Question

Consider a circle whose size can vary. Let r represent the radius of the circle (in cm) and let C represent the circumference of the circle (in cm). Suppose the function g determines the radius of the circle in cm, r, given its circumference in cm, C. Write a function formula for g.

Answer 1

Answer:

$g(C)=\frac{C}{2\pi}$

Step-by-step explanation:

Let r represent the radius of the circle (in cm) and

let C represent the circumference of the circle (in cm).

First solve the equation for 'r' using circumference formula

Circumference of circle formula is $C= 2\pi r$

Solve for r, divide both sides by 2pi

$r=\frac{C}{2\pi}$

the function g determines the radius of the circle in cm

So we replace 'r' with g(C), where C is the circumference

$g(C)=\frac{C}{2\pi}$