how long is the arc intersected by a central angle of $\frac{5pi}{3}$ radians in a circle with a radius of 2…

Explanation:

Step1: Recall arc - length formula

The formula for the length of an arc $s$ of a circle is $s = r\theta$, where $r$ is the radius of the circle and $\theta$ is the central angle in radians.

Step2: Substitute given values

We are given that $r = 2$ ft and $\theta=\frac{5\pi}{3}$. Substituting these values into the formula, we get $s=2\times\frac{5\pi}{3}=\frac{10\pi}{3}$.

Step3: Approximate the value

Since $\pi\approx3.14$, then $s=\frac{10\times3.14}{3}=\frac{31.4}{3}\approx10.5$ ft.

Answer:

C. 10.5 ft