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The length of an arc intercepted by a central angle measuring 5π7 radians is 10 inches.

What is the radius of the circle?
Responses

7/π in.

14/π in.


28/π in.

35/π in.

1 Answer

5 votes

Answer:

Explanation:

To solve this problem, you can use the formula:

length of arc = radius x central angle

We know the length of the arc is 10 inches, and the central angle measures 5π/7 radians. We can use algebra to solve for the radius "r":

10 = r x (5π/7)

To isolate "r," we can divide both sides of the equation by 5π/7:

r = 10 ÷ (5π/7)

To simplify this expression, we can multiply the top and bottom of the fraction by the reciprocal of 5π/7, which is 7/5π:

r = 10 x (7/5π)

r = 14/π

So the radius of the circle is 14/π inches (or approximately 4.45 inches, rounded to two decimal places).

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