QUESTION IMAGE
Question
select the correct answer
arc xy located on circle a has a length of 40 centimeters. the radius of the circle is 10 centimeters. what is the measure of the corresponding central angle for \\(\overset{\frown}{xy}\\) in radians?
a. \\(4\\)
b. \\(3\\)
c. \\(\frac{4}{3}\pi\\)
d. \\(\frac{3}{4}\pi\\)
Step1: Recall arc length formula
The arc length formula relating arc length $s$, radius $r$, and central angle $\theta$ (in radians) is $s = r\theta$.
Step2: Rearrange to solve for $\theta$
Isolate $\theta$ by dividing both sides by $r$: $\theta = \frac{s}{r}$
Step3: Substitute given values
Substitute $s = 40$ cm and $r = 10$ cm:
$\theta = \frac{40}{10}$
Step4: Calculate the value
$\theta = 4$
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A. 4