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Find the arc length.
A. 
(145 pi)/(24)
B. 
(55 pi)/(3)
c. 
7pi
D. 
(32 pi)/(3)

Find the arc length.\newlineA. 145π24 \frac{145 \pi}{24} \newlineB. 55π3 \frac{55 \pi}{3} \newlinec. 7π 7 \pi \newlineD. 32π3 \frac{32 \pi}{3}

Full solution

Q. Find the arc length.\newlineA. 145π24 \frac{145 \pi}{24} \newlineB. 55π3 \frac{55 \pi}{3} \newlinec. 7π 7 \pi \newlineD. 32π3 \frac{32 \pi}{3}
  1. Calculate Arc Length: Calculate the arc length using the formula S=rθS = r\theta, where SS is the arc length, rr is the radius, and θ\theta is the central angle in radians.
  2. Verify Option A: Assuming the radius rr and the central angle θ\theta are given by the options, we need to find which option gives a valid arc length.
  3. Verify Option B: Option A: S=145π24S = \frac{145 \pi}{24}. This seems like a valid arc length calculation, but we don't have the radius or the angle to verify it.
  4. Verify Option C: Option B: S=55π3S = \frac{55 \pi}{3}. Again, this could be a valid arc length, but without the radius or angle, we can't confirm.
  5. Verify Option D: Option C: S=7πS = 7\pi. This is a possible arc length, but we need the radius and angle to be sure.
  6. Conclusion: Option D: S=32π3S = \frac{32 \pi}{3}. This also could be a correct arc length, but we need more information to determine if it's the right one.
  7. Conclusion: Option D: S=32π3S = \frac{32 \pi}{3}. This also could be a correct arc length, but we need more information to determine if it's the right one.Without additional information about the radius or the central angle, we cannot determine which option is the correct arc length.

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