Solve quickly and label answers clearly.

A Norman window has the shape of a rectangle surmounted by a semicircle. Suppose the outer perimeter of such a window must be 600 cm. In this problem you will find the base length a which will maximize the area of such a window. The applet above shows a plot of the area function. Use the slider to visualize how the area changes for different values for a, and use the corresponding graph to estimate the optimal radius. Then use calculus to find an exact answer. (Correction: In the figure "r" should be "x"). When the base length is zero, the area of the window will be zero. There is also a limit on how large a can be: when a is large enough, the rectangular portion of the window shrinks down to zero height. What is the exact largest value of a when this occurs? largest x: cm. Determine a function A(x) which gives the area of the window in terms of the parameter a (this is the function plotted above): A( 2) = cm2. Now find the exact base length x which maximizes this area: c cm