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

`g(C)=(C)/(2\pi)`

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=(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)=(C)/(2\pi)`