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Question 3

1pts
Find the length of an arc whose central angle measures
90^(@) that is on a circle whose diameter is 20 .

2pi

4pi

5pi

10 pi

Question $3$ $\newline$ $1$ pts $\newline$ Find the length of an arc whose central angle measures $\newline$ $90^\circ$ that is on a circle whose diameter is $20$ . $\newline$ $2\pi$ $\newline$ $4\pi$ $\newline$ $5\pi$ $\newline$ $10\pi$

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Find Coordinate on Unit Circle

Full solution

Q. Question

3

\newline

1

pts

\newline

Find the length of an arc whose central angle measures

\newline

90^\circ

that is on a circle whose diameter is

20

.

\newline

2\pi

\newline

4\pi

\newline

5\pi

\newline

10\pi

Identify arc length formula: Step $1$ : Identify the formula for the length of an arc. $\newline$ The formula for the length of an arc $s$ is $s = r\theta$ , where $r$ is the radius of the circle and $\theta$ is the central angle in radians.
Convert angle to radians: Step $2$ : Convert the central angle from degrees to radians. $\newline$ Given angle = $90$ degrees. To convert degrees to radians, multiply by $\pi/180$ . $\newline$ $\theta = 90 \times (\pi/180) = \pi/2$ radians.
Calculate circle radius: Step $3$ : Calculate the radius of the circle. $\newline$ The diameter of the circle is given as $20$ . The radius $(r)$ is half of the diameter. $\newline$ $r = \frac{20}{2} = 10$ .
Calculate arc length: Step $4$ : Calculate the length of the arc using the formula. $\newline$ Substitute $r = 10$ and $\theta = \frac{\pi}{2}$ into the formula $s = r\theta$ . $\newline$ $s = 10 \times \left(\frac{\pi}{2}\right) = 5\pi$ .

More problems from Find Coordinate on Unit Circle

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Marco's class is painting a mural on the side of their school. The mural covers a

3 \frac{1}{2} \mathrm{~m}

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What is the length of the mural?

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A cup of hot coffee has been left to cool in a room with an ambient temperature of

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T(m)=21+74 \cdot 10^{-0.03 m}

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\newline

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\newline

{ }^{\circ} C

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Takumi plants a tree in his backyard and studies how the number of branches grows over time.

\newline

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\newline

N=5 \cdot 10^{0.3 t}

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g(x)=2^{x}

\newline

Can we use the mean value theorem to say the equation

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has a solution where

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\newline

1

\newline

(A) No, since the function is not differentiable on that interval.

\newline

(B) No, since the average rate of change of

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(C) Yes, both conditions for using the mean value theorem have been met.

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\newline

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\newline

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