// Numbas version: finer_feedback_settings
{"name": "Vector addition by summing scalar components", "extensions": ["geogebra", "weh", "quantities"], "custom_part_types": [{"source": {"pk": 24, "author": {"name": "William Haynes", "pk": 2530}, "edit_page": "/part_type/24/edit"}, "name": "Angle quantity", "short_name": "angle-quantity-from-reference", "description": "<p>Angle&nbsp;as a quantity in degrees.</p>", "help_url": "", "input_widget": "string", "input_options": {"correctAnswer": "plain_string(settings['correct_quantity'])", "hint": {"static": true, "value": ""}, "allowEmpty": {"static": true, "value": false}}, "can_be_gap": true, "can_be_step": true, "marking_script": "mark:\nswitch( \nright and good_units and right_sign and angle_in_range, add_credit(1.0,'Correct.'),\nright and good_units and not right_sign, add_credit(settings['C2'],'Wrong sign.'),\nright and right_sign and not good_units, add_credit(settings['C2'],'Correct angle, but missing degree symbol.'),\nright and good_units and right_sign and not angle_in_range,add_credit(settings['C1'],'Angle is out of range.'),\nclose and good_units, add_credit(settings['C1'],'Close.'),\nclose and not good_units, add_credit(settings['C3'],'Answer is close, but missing degree symbol.'),\nincorrect('Wrong answer.')\n)\n\ninterpreted_answer:\nqty(student_scalar, student_units)\n\ncorrect_scalar:\nscalar(correct_quantity)\n  \n\ncorrect_quantity:\nsettings['correct_quantity']\n\ncorrect_units:\nunits(correct_quantity)\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:\njoin(\nsplit(studentAnswer[len(match_student_number[0])..len(studentAnswer)]\n,\"\u00b0\"),\" deg\")\n\n\n\ngood_units:\ntry(\nkind(quantity(1, student_units))= kind(correct_quantity),\nmsg,\nfeedback(msg);false)\n\nstudent_quantity:\nswitch(not good_units, \nstudent_scalar * correct_units, \nnot right_sign,\n-quantity(student_scalar, student_units),\nquantity(student_scalar,student_units)\n)\n\nright_sign:\nsign(student_scalar) = sign(correct_quantity)\n\nangle_in_range:\nif(settings['restrict_angle'], abs(student_scalar) <= 90, true)\n\nright:\nwithinTolerance(abs(student_scalar), abs(correct_scalar), settings['right'])\n\nclose:\nwithinTolerance(student_scalar, correct_scalar, settings['close'])", "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( \nright and good_units and right_sign and angle_in_range, add_credit(1.0,'Correct.'),\nright and good_units and not right_sign, add_credit(settings['C2'],'Wrong sign.'),\nright and right_sign and not good_units, add_credit(settings['C2'],'Correct angle, but missing degree symbol.'),\nright and good_units and right_sign and not angle_in_range,add_credit(settings['C1'],'Angle is out of range.'),\nclose and good_units, add_credit(settings['C1'],'Close.'),\nclose and not good_units, add_credit(settings['C3'],'Answer is close, but missing degree symbol.'),\nincorrect('Wrong answer.')\n)"}, {"name": "interpreted_answer", "description": "A value representing the student's answer to this part.", "definition": "qty(student_scalar, student_units)"}, {"name": "correct_scalar", "description": "", "definition": "scalar(correct_quantity)\n  "}, {"name": "correct_quantity", "description": "", "definition": "settings['correct_quantity']"}, {"name": "correct_units", "description": "", "definition": "units(correct_quantity)"}, {"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": "", "definition": "join(\nsplit(studentAnswer[len(match_student_number[0])..len(studentAnswer)]\n,\"\u00b0\"),\" deg\")\n\n"}, {"name": "good_units", "description": "", "definition": "try(\nkind(quantity(1, student_units))= kind(correct_quantity),\nmsg,\nfeedback(msg);false)"}, {"name": "student_quantity", "description": "", "definition": "switch(not good_units, \nstudent_scalar * correct_units, \nnot right_sign,\n-quantity(student_scalar, student_units),\nquantity(student_scalar,student_units)\n)"}, {"name": "right_sign", "description": "", "definition": "sign(student_scalar) = sign(correct_quantity)"}, {"name": "angle_in_range", "description": "", "definition": "if(settings['restrict_angle'], abs(student_scalar) <= 90, true)"}, {"name": "right", "description": "<p>Will check for correct sign elswhere.</p>", "definition": "withinTolerance(abs(student_scalar), abs(correct_scalar), settings['right'])"}, {"name": "close", "description": "<p>Must have correct sign to be close.</p>", "definition": "withinTolerance(student_scalar, correct_scalar, settings['close'])\n"}], "settings": [{"name": "correct_quantity", "label": "Correct Angle as quantity ", "help_url": "", "hint": "", "input_type": "code", "default_value": "qty(45,'deg')", "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 &plusmn; this amount from the correct value.", "input_type": "code", "default_value": "0.1", "evaluate": true}, {"name": "restrict_angle", "label": "Less than 90\u00b0", "help_url": "", "hint": "When checked, angle must be between -90&deg; and +90&deg;.", "input_type": "checkbox", "default_value": true}, {"name": "C1", "label": "Close with units.", "help_url": "", "hint": "Partial Credit for close value with appropriate units.", "input_type": "percent", "default_value": "75"}, {"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 &plusmn; this amount from the correct value.", "input_type": "code", "default_value": "0.5", "evaluate": true}, {"name": "C2", "label": "No units or wrong sign", "help_url": "", "hint": "Partial credit for forgetting units or using wrong sign.", "input_type": "percent", "default_value": "50"}, {"name": "C3", "label": "Close, no units.", "help_url": "", "hint": "Partial Credit for close value without units.", "input_type": "percent", "default_value": "25"}], "public_availability": "restricted", "published": false, "extensions": ["quantities"]}, {"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}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "variables": {"theta": {"description": "", "name": "theta", "definition": "degrees(atan2(FR[1],FR[0]))", "group": "Outputs", "templateType": "anything"}, "units": {"description": "", "name": "units", "definition": "random(['m','kN'],['cm','N'])", "group": "Inputs", "templateType": "anything"}, "resultant": {"description": "", "name": "resultant", "definition": "qty(abs(FR),units[1]) scale", "group": "Outputs", "templateType": "anything"}, "FR": {"description": "", "name": "FR", "definition": "FA + FB + FC", "group": "Outputs", "templateType": "anything"}, "D": {"description": "", "name": "D", "definition": "vector(0,-8)", "group": "Inputs", "templateType": "anything"}, "angle_from_ref": {"description": "", "name": "angle_from_ref", "definition": "let(ang,theta,\n[if(ang>180,ang-360,ang),\nif(ang>270,ang-450,if(ang < -90,ang+270,ang-90)),\nif(ang>0,ang-180,ang+180),\nif(ang>90,ang-270,90+ang)])", "group": "Outputs", "templateType": "anything"}, "C1": {"description": "<p>Position of point C</p>", "name": "C1", "definition": "vector(5,0)\n", "group": "Inputs", "templateType": "anything"}, "FB": {"description": "", "name": "FB", "definition": "vector(random(-5..5),random(-5..5 except 0))", "group": "Inputs", "templateType": "anything"}, "debug": {"description": "", "name": "debug", "definition": "false", "group": "Inputs", "templateType": "anything"}, "scale": {"description": "", "name": "scale", "definition": "random(0.1,0.2,0.5,2,4,5,10,20)", "group": "Inputs", "templateType": "anything"}, "B1": {"description": "<p>Position of point B</p>", "name": "B1", "definition": "vector(0,0)\n", "group": "Inputs", "templateType": "anything"}, "A1": {"description": "<p>Position of point A</p>", "name": "A1", "definition": "vector(-5,0)", "group": "Inputs", "templateType": "anything"}, "FA": {"description": "", "name": "FA", "definition": "vector(random(-5..5 except 0),random(-5..5))", "group": "Inputs", "templateType": "anything"}, "ref": {"description": "<p>placeholder for reference axis</p>", "name": "ref", "definition": "0", "group": "Outputs", "templateType": "anything"}, "FC": {"description": "", "name": "FC", "definition": "vector(random(-5..5 except 0),random(-5..5 except 0))", "group": "Inputs", "templateType": "anything"}}, "rulesets": {}, "statement": "<p><strong></strong>Three forces, <strong style=\"color: red;\">A</strong>, <strong style=\"color: blue;\">B</strong>, and <strong style=\"color: green;\">C</strong>&nbsp;are drawn&nbsp;to scale of 1 square = {scale} {units[1]}. &nbsp;Find the resultant by summing the scalar components.</p>\n<p><em>Note: For full marks don't forget to add a zero for decimal numbers less than one, add negative signs if required and don't forget the&nbsp;correct units.</em></p>\n<p>{geogebra_applet('vpfnqe8q', [['fa',FA],['fb',FB],['fc',FC]])}</p>\n<p></p>", "variablesTest": {"condition": "abs(FR) >=3", "maxRuns": "100"}, "tags": [], "metadata": {"licence": "Creative Commons Attribution-NonCommercial 4.0 International", "description": "<p>Add three vectors by determining their scalar components, summing them and then resolving the rectangular components to find the magnitude and direction of the resultant.</p>"}, "advice": "<p>Vector Addition: &nbsp;</p>\n<p>$R_x = \\Sigma F_x = \\var{scale FA[0]}+\\var{scale FB[0]}+\\var{scale FC[0]} =\\var{scale FR[0]}$ {units[1]}</p>\n<p>$R_y = \\Sigma F_y = \\var{scale FA[1]}+\\var{scale FB[1]}+\\var{scale FC[1]} =\\var{scale FR[1]}$&nbsp;{units[1]}</p>\n<p>$R=\\sqrt{R_x^2 + R_y^2}&nbsp;= \\var{siground(resultant,4)}$&nbsp;</p>\n<p>$\\theta = \\tan^{-1}\\left(\\left|\\frac{R_y}{R_x}\\right| \\right) =$ {siground(degrees(arctan(FR[0]/FR[1])),4)}&deg;</p>\n<p></p>", "variable_groups": [{"name": "Inputs", "variables": ["A1", "FA", "B1", "FB", "C1", "FC", "units", "debug", "D", "scale"]}, {"name": "Outputs", "variables": ["FR", "theta", "ref", "angle_from_ref", "resultant"]}], "preamble": {"css": "", "js": ""}, "ungrouped_variables": [], "name": "Vector addition by summing scalar components", "parts": [{"useCustomName": false, "variableReplacements": [], "showFeedbackIcon": true, "sortAnswers": false, "showCorrectAnswer": true, "marks": 0, "unitTests": [], "extendBaseMarkingAlgorithm": true, "type": "gapfill", "customName": "", "scripts": {}, "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "prompt": "<p>First, find the scalar components of the&nbsp;three forces. These are divided into the X and Y components and multipled by the force.</p>\n<p>$A_x =$&nbsp;[[0]]&nbsp; $B_x =$&nbsp;[[2]]&nbsp; $C_x =$&nbsp;[[4]]</p>\n<p>$A_y =$&nbsp;[[1]]&nbsp; $B_y =$&nbsp;[[3]]&nbsp; $C_y =$&nbsp;[[5]]</p>", "gaps": [{"useCustomName": false, "variableReplacements": [], "showFeedbackIcon": true, "showCorrectAnswer": true, "marks": "4", "unitTests": [], "extendBaseMarkingAlgorithm": true, "type": "engineering-answer", "customName": "", "scripts": {}, "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "settings": {"correctAnswer": "qty(FA[0],units[1]) scale", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"useCustomName": false, "variableReplacements": [], "showFeedbackIcon": true, "showCorrectAnswer": true, "marks": "4", "unitTests": [], "extendBaseMarkingAlgorithm": true, "type": "engineering-answer", "customName": "", "scripts": {}, "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "settings": {"correctAnswer": "qty(FA[1],units[1]) scale", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"useCustomName": false, "variableReplacements": [], "showFeedbackIcon": true, "showCorrectAnswer": true, "marks": "4", "unitTests": [], "extendBaseMarkingAlgorithm": true, "type": "engineering-answer", "customName": "", "scripts": {}, "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "settings": {"correctAnswer": "qty(FB[0],units[1]) scale", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"useCustomName": false, "variableReplacements": [], "showFeedbackIcon": true, "showCorrectAnswer": true, "marks": "4", "unitTests": [], "extendBaseMarkingAlgorithm": true, "type": "engineering-answer", "customName": "", "scripts": {}, "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "settings": {"correctAnswer": "qty(FB[1],units[1]) scale", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"useCustomName": false, "variableReplacements": [], "showFeedbackIcon": true, "showCorrectAnswer": true, "marks": "4", "unitTests": [], "extendBaseMarkingAlgorithm": true, "type": "engineering-answer", "customName": "", "scripts": {}, "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "settings": {"correctAnswer": "qty(FC[0],units[1]) scale", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"useCustomName": false, "variableReplacements": [], "showFeedbackIcon": true, "showCorrectAnswer": true, "marks": "4", "unitTests": [], "extendBaseMarkingAlgorithm": true, "type": "engineering-answer", "customName": "", "scripts": {}, "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "settings": {"correctAnswer": "qty(FC[1],units[1]) scale", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}]}, {"useCustomName": false, "variableReplacements": [], "showFeedbackIcon": true, "sortAnswers": false, "showCorrectAnswer": true, "marks": 0, "unitTests": [], "extendBaseMarkingAlgorithm": true, "type": "gapfill", "customName": "", "scripts": {}, "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "prompt": "<p>Then, sum the scalar components to get&nbsp;the scalar components of the resultant <strong>R</strong>.</p>\n<p>$R_x = \\Sigma F_x &nbsp;= A_x + B_x + C_x =$&nbsp;[[0]]&nbsp;</p>\n<p>$R_y = \\Sigma F_y &nbsp;= A_y + B_y + C_y =$ [[1]]&nbsp;&nbsp;</p>", "gaps": [{"useCustomName": false, "variableReplacements": [], "showFeedbackIcon": true, "showCorrectAnswer": true, "marks": "4", "unitTests": [], "extendBaseMarkingAlgorithm": true, "type": "engineering-answer", "customName": "", "scripts": {}, "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "settings": {"correctAnswer": "qty(FR[0],units[1]) scale", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"useCustomName": false, "variableReplacements": [], "showFeedbackIcon": true, "showCorrectAnswer": true, "marks": "4", "unitTests": [], "extendBaseMarkingAlgorithm": true, "type": "engineering-answer", "customName": "", "scripts": {}, "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "settings": {"correctAnswer": "qty(FR[1],units[1]) scale", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}]}, {"useCustomName": false, "variableReplacements": [], "showFeedbackIcon": true, "sortAnswers": false, "showCorrectAnswer": true, "marks": 0, "unitTests": [], "extendBaseMarkingAlgorithm": true, "type": "gapfill", "customName": "", "scripts": {"mark": {"script": "numbasGGBApplet0.setValue('show',true);", "order": "after"}}, "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "prompt": "<p>Finally, resolve&nbsp;$R_x$ and $R_y$ to find the magnitude and direction of <strong>R</strong>. <br/><em><strong>Note:</strong> Round your answer to 2 decimal places.</em></p>\n<p>$R = \\sqrt{{R_x}^2 +{R_y}^2}$ =&nbsp;[[0]]&nbsp;</p>\n<p>&nbsp;$\\theta = \\tan^{-1}\\left(\\left|\\dfrac{R_y}{R_x}\\right| \\right)$ =&nbsp;[[2]]&nbsp; measured from the&nbsp;&nbsp;[[1]]&nbsp;</p>\n<p><span data-jme-visible=\"debug\">magnitude&nbsp;= {siground(resultant,4)} direction={theta}</span></p>", "gaps": [{"useCustomName": false, "variableReplacements": [], "showFeedbackIcon": true, "showCorrectAnswer": true, "marks": "4", "unitTests": [], "extendBaseMarkingAlgorithm": true, "type": "engineering-answer", "customName": "", "scripts": {}, "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "settings": {"correctAnswer": "resultant", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"useCustomName": false, "variableReplacements": [], "showFeedbackIcon": true, "showCorrectAnswer": true, "marks": "0", "unitTests": [], "extendBaseMarkingAlgorithm": true, "type": "drop-down-axis-reference", "customName": "", "scripts": {"mark": {"script": "index = Numbas.jme.unwrapValue(this.studentAnswerAsJME());\nangles = Numbas.jme.unwrapValue(Numbas.exam.currentQuestion.scope.getVariable('angle_from_ref'));\nans =  Qty(angles[index],'deg');\nthis.parentPart.gaps[2].settings.correct_quantity.value= ans;\nthis.markingComment(\"For your axis, the direction is \" +  ans.toPrec('0.1 deg') +'.');\n", "order": "after"}}, "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "settings": {"dummy": "'ignore'"}}, {"useCustomName": false, "variableReplacements": [], "showFeedbackIcon": true, "showCorrectAnswer": true, "marks": "4", "unitTests": [], "extendBaseMarkingAlgorithm": true, "type": "angle-quantity-from-reference", "customName": "", "scripts": {}, "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "settings": {"right": "0.2", "correct_quantity": "qty(123,'deg')", "restrict_angle": true, "close": "1.01", "C1": "75", "C2": "50", "C3": "25"}}]}], "extensions": ["geogebra", "quantities", "weh"], "type": "question", "contributors": [{"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}, {"name": "Chris King", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3543/"}]}]}], "contributors": [{"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}, {"name": "Chris King", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3543/"}]}