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Designing a Race Track
An architect is designing a race track that will be 60 feel wide and have semicircular ends, as shown in the accompanying figure. The length of the track is to he one mile. measured on the inside edge of the track.
a) Find the exact dimensions for x and y in the figure that will maximize the area of the rectangular center section.
b) Round the answers to part (a) to the nearest tenth of a foot and make an accurate drawing of the track.
c) Find the exact dimensions for x and y that will maximize the total area enclosed by the track.
d) Repeat parts (a), (b), and (c) assuming that the one-mile length is measured on the outside edge of the track.
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College Algebra (6th Edition)
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