Question

a circle has a central angle of 6 radians that intersects an arc of length 14 in. which equation finds the length of the radius, r, of the circle?
\\( r = \frac{6}{14} \\)
\\( r = \frac{14}{6} \\)
\\( r = 6 + 14 \\)
\\( r = 6 \cdot 14 \\)

Explanation:

Step1: Recall arc length formula

The formula for arc length \( s \) in radians is \( s = r\theta \), where \( r \) is the radius and \( \theta \) is the central angle in radians.

Step2: Solve for \( r \)

Given \( s = 14 \) and \( \theta = 6 \), we rearrange \( s = r\theta \) to \( r=\frac{s}{\theta} \). Substituting the values, we get \( r = \frac{14}{6} \).

Answer:

\( r=\frac{14}{6} \) (the second option: \( r=\frac{14}{6} \))