To solve for [tex]\( r \)[/tex] in the given formula:
[tex]\[
C = 2 \pi r
\][/tex]
we need to isolate [tex]\( r \)[/tex].
1. Start with the given formula: [tex]\[
C = 2 \pi r
\][/tex]
2. Divide both sides of the equation by [tex]\( 2 \pi \)[/tex]: [tex]\[
\frac{C}{2 \pi} = r
\][/tex]
3. Simplify the right-side: [tex]\[
r = \frac{C}{2 \pi}
\][/tex]
So, the correct expression for [tex]\( r \)[/tex] in terms of [tex]\( C \)[/tex] is:
[tex]\[
r = \frac{C}{2 \pi}
\][/tex]
Now, let's match this expression with the given choices:
A. [tex]\( r = \frac{C}{2 \pi} \)[/tex] - This is correct.
B. [tex]\( r = \frac{C - \pi}{2} \)[/tex] - This is incorrect because it does not effectively isolate [tex]\( r \)[/tex] according to the given formula.
C. [tex]\( r = 2 \pi C \)[/tex] - This is incorrect because it multiplies [tex]\( C \)[/tex] by [tex]\( 2 \pi \)[/tex] instead of dividing by [tex]\( 2 \pi \)[/tex].
D. [tex]\( r = C - 2 \pi \)[/tex] - This is incorrect because it subtracts instead of dividing by [tex]\( 2 \pi \)[/tex].
