Clear Sailing A sailor plans to install a windshield wiper on a porthole that has ra...

Clear Sailing A sailor plans to install a windshield wiper on a porthole that has radius 1 ft. The wiper blade of length x ft is to be attached to the edge of the porthole, as shown in the figure. The area cleaned by the blade is a sector of a circle centered at the point of attachment.

a. Write the area cleaned by the blade as a function of x.

b. If the blade cleans half of the window, then what is the exact length of the blade?

c. Use a graphing calculator to find the length for the blade that would maximize the area cleaned.