Question
Solve for the indicated variable. Include all of your work in your answer. Submit your solution. \( C=2 \pi r \), for r
Ask by Erickson Bob. in South Africa
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( r = \frac{C}{2\pi} \)
Solution
To solve for \( r \) in the equation \( C = 2\pi r \), follow these steps:
1. **Start with the given equation:**
\[
C = 2\pi r
\]
2. **Isolate \( r \) by dividing both sides of the equation by \( 2\pi \):**
\[
\frac{C}{2\pi} = \frac{2\pi r}{2\pi}
\]
3. **Simplify the right side of the equation:**
\[
\frac{C}{2\pi} = r
\]
4. **Rearrange the equation to express \( r \) clearly:**
\[
r = \frac{C}{2\pi}
\]
**Final Answer:**
\[
r = \frac{C}{2\pi}
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Extra Insights
To solve for \( r \) in the equation \( C = 2 \pi r \), we need to isolate \( r \). 1. Start with the original equation: \[ C = 2 \pi r \] 2. Divide both sides of the equation by \( 2 \pi \) to solve for \( r \): \[ r = \frac{C}{2 \pi} \] And voila! We've isolated \( r \). The final expression shows that the radius \( r \) is equal to the circumference \( C \) divided by \( 2 \pi \).
