A landscaper plants circular flowerbeds in square plots of v

A landscaper plants circular flowerbeds in square plots of various sizes. After planting flowers (shaded region shown), grass is put down to form a lawn in the remaining area of the square (white regions).

A. Define a function ff that determines the radius of the circular flowerbed in terms of the side length of the square plot, x.

B. Define a function g that determines the area of the circular flowerbed as a function of the radius of the circular flowerbed, r.

C. Define a function hh that determines the area of the circular flowerbed in terms of the side length of the square, x.

D. Define a function k that determines the area of the square plot in terms of the side length of the square plot, x.

E. Define a function l that determines the area of grass in terms of the side length of the square plot, x.

Solution

A. Since the diameter is equal to the side of the square,

x=2r

F=r=x/2

B. Function g = Area= * r * r

C. function h = * (x/2)² = x²/4

D. Function k = x²

E. Function l = x²-r² = x²- ( x²/4)