what is the length of $\widehat{pq}$?

write your answer using \pi\ with no spaces.

$\text{length}_{\widehat{pq}} =$ units

Question

what is the length of $\widehat{pq}$?

write your answer using \pi\ with no spaces.

$\text{length}_{\widehat{pq}} =$   units

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": true, "concepts_used": [ "Arc Length Formula" ], "new_concepts": [], "current_concepts": [ "Arc Length Formula", "Central Angle Measure" ] } ## Identify the given values and formula $$ \begin{aligned} &r = 18\ &\theta = 150^\circ\ &s = \frac{\theta}{360^\circ} \cdot 2\pi r \end{aligned} $$ ## Calculate the arc length of PQ $$ \begin{aligned} &s = \frac{150}{360} \cdot 2\pi (18)\ &s = \frac{5}{12} \cdot 36\pi\ &s = 15\pi \end{aligned} $$ What is the length of $\widehat{PQ}$? Write your answer using "pi" with no spaces. Length$_{\widehat{PQ}} =$ 15pi units { "elements": [ { "type": "point", "params": [[0, 0]], "properties": { "name": "A", "size": 4, "color": "#583C87", "withLabel": true, "labelPosition": [0, -1] } }, { "type": "circle", "params": [[0, 0], 4], "properties": { "strokeColor": "#583C87", "strokeWidth": 2 } }, { "type": "point", "params": [[4, 0]], "properties": { "name": "Q", "size": 4, "color": "#8C55F2", "withLabel": true, "labelPosition": [1, 0] } }, { "type": "point", "params": [[-3.464, 2]], "properties": { "name": "P", "size": 4, "color": "#8C55F2", "withLabel": true, "labelPosition": [-1, 1] } }, { "type": "segment", "params": [[0, 0], [4, 0]], "properties": { "strokeColor": "#5583F2", "strokeWidth": 2 } }, { "type": "segment", "params": [[0, 0], [-3.464, 2]], "properties": { "strokeColor": "#5583F2", "strokeWidth": 2 } }, { "type": "text", "params": [[1, 0.5], "150^{\circ}"], "properties": { "color": "#583C87" } }, { "type": "text", "params": [[2, -0.5], "r = 18"], "properties": { "color": "#5583F2" } } ] } { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Arc Length Formula" ] }

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Question

Explanation:

Identify the given values and formula

Calculate the arc length of PQ

Answer: