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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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\n" ); document.write( "Draw a sketch of a hyperbola with a base=228.
\n" ); document.write( "Length of horizontal transverse axis=76
\n" ); document.write( "Top=152
\n" ); document.write( "Set center at origin (0,0)
\n" ); document.write( "right endpoint of base: (114,-72)
\n" ); document.write( "Equation of hyperbola:x^2/a^2-y^2/b^2=1
\n" ); document.write( "given length of horizontal transverse axis=76=2a
\n" ); document.write( "a=38
\n" ); document.write( "a^2=1444
\n" ); document.write( "Using coordinates from endpoint of base, solve for b^2
\n" ); document.write( "Equation: 114^2/1444-72^2/b^2=1
\n" ); document.write( "114^2/1444-72^2/b^2=1
\n" ); document.write( "9-5184/b^2=1
\n" ); document.write( "5184/b^2=8
\n" ); document.write( "b^2=5184/8
\n" ); document.write( "b^2=648
\n" ); document.write( "Equation: x^2/1444-y^2/648=1
\n" ); document.write( "plug-in x=76, then solve for y
\n" ); document.write( "76^2/1444-y^2/648=1
\n" ); document.write( "4-y^2/648=1
\n" ); document.write( "y^2/648=3
\n" ); document.write( "y^2=3*648=1944
\n" ); document.write( "y≈√1944≈44.1
\n" ); document.write( "height of tower≈y+72≈116.1 meters\r
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