|
1 | 1 | { |
2 | | - "message": "i dont remember anything", |
3 | | - "params": { |
4 | | - "include_test_data": true, |
5 | | - "conversation_history": [ |
6 | | - { "type": "user", "content": "what should I do?" }, |
7 | | - { |
8 | | - "type": "assistant", |
9 | | - "content": "It seems like you're currently working on Part (a) of the dot product question. Since you haven't submitted an answer yet, let's take a moment to break it down together. \n\nWhat do you remember about how to calculate the dot product of two vectors? Can you describe the steps you would take?" |
10 | | - }, |
11 | | - { "type": "user", "content": "i dont remember anything" } |
12 | | - ], |
13 | | - "summary": "", |
14 | | - "conversational_style": "", |
15 | | - "question_response_details": { |
16 | | - "questionSubmissionSummary": [ |
17 | | - { |
18 | | - "publishedPartId": "0e0432e4-90a2-47a1-b597-55f76596b7d5", |
19 | | - "publishedPartPosition": 0, |
20 | | - "publishedResponseAreaId": "ce28b12b-f583-4d83-a0e4-36b17127746a", |
21 | | - "publishedResponseAreaPosition": 0, |
22 | | - "responseAreaUniversalId": "f8857876-482d-411c-8ffc-734fb07712cf", |
23 | | - "publishedResponseAreaPreResponseText": "$\\vec{a} \\ \\cdot \\ \\vec{b} \\ =$", |
24 | | - "publishedResponseType": "NUMBER", |
25 | | - "publishedResponseConfig": null, |
26 | | - "totalSubmissions": 0, |
27 | | - "totalWrongSubmissions": 0 |
28 | | - }, |
29 | | - { |
30 | | - "publishedPartId": "a74a6fef-8c94-474c-b381-8d97a4b54725", |
31 | | - "publishedPartPosition": 1, |
32 | | - "publishedResponseAreaId": "f3be55ed-af9b-4483-ba45-636ccbad7a24", |
33 | | - "publishedResponseAreaPosition": 0, |
34 | | - "responseAreaUniversalId": "054bbcce-facb-4aaa-a1d2-7bec7627a6ef", |
35 | | - "publishedResponseAreaPreResponseText": "$\\left(\\vec{a} - \\vec{b}\\right)\\cdot \\vec{c}\\ =$", |
36 | | - "publishedResponseType": "NUMBER", |
37 | | - "publishedResponseConfig": null, |
38 | | - "totalSubmissions": 0, |
39 | | - "totalWrongSubmissions": 0 |
40 | | - }, |
41 | | - { |
42 | | - "publishedPartId": "66160c45-0554-470a-88ae-82f36e755ef6", |
43 | | - "publishedPartPosition": 2, |
44 | | - "publishedResponseAreaId": "79260525-1edb-4f19-bcdd-d827b5b692f3", |
45 | | - "publishedResponseAreaPosition": 0, |
46 | | - "responseAreaUniversalId": "bba9308c-55c7-4733-9315-37bc26fc8ec1", |
47 | | - "publishedResponseAreaPreResponseText": "$\\left( \\ \\vec{a} \\cdot \\vec{c} \\ \\right) \\vec{b}\\ =$", |
48 | | - "publishedResponseType": "MATRIX", |
49 | | - "publishedResponseConfig": { "cols": 1, "rows": 3 }, |
50 | | - "totalSubmissions": 0, |
51 | | - "totalWrongSubmissions": 0 |
52 | | - } |
53 | | - ], |
54 | | - "questionInformation": { |
55 | | - "questionTitle": "Dot Product", |
56 | | - "questionGuidance": "", |
57 | | - "questionContent": "$$\n\\vec{a}=\\begin{bmatrix}1 \\\\ 3\\\\ -2\\end{bmatrix} \\quad \\vec{b}=\\begin{bmatrix}0 \\\\ 3\\\\ 1\\end{bmatrix} \\quad \\vec{c}=\\begin{bmatrix} 1 \\\\\\ -1\\\\ -3\\end{bmatrix}\n$$", |
58 | | - "durationLowerBound": 1, |
59 | | - "durationUpperBound": 4, |
60 | | - "parts": [ |
| 2 | + "conversationId": "9f4d40af-5f65-4f90-ac8e-9b92fea92f9f", |
| 3 | + "messages": [ |
| 4 | + { "role": "USER", "content": "How can I start solving this question?" } |
| 5 | + ], |
| 6 | + "user": { |
| 7 | + "userId": "a6632248-578b-4976-9d42-7daea459a905", |
| 8 | + "type": "LEARNER", |
| 9 | + "preference": { "conversationalStyle": "" }, |
| 10 | + "taskProgress": { |
| 11 | + "currentQuestionId": "c5b258ec-0165-4595-a7ee-cbe0cd5dc012", |
| 12 | + "timeSpentOnQuestion": "58 minutes", |
| 13 | + "accessStatus": "too much time spent on this question today.", |
| 14 | + "markedDone": "This question is still being worked on.", |
| 15 | + "currentPart": { |
| 16 | + "partId": "bbfcc2e4-3bf7-4016-a300-f09e3204ed8e", |
| 17 | + "position": 0, |
| 18 | + "timeSpentOnPart": "37 minutes", |
| 19 | + "markedDone": "This part is not marked done.", |
| 20 | + "responseAreas": [ |
61 | 21 | { |
62 | | - "publishedPartId": "0e0432e4-90a2-47a1-b597-55f76596b7d5", |
63 | | - "publishedPartPosition": 0, |
64 | | - "publishedPartContent": "", |
65 | | - "publishedPartAnswerContent": "", |
66 | | - "publishedWorkedSolutionSections": [ |
67 | | - { |
68 | | - "id": "a7b1150a-05b7-4337-b902-5c6b1835cc74", |
69 | | - "position": 0, |
70 | | - "title": "", |
71 | | - "content": "Assuming the given basis is orthonormal, the dot product between two vectors, $\\vec{a}$ and $\\vec{b}$, can be calculated simply by multiplying their corresponding components and summing them up:\n\n   \n\n$$\n\\begin{array}{rl}\\vec{a} \\cdot \\vec{b} &=\\begin{bmatrix}1 \\\\ 3\\\\ -2\\end{bmatrix}•\\begin{bmatrix}0 \\\\ 3\\\\ 1\\end{bmatrix} \\\\\\\\ &= (1 \\cdot 0) + (3 \\cdot 3) + (-2 \\cdot 1) \\\\\\\\ &= 0 + 9 + (-2) \\\\\\\\ &= 7\\end{array}\n$$\n\n   \n\nTherefore, the dot product between vectors $\\vec{a}$ and $\\vec{b}$ is \\$7\\$" |
72 | | - } |
73 | | - ], |
74 | | - "publishedResponseAreas": [ |
75 | | - { |
76 | | - "id": "ce28b12b-f583-4d83-a0e4-36b17127746a", |
77 | | - "position": 0, |
78 | | - "universalResponseAreaId": "f8857876-482d-411c-8ffc-734fb07712cf", |
79 | | - "preResponseText": "$\\vec{a} \\ \\cdot \\ \\vec{b} \\ =$", |
80 | | - "Response": { |
81 | | - "id": "4d0dfa85-fc34-4649-bb6e-0f194e8a5a04", |
82 | | - "responseType": "NUMBER", |
83 | | - "config": null, |
84 | | - "answer": 7 |
85 | | - }, |
86 | | - "responseType": "NUMBER", |
87 | | - "answer": 7 |
88 | | - } |
89 | | - ] |
| 22 | + "responseAreaId": "4ceb8d4b-b892-4388-a1b0-d80219e5b86e", |
| 23 | + "responseType": "NUMBER", |
| 24 | + "totalSubmissions": 1, |
| 25 | + "wrongSubmissions": 1, |
| 26 | + "latestSubmission": { |
| 27 | + "submission": 1, |
| 28 | + "feedback": "Incorrect", |
| 29 | + "answer": "26" |
| 30 | + } |
90 | 31 | }, |
91 | 32 | { |
92 | | - "publishedPartId": "a74a6fef-8c94-474c-b381-8d97a4b54725", |
93 | | - "publishedPartPosition": 1, |
94 | | - "publishedPartContent": "", |
95 | | - "publishedPartAnswerContent": "", |
96 | | - "publishedWorkedSolutionSections": [ |
97 | | - { |
98 | | - "id": "0e91a91d-c536-4120-a70f-5cfea57b4235", |
99 | | - "position": 0, |
100 | | - "title": "", |
101 | | - "content": "To calculate $\\left(\\vec{a} - \\vec{b}\\right) \\cdot \\vec{c}$ , we first need to find the vector resulting from the subtraction of $\\vec{b}$ from $\\vec{a}$:\n\n   \n\n$$\n\\begin{array}{rl}\\vec{a} - \\vec{b} &= \\begin{bmatrix}1 \\\\ 3 \\\\ -2\\end{bmatrix} - \\begin{bmatrix}0 \\\\ 3 \\\\ 1\\end{bmatrix} \\\\\\\\&= \\begin{bmatrix}1 - 0 \\\\ 3 - 3 \\\\ -2 - 1\\end{bmatrix} \\\\\\\\&= \\begin{bmatrix}1 \\\\ 0 \\\\ -3\\end{bmatrix}\\end{array}\n$$\n\n\n\nNext, we can compute the dot product of $\\left(\\vec{a} - \\vec{b}\\right)$ and $\\vec{c}$\n\n   \n\n$$\n\\begin{array}{rl}\\left(\\vec{a} - \\vec{b}\\right) \\cdot \\vec{c} &= \\begin{bmatrix}1 \\\\ 0 \\\\ -3\\end{bmatrix} \\cdot \\begin{bmatrix}1 \\\\ -1 \\\\ -3\\end{bmatrix} \\\\\\\\ &= (1 \\cdot 1) + (0 \\cdot -1) + (-3 \\cdot -3) \\\\\\\\&= 1 + 0 + 9 \\\\\\\\&= 10\\end{array}\n$$\n\n\n\nTherefore, $\\left(\\vec{a} - \\vec{b}\\right) \\cdot \\vec{c}$ is equal to \\$10" |
102 | | - } |
103 | | - ], |
104 | | - "publishedResponseAreas": [ |
105 | | - { |
106 | | - "id": "f3be55ed-af9b-4483-ba45-636ccbad7a24", |
107 | | - "position": 0, |
108 | | - "universalResponseAreaId": "054bbcce-facb-4aaa-a1d2-7bec7627a6ef", |
109 | | - "preResponseText": "$\\left(\\vec{a} - \\vec{b}\\right)\\cdot \\vec{c}\\ =$", |
110 | | - "Response": { |
111 | | - "id": "01edd054-b1fd-4049-8551-a8551d7a63ea", |
112 | | - "responseType": "NUMBER", |
113 | | - "config": null, |
114 | | - "answer": 10 |
115 | | - }, |
116 | | - "responseType": "NUMBER", |
117 | | - "answer": 10 |
118 | | - } |
119 | | - ] |
120 | | - }, |
121 | | - { |
122 | | - "publishedPartId": "66160c45-0554-470a-88ae-82f36e755ef6", |
123 | | - "publishedPartPosition": 2, |
124 | | - "publishedPartContent": "", |
125 | | - "publishedPartAnswerContent": "", |
126 | | - "publishedWorkedSolutionSections": [ |
127 | | - { |
128 | | - "id": "c3225276-7bf8-4962-a459-d9583442c26e", |
129 | | - "position": 0, |
130 | | - "title": "", |
131 | | - "content": "To calculate $\\left( \\ \\vec{a} \\cdot \\vec{c} \\ \\right) \\vec{b}$ , we first need to find the dot product of vectors $\\vec{a}$ and $\\vec{c}$\n\n   \n\n$$\n\\begin{array}{rl}\\vec{a} \\cdot \\vec{c} &= \\begin{bmatrix}1 \\\\ 3 \\\\ -2\\end{bmatrix} \\cdot \\begin{bmatrix}1 \\\\ -1 \\\\ -3\\end{bmatrix} \\\\\\\\ &= (1 \\cdot 1) + (3 \\cdot -1) + (-2 \\cdot -3) \\\\\\\\&= 1 - 3 + 6 \\\\\\\\&= 4\\end{array}\n$$\n\n   \n\nNext, we can scale $\\vec{b}$ by $\\vec{a} \\cdot \\vec{c}$\n\n   \n\n$$\n\\begin{array}{rl}\\left( \\ \\vec{a} \\cdot \\vec{c} \\ \\right) \\vec{b} &= 4\\begin{bmatrix}0 \\\\ 3 \\\\ 1\\end{bmatrix} \\\\\\\\ &= \\begin{bmatrix}4\\cdot0 \\\\ 4\\cdot3 \\\\ 4\\cdot1\\end{bmatrix} \\\\\\\\&= \\begin{bmatrix}0 \\\\ 12 \\\\ 4\\end{bmatrix} \\end{array}\n$$\n\n   \n" |
132 | | - } |
133 | | - ], |
134 | | - "publishedResponseAreas": [ |
135 | | - { |
136 | | - "id": "79260525-1edb-4f19-bcdd-d827b5b692f3", |
137 | | - "position": 0, |
138 | | - "universalResponseAreaId": "bba9308c-55c7-4733-9315-37bc26fc8ec1", |
139 | | - "preResponseText": "$\\left( \\ \\vec{a} \\cdot \\vec{c} \\ \\right) \\vec{b}\\ =$", |
140 | | - "Response": { |
141 | | - "id": "cc759374-175f-40be-8481-2c81e34795b6", |
142 | | - "responseType": "MATRIX", |
143 | | - "config": { "cols": 1, "rows": 3 }, |
144 | | - "answer": [["0"], ["12"], ["4"]] |
145 | | - }, |
146 | | - "responseType": "MATRIX", |
147 | | - "answer": [["0"], ["12"], ["4"]] |
148 | | - } |
149 | | - ] |
| 33 | + "responseAreaId": "dbff8fab-b129-4a6c-a768-52f5c5923934", |
| 34 | + "responseType": "NUMBER", |
| 35 | + "totalSubmissions": 1, |
| 36 | + "wrongSubmissions": 1, |
| 37 | + "latestSubmission": { |
| 38 | + "submission": 20, |
| 39 | + "feedback": "Incorrect", |
| 40 | + "answer": "53" |
| 41 | + } |
150 | 42 | } |
151 | 43 | ] |
152 | | - }, |
153 | | - "questionAccessInformation": { |
154 | | - "estimatedMinimumTime": "1 minute", |
155 | | - "estimaredMaximumTime": "4 minutes", |
156 | | - "timeTaken": "20 minutes", |
157 | | - "accessStatus": "too much time spent on this question.", |
158 | | - "markedDone": "", |
159 | | - "currentPart": { |
160 | | - "id": "0e0432e4-90a2-47a1-b597-55f76596b7d5", |
161 | | - "position": 0 |
162 | | - } |
163 | 44 | } |
| 45 | + } |
| 46 | + }, |
| 47 | + "context": { |
| 48 | + "summary": "", |
| 49 | + "set": { |
| 50 | + "title": "Computing", |
| 51 | + "number": 8, |
| 52 | + "description": "Exercises on number systems and binary arithmetic." |
164 | 53 | }, |
165 | | - "conversation_id": "7a65b6ed-85d1-4621-8efb-4fc8e9c5a8de", |
166 | | - "agent_type": "base" |
| 54 | + "question": { |
| 55 | + "title": "Binary Numbers", |
| 56 | + "number": 0, |
| 57 | + "guidance": "", |
| 58 | + "content": "", |
| 59 | + "estimatedTime": "5-10 minutes", |
| 60 | + "parts": [ |
| 61 | + { |
| 62 | + "partId": "bbfcc2e4-3bf7-4016-a300-f09e3204ed8e", |
| 63 | + "position": 0, |
| 64 | + "content": "Convert the following numbers to decimal: $11010_2$, $110101_2$.", |
| 65 | + "answerContent": "$11010_2 = 26_{10}$\\n\\n$110101_2 = 53_{10}$ \\n\\n  ", |
| 66 | + "workedSolutionSections": [ |
| 67 | + { |
| 68 | + "id": "df588439-f183-4161-ade3-41559113e447", |
| 69 | + "position": 0, |
| 70 | + "title": "", |
| 71 | + "content": "$11010_2 = (0\\\\times1) + (1\\\\times2) + (0\\\\times4) + (1\\\\times8) + (1\\\\times16) = \\\\boxed{26_{10}}$ \\n\\n***\\n\\n$110101_2 = (1\\\\times1) + (0\\\\times2) + (1\\\\times4) + (0\\\\times8) + (1\\\\times16) + (1\\\\times32) = \\\\boxed{53_{10}}$ \\n\\n " |
| 72 | + } |
| 73 | + ], |
| 74 | + "structuredTutorialSections": [], |
| 75 | + "responseAreas": [ |
| 76 | + { |
| 77 | + "responseAreaId": "4ceb8d4b-b892-4388-a1b0-d80219e5b86e", |
| 78 | + "position": 0, |
| 79 | + "responseType": "NUMBER", |
| 80 | + "answer": 26, |
| 81 | + "preResponseText": "$11010_2 =$" |
| 82 | + }, |
| 83 | + { |
| 84 | + "responseAreaId": "dbff8fab-b129-4a6c-a768-52f5c5923934", |
| 85 | + "position": 1, |
| 86 | + "responseType": "NUMBER", |
| 87 | + "answer": 53, |
| 88 | + "preResponseText": "$110101_2$" |
| 89 | + } |
| 90 | + ] |
| 91 | + }, |
| 92 | + { |
| 93 | + "partId": "cdf7de05-0bea-43e4-8c9a-5d47e835e6bd", |
| 94 | + "position": 1, |
| 95 | + "content": "Convert the following numbers to binary: $101_{10}$, $16_{10}$.", |
| 96 | + "answerContent": "$101_{10} = 1100101_2$ \\n\\n$16_{10} = 10000_2$ \\n\\n  ", |
| 97 | + "workedSolutionSections": [ |
| 98 | + { |
| 99 | + "id": "aff42475-f0c0-4416-b1da-5cbae086d3f4", |
| 100 | + "position": 0, |
| 101 | + "title": "", |
| 102 | + "content": "" |
| 103 | + }, |
| 104 | + { |
| 105 | + "id": "3bb12dbb-f558-4df3-9db7-a31733143d71", |
| 106 | + "position": 0, |
| 107 | + "title": "By repeated division", |
| 108 | + "content": "$101_{10}$ can be divided by 2 to give a quotient of 50 and a remainder of 1. The remainder is the first binary digit: $1_2$.\\n\\n***\\n\\n$50_{10}$ divided by 2 gives a quotient of 25 and a remainder of zero, so the second binary digit is 0: $01_2$.\\n\\n***\\n\\n$25_{10}$ divided by 2 gives a quotient of 12 and a remainder of 1, so the third binary digit is 1: $101_2$\\n\\n***\\n\\n$12_{10}$ divided by 2 gives a quotient of 6 and a remainder of 0, so the fourth binary digit is 0: $0101_2$\\n\\n***\\n\\n$6_{10}$ divided by 2 gives a quotient of 3 and a remainder of 0, so the fifth binary digit is 0: $00101_2$\\n\\n***\\n\\n$3_{10}$ divided by 2 gives a quotient of 1 and a remainder of 1, so the sixth binary digit is 1: $100101_2$\\n\\n***\\n\\n$1_{10}$ divided by 2 gives a quotient of zero and a remainder of 1, so the seventh binary digit is 1: $\\\\boxed{1100101_2}$. \\n\\n  " |
| 109 | + }, |
| 110 | + { |
| 111 | + "id": "d95da3de-eafa-4cab-98d8-005b1268393b", |
| 112 | + "position": 1, |
| 113 | + "title": "By inspection", |
| 114 | + "content": "$101_{10}$ can be written in terms of powers of 2 as $101 = 64 + 32 + 4 + 1 = 2^6 + 2^5 + 2^2 + 2^0$, so its binary representation is $\\\\boxed{1100101_2}$.\\n\\n***\\n\\n$16_{10}$ is already a power of 2 ($2^4$), so its binary representation will have 1 bit set: $\\\\boxed{10000_2}$. \\n\\n   " |
| 115 | + } |
| 116 | + ], |
| 117 | + "structuredTutorialSections": [], |
| 118 | + "responseAreas": [ |
| 119 | + { |
| 120 | + "responseAreaId": "9a307730-7525-4b6e-976a-d8a434c6503a", |
| 121 | + "position": 0, |
| 122 | + "responseType": "NUMBER", |
| 123 | + "answer": 1100101, |
| 124 | + "preResponseText": "$101_{10} = $" |
| 125 | + }, |
| 126 | + { |
| 127 | + "responseAreaId": "05df22cc-4afd-499c-8533-5f34dfec7844", |
| 128 | + "position": 1, |
| 129 | + "responseType": "NUMBER", |
| 130 | + "answer": 10000, |
| 131 | + "preResponseText": "$16_{10} = $" |
| 132 | + } |
| 133 | + ] |
| 134 | + } |
| 135 | + ] |
| 136 | + } |
167 | 137 | } |
168 | 138 | } |
0 commit comments