Achurch window consisting of a rectangle topped by a semicircle is to have perimeter p . find the radius of the semicircle if the area of the window is to be maximum.

Step-by-step explanation:

Let r be the radius of the semicircle, then 2r is the width of the rectangle. Let y be the length of the rectangle. The perimeter of the window consists of two lengths, one width and length of semicircle, then

Express y:

The area of the window is

Substitute y into the area expression:

Find the derivative A':

Equate A' to 0:

When then and the function A is increasing, when then and the function A is decreasing. This means that at point the function A takes it maximal value (the area is maximal).

sorry not sure

step-by-step explanation:

no this is a nonlinear negative