To solve the equation [tex]\( c = 2 \pi r \)[/tex] for the variable [tex]\( r \)[/tex], we need to isolate [tex]\( r \)[/tex] on one side of the equation. Here are the steps to do that:
1. Start with the given equation:
[tex]\[ c = 2 \pi r \][/tex]
2. Isolate [tex]\( r \)[/tex]:
Since [tex]\( r \)[/tex] is being multiplied by [tex]\( 2 \pi \)[/tex], we can get [tex]\( r \)[/tex] by itself by dividing both sides of the equation by [tex]\( 2 \pi \)[/tex]:
[tex]\[ r = \frac{c}{2 \pi} \][/tex]
3. Simplify the expression:
Notice that the variable [tex]\( c \)[/tex] in the given options is denoted as [tex]\( C \)[/tex], but this doesn't change the algebraic manipulation. Thus the simplified version of the equation is:
[tex]\[ r = \frac{C}{2 \pi} \][/tex]
Now, let’s match this result with the provided choices:
- A. [tex]\( r = \frac{C}{2 \pi} \)[/tex]
- B. [tex]\( r = \frac{2 \pi}{C} \)[/tex]
- C. [tex]\( r = \frac{2 C}{\pi} \)[/tex]
- D. [tex]\( r = \frac{\pi}{2 C} \)[/tex]
Comparing our simplified result [tex]\( r = \frac{C}{2 \pi} \)[/tex], we see that it matches choice A.
Therefore, the correct answer is:
A. [tex]\( r = \frac{C}{2 \pi} \)[/tex]
