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Question 691504: the cross section of a nuclear power plant cooling tower is in the shape of a hyperbola. suppose the tower has a base diameter of 228 meters and the narrowest point, 72 meters above ground is 76 meters. if the diameter at the top is 152 meters. how tall is the tower
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! the cross section of a nuclear power plant cooling tower is in the shape of a hyperbola. suppose the tower has a base diameter of 228 meters and the narrowest point, 72 meters above ground is 76 meters. if the diameter at the top is 152 meters. how tall is the tower
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Draw a sketch of a hyperbola with a base=228.
Length of horizontal transverse axis=76
Top=152
Set center at origin (0,0)
right endpoint of base: (114,-72)
Equation of hyperbola:x^2/a^2-y^2/b^2=1
given length of horizontal transverse axis=76=2a
a=38
a^2=1444
Using coordinates from endpoint of base, solve for b^2
Equation: 114^2/1444-72^2/b^2=1
114^2/1444-72^2/b^2=1
9-5184/b^2=1
5184/b^2=8
b^2=5184/8
b^2=648
Equation: x^2/1444-y^2/648=1
plug-in x=76, then solve for y
76^2/1444-y^2/648=1
4-y^2/648=1
y^2/648=3
y^2=3*648=1944
y≈√1944≈44.1
height of tower≈y+72≈116.1 meters
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