n  //alternate method, load from file.\n  //filename: \"resources/question-resources/centroid-t-r.ggb\",\n  //width:400,\n  //height:300\n  // was geogebra_applet('ftkm8mfx',[['A',A],['B',B],['C',C]])\n}\n\nvar result = Numbas.extensions.geogebra.createGeogebraApplet(params);\n\n// Once the applet has loaded, run some commands to manipulate the worksheet.\nresult.promise.then(function(d) {\n  var app = d.app;\n  question.applet = d;\n  \n  \nfunction setGGBPoint(name) {\n    // moves point in GGB to location of Numbas Vector Variable\n    var pt = question.scope.evaluate(name).value\n    app.setFixed(name,false,false);\n    app.setCoords(name, pt[0], pt[1]);\n    app.setFixed(name,true,true);\n  }\n\n  setGGBPoint(\"A\");\n  setGGBPoint(\"B\");\n  setGGBPoint(\"C\");\n  setGGBPoint(\"D\");\n  app.setVisible(\"Centroid\",false);\n  \n});\n\n// This function returns the result of `createGeogebraApplet` as an object \n// with the JME data type 'ggbapplet', which can be substituted into the question's content.\nreturn new Numbas.jme.types.ggbapplet(result);"}}, "preamble": {"js": "question.signals.on('adviceDisplayed',function() {\n   try{\n    var app = question.applet.app;\n \n  app.setVisible(\"Centroid\",true);\n  \n  }\n  catch(err){}  \n})\n\n\n\n", "css": "table.centroid{margin-left:0;}\n\ntable.centroid td {\n  width:6em; \n  vertical-align:center; \n  text-align:center;}\ntable.centroid *.underline {border-bottom: 2px solid black;}\n\n"}, "parts": [{"type": "gapfill", "useCustomName": true, "customName": "Info Table", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<table style=\"float: left; width: 625px;\" class=\"centroid\">\n<tbody>\n<tr class=\"underline\">\n<th style=\"width: 120px;\">Part</th>\n<td style=\"width: 120px; text-align: center;\">$A_i$</td>\n<td style=\"width: 120px; text-align: 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"extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "a0 * c0[1] * qty(1,units)", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "Q_{x_1}", "marks": "0", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "a1 * c1[1] * qty(1,units)", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "Q_{x_2}", "marks": "0", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "a2 * c2[1] * qty(1,units)", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "$Q_y$", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "xbar * AT", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "$Q_x$", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "ybar * AT", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "Results", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>$\\bar{x} =\\dfrac{Q_y}{A} = $&nbsp;[[0]] &nbsp;$\\qquad \\bar{y} =\\dfrac{Q_x}{A} =$&nbsp;[[1]]</p>", "gaps": [{"type": "engineering-answer", "useCustomName": true, "customName": "$\\bar{x}$", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "xbar", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "$\\bar{y}$", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": 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"reviewshowfeedback": true, "reviewshowexpectedanswer": true, "reviewshowadvice": true, "feedbackmessages": []}, "diagnostic": {"knowledge_graph": {"topics": [], "learning_objectives": []}, "script": "diagnosys", "customScript": ""}, "contributors": [{"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}], "extensions": ["geogebra", "quantities"], "custom_part_types": [{"source": {"pk": 19, "author": {"name": "William Haynes", "pk": 2530}, "edit_page": "/part_type/19/edit"}, "name": "Engineering Accuracy with units", "short_name": "engineering-answer", "description": "<p>A value with units marked right if within an adjustable % error of the correct value. &nbsp;Marked close if within a wider margin of error.</p>", "help_url": "", "input_widget": "string", "input_options": {"correctAnswer": "siground(settings['correctAnswer'],4)", "hint": {"static": true, "value": ""}, "allowEmpty": {"static": true, "value": true}}, "can_be_gap": true, "can_be_step": true, "marking_script": "mark:\nswitch( \n  right and good_units and right_sign, add_credit(1.0,'Correct.'),\n  right and good_units and not right_sign, add_credit(settings['C2'],'Wrong sign.'),\n  right and right_sign and not good_units, add_credit(settings['C2'],'Correct value, but wrong or missing units.'),\n  close and good_units, add_credit(settings['C1'],'Close.'),\n  close and not good_units, add_credit(settings['C3'],'Answer is close, but wrong or missing units.'),\n  incorrect('Wrong answer.')\n)\n\n\ninterpreted_answer:\nqty(student_scalar, student_units)\n\n\n\ncorrect_quantity:\nsettings[\"correctAnswer\"]\n\n\n\ncorrect_units:\nunits(correct_quantity)\n\n\nallowed_notation_styles:\n[\"plain\",\"en\"]\n\nmatch_student_number:\nmatchnumber(studentAnswer,allowed_notation_styles)\n\nstudent_scalar:\nmatch_student_number[1]\n\nstudent_units:\nreplace_regex('ohms','ohm',\n  replace_regex('\u00b0', ' deg',\n    replace_regex('-', ' ' ,\n      studentAnswer[len(match_student_number[0])..len(studentAnswer)])),\"i\")\n\ngood_units:\ntry(\ncompatible(quantity(1, student_units),correct_units),\nmsg,\nfeedback(msg);false)\n\n\nstudent_quantity:\nswitch(not good_units, \n       student_scalar * correct_units, \n       not right_sign,\n       -quantity(student_scalar, student_units),\n       quantity(student_scalar,student_units)\n)\n  \n\n\npercent_error:\ntry(\nscalar(abs((correct_quantity - student_quantity)/correct_quantity))*100  \n,msg,\nif(student_quantity=correct_quantity,0,100))\n   \n\nright:\npercent_error <= settings['right']\n\n\nclose:\nright_sign and percent_error <= settings['close']\n\nright_sign:\nsign(student_scalar) = sign(correct_quantity)", "marking_notes": [{"name": "mark", "description": "This is the main marking note. It should award credit and provide feedback based on the student's answer.", "definition": "switch( \n  right and good_units and right_sign, add_credit(1.0,'Correct.'),\n  right and good_units and not right_sign, add_credit(settings['C2'],'Wrong sign.'),\n  right and right_sign and not good_units, add_credit(settings['C2'],'Correct value, but wrong or missing units.'),\n  close and good_units, add_credit(settings['C1'],'Close.'),\n  close and not good_units, add_credit(settings['C3'],'Answer is close, but wrong or missing units.'),\n  incorrect('Wrong answer.')\n)\n"}, {"name": "interpreted_answer", "description": "A value representing the student's answer to this part.", "definition": "qty(student_scalar, student_units)\n\n"}, {"name": "correct_quantity", "description": "", "definition": "settings[\"correctAnswer\"]\n\n"}, {"name": "correct_units", "description": "", "definition": "units(correct_quantity)\n"}, {"name": "allowed_notation_styles", "description": "", "definition": "[\"plain\",\"en\"]"}, {"name": "match_student_number", "description": "", "definition": "matchnumber(studentAnswer,allowed_notation_styles)"}, {"name": "student_scalar", "description": "", "definition": "match_student_number[1]"}, {"name": "student_units", "description": "<p>Modify&nbsp;the&nbsp;unit portion of&nbsp;the student's answer by</p>\n<p>1. replacing \"ohms\" with \"ohm\" &nbsp;case insensitive</p>\n<p>2.&nbsp;replacing '-'&nbsp;with ' '&nbsp;</p>\n<p>3. replacing '&deg;' with ' deg'&nbsp;</p>\n<p>to allow answers like 10 ft-lb and 30&deg;</p>", "definition": "replace_regex('ohms','ohm',\n  replace_regex('\u00b0', ' deg',\n    replace_regex('-', ' ' ,\n      studentAnswer[len(match_student_number[0])..len(studentAnswer)])),\"i\")"}, {"name": "good_units", "description": "", "definition": "try(\ncompatible(quantity(1, student_units),correct_units),\nmsg,\nfeedback(msg);false)\n"}, {"name": "student_quantity", "description": "<p>This fixes the student answer for two common errors. &nbsp;</p>\n<p>If student_units are wrong&nbsp;&nbsp;- replace with correct units</p>\n<p>If student_scalar has the wrong sign - replace with right sign</p>\n<p>If student makes both errors, only one gets fixed.</p>", "definition": "switch(not good_units, \n       student_scalar * correct_units, \n       not right_sign,\n       -quantity(student_scalar, student_units),\n       quantity(student_scalar,student_units)\n)\n  \n"}, {"name": "percent_error", "description": "", "definition": "try(\nscalar(abs((correct_quantity - student_quantity)/correct_quantity))*100  \n,msg,\nif(student_quantity=correct_quantity,0,100))\n   "}, {"name": "right", "description": "", "definition": "percent_error <= settings['right']\n"}, {"name": "close", "description": "<p>Only marked close if the student actually has the right sign.</p>", "definition": "right_sign and percent_error <= settings['close']"}, {"name": "right_sign", "description": "", "definition": "sign(student_scalar) = sign(correct_quantity) "}], "settings": [{"name": "correctAnswer", "label": "Correct Quantity.", "help_url": "", "hint": "The correct answer given as a JME quantity.", "input_type": "code", "default_value": "", "evaluate": true}, {"name": "right", "label": "% Accuracy for right.", "help_url": "", "hint": "Question will be considered correct if the scalar part of the student's answer is within this % of correct value.", "input_type": "code", "default_value": "0.2", "evaluate": true}, {"name": "close", "label": "% Accuracy for close.", "help_url": "", "hint": "Question will be considered close if the scalar part of the student's answer is within this % of correct value.", "input_type": "code", "default_value": "1.0", "evaluate": true}, {"name": "C1", "label": "Close with units.", "help_url": "", "hint": "Partial Credit for close value with appropriate units. &nbsp;if correct answer is 100 N and close is &plusmn;1%,<br />99 &nbsp;N is accepted.", "input_type": "percent", "default_value": "75"}, {"name": "C2", "label": "No units or wrong sign", "help_url": "", "hint": "Partial credit for forgetting units or using wrong sign.<br />If the correct answer is 100 N, both 100 and -100 N are accepted.", "input_type": "percent", "default_value": "50"}, {"name": "C3", "label": "Close, no units.", "help_url": "", "hint": "Partial Credit for close value but forgotten units.<br />This value would be close&nbsp;if the expected units were provided. &nbsp;If the correct answer is 100 N, and close is &plusmn;1%,<br />99 is accepted.", "input_type": "percent", "default_value": "25"}], "public_availability": "always", "published": true, "extensions": ["quantities"]}], "resources": [["question-resources/centroids.png", "/srv/numbas/media/question-resources/centroids.png"], ["question-resources/centroids_3A0rXlj.png", "/srv/numbas/media/question-resources/centroids_3A0rXlj.png"], ["question-resources/centroids_zSOgoBb.png", "/srv/numbas/media/question-resources/centroids_zSOgoBb.png"], ["question-resources/centroid-t-r.ggb", "/srv/numbas/media/question-resources/centroid-t-r.ggb"]]}