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.

$x = \box$
$y = \box$

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.

$x = \box$
$y = \box$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Coordinate Conversion", "Polar to Rectangular" ], "new_concepts": [ "Vector Components", "Trigonometric Resolution" ], "current_concepts": [ "Coordinate Conversion", "Polar to Rectangular", "Vector Components", "Trigonometric Resolution" ] } ## Identify the vector magnitude and direction Using the **Coordinate Conversion** and **Polar to Rectangular** knowledge points $$ \begin{aligned} &r = 46\ &\theta = 180^\circ + 42^\circ = 222^\circ \end{aligned} $$ ## Calculate the x-component Using the **Polar to Rectangular** knowledge point $$ \begin{aligned} &x = r \cos(\theta) = 46 \cos(222^\circ)\ &x \approx -34.1843 \approx -34.18 \end{aligned} $$ ## Calculate the y-component Using the **Polar to Rectangular** knowledge point $$ \begin{aligned} &y = r \sin(\theta) = 46 \sin(222^\circ)\ &y \approx -30.7801 \approx -30.78 \end{aligned} $$ 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. $x =$ -34.18 $y =$ -30.78 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Coordinate Conversion" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the vector magnitude and direction

Calculate the x-component

Calculate the y-component

Answer: