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Caroline has a rock stuck in her Jeep's tire. If the tire has a 48-inch diameter, how far does the rock travel in 94° of rotation? A. 188 pi over 15 B. 47 pi over 90 C. 24π D. 47π

Answer :

meerkat18
So the problem ask to calculate the arc length of the tire if the rock is located at the 94 degree of the rotation and its diameter is 48 inches so the possible answer base on my calculation is letter A. 188 pi over 15. I hope you are satisfied with my answer and feel free to ask for more 
calculista

Answer:

Option A

[tex]188[/tex] pi over [tex]15[/tex]

Step-by-step explanation:

Step 1

Find the circumference of the tire

[tex]C=\pi D[/tex]

where

D is the diameter of the tire

In this problem we have

[tex]D=48\ in[/tex]

substitute the value

[tex]C=\pi (48)[/tex]

[tex]C=48\pi\ in[/tex]

Remember that

[tex]360\°[/tex] subtends the complete circle the arc length [tex]48\pi\ in[/tex]

so

by proportion

Find how far does the rock travel in [tex]94\°[/tex] of rotation

[tex]\frac{48\pi }{360}=\frac{x}{94}\\ \\x=94*48\pi /360\\ \\x=\frac{4,512}{360}\pi[/tex]

Simplify

[tex]x=\frac{188}{15}\pi[/tex]

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