calculate the $x$ and $y$ components of the vector given below.
do not round any intermediate computations, and round your responses to the nearest hundredth.

$x = $
$y = $

Question

calculate the $x$ and $y$ components of the vector given below.
do not round any intermediate computations, and round your responses to the nearest hundredth.

$x = $
$y = $

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": true, "concepts_used": [ "Vector Components", "Trigonometric Resolution" ], "new_concepts": [], "current_concepts": [ "Vector Components", "Trigonometric Resolution" ] } ## Identify the vector parameters Using the *Vector Components* and *Trigonometric Resolution* knowledge points $$ \begin{aligned} &\|\vec{v}\| = 74\ &\theta_{\text{ref}} = 70^\circ \quad (\text{measured below the positive } x\text{-axis})\ &\theta = -70^\circ \quad \text{or} \quad 290^\circ \end{aligned} $$ ## Calculate the x-component Using the *Vector Components* and *Trigonometric Resolution* knowledge points $$ \begin{aligned} &v_x = 74 \cdot \cos(-70^\circ)\ &v_x \approx 74 \cdot 0.342020143\ &v_x \approx 25.30949\ &v_x \approx 25.31 \end{aligned} $$ ## Calculate the y-component Using the *Vector Components* and *Trigonometric Resolution* knowledge points $$ \begin{aligned} &v_y = 74 \cdot \sin(-70^\circ)\ &v_y \approx 74 \cdot (-0.93969262)\ &v_y \approx -69.53725\ &v_y \approx -69.54 \end{aligned} $$ Calculate the $x$ and $y$ components of the vector given below. Do not round any intermediate computations, and round your responses to the nearest hundredth. $x =$ $25.31$ $y =$ $-69.54$ { "elements": [ { "type": "line", "params": [[-1, 0], [5, 0]], "properties": { "strokeColor": "#cccccc", "strokeWidth": 1 } }, { "type": "line", "params": [[0, 1], [0, -8]], "properties": { "strokeColor": "#cccccc", "strokeWidth": 1 } }, { "type": "arrow", "params": [[0, 0], [2.53, -6.95]], "properties": { "strokeColor": "#8C55F2", "strokeWidth": 3, "name": "v", "withLabel": true } }, { "type": "angle", "params": [[1, 0], [0, 0], [2.53, -6.95]], "properties": { "radius": 1.2, "strokeColor": "#F2557F", "fillColor": "rgba(242, 85, 127, 0.3)", "name": "70°", "withLabel": true } }, { "type": "text", "params": [1.5, -3.5, "74"], "properties": { "color": "#583C87" } } ] } { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Vector Components" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the vector parameters

Calculate the x-component

Calculate the y-component

Answer: