A mirror in the shape of a rectangle capped by a semicircle is to have perimeter 100 inches. Choose the radius of the semicircular part so that the mirror has maximum area. [Note: The perimeter consists of three sides of the rectangle and the semicircle.] 25 (a) Find an equation for the A, the area of the mirror, in terms of the variables r and y shown in the diagram below. (b) Write an equation for the constraint (s) in this problem. (c) Write A as a function of only the variable r. You can use your equality constraint from part (b) to substitute for y in your equation for A. (You do not need to simplify your answer.)