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Question 607298: A vertical cross section of a cooling tower is a portion of a hyperbola. The standard form of the equation of the hyperbolic cross section is x^2/80^2 - (y-240)^2/160^2 = 1 , 0 less than or equal to y less than or equal to 380 Where x and y are measured in feet. The horizontal cross sections of the tower are circles. What is the smallest radius of a horizontal cross section. Round to the nearest foot.
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! A vertical cross section of a cooling tower is a portion of a hyperbola. The standard form of the equation of the hyperbolic cross section is x^2/80^2 - (y-240)^2/160^2 = 1 , 0 less than or equal to y less than or equal to 380 Where x and y are measured in feet. The horizontal cross sections of the tower are circles. What is the smallest radius of a horizontal cross section. Round to the nearest foot.
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x^2/80^2 - (y-240)^2/160^2 = 1
Base of tower at origin, (0,0)
The smallest radius or diameter horizontal cross-section of the tower is at the center (0,240) of the hyperbola.
The diameter=length of the transverse axis=160
The y-coordinate of the center (240 ft) is within the given range of 0 ≤ y ≤ 380
Smallest radius of a horizontal cross section=80 ft
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