SOLUTION: A 1/4 -mile track for racing stock cars consists of two semicircles connected by parallel straightaway. In order to provide sufficient room for pit crews, emergency vehicles, and

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Question 1079274: A 1/4 -mile track for racing stock cars consists
of two semicircles connected by parallel straightaway. In order to provide sufficient room for pit crews,
emergency vehicles, and spectator parking, the track must enclose an area of 100,000 square feet. Find the length of the
straightaways and the diameter of the semicircles to the nearest foot.

Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Perimeter in feet, %281%2F4%29mile%2A5280%28feet%2Fmile%29=1320%2Afeet


x, rectangular dimension capped with each semicircle part
y, rectangular dimension not capped with the semicircle part
radius of each semicircle is x%2F2.

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Accounting for perimeter and area and simplifying,
system%28pi%2Ax%2B2y=1320%2C4xy%2Bpi%2Ax%5E2=400000%29
.

Solving for y and substituting, and then simplifying,...
pi%2Ax%5E2-2640x%2B40000=0


x=198, diameter of semicircle parts, in feet
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y=349, each straight-way part