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An indoor physical fitness room consists of a rectangular region with a semicircle on each end. The perimeter of the room is to be a -meter running track. Let be the area of the rectangular region. Label all parts of the diagram. Note that is the radius of the circular portion.Horizontal rectangle, bottom edge labeled, y, with semi-circles, one on each right & left  edge, with edge as the diameter, radius on right semicircle labeled, x.  

  1. Write an equation for in terms of .

    circumference (or in this case)

  2. Express as a function of .

    Use the information from part (a).

  3. What diameter will create a maximum area for the physical fitness room?

    Graph your function from part (b) on a calculator. Locate the point that represents a maximum.