SOLUTION: A cooling tower is a hyperbolic structure. Suppose its base diamter is 100 meters and its smallest diameter of 48 meters oocurs 84 meters above the base. If the tower is 120 meters

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: A cooling tower is a hyperbolic structure. Suppose its base diamter is 100 meters and its smallest diameter of 48 meters oocurs 84 meters above the base. If the tower is 120 meters      Log On


   

Question 628867: A cooling tower is a hyperbolic structure. Suppose its base diamter is 100 meters and its smallest diameter of 48 meters oocurs 84 meters above the base. If the tower is 120 meters tall, find the diameter at the top.
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
A cooling tower is a hyperbolic structure. Suppose its base diamter is 100 meters and its smallest diameter of 48 meters oocurs 84 meters above the base. If the tower is 120 meters tall, find the diameter at the top.
**
Standard form of hyperbola with horizontal transverse axis with center at (0,0):
x%5E2%2Fa%5E2-y%5E2%2Fb%5E2=1
Draw a hyperbola with a horizontal transverse axis with center at (0,0)
length of horizontal transverse axis=48=2a
a=24
two points on the hyperbola to work with:
one corner of the base: (50,-84)
one corner of the top: (x,36)
Using point (50,-84) to find b^2
50%5E2%2F24%5E2-%28-84%29%5E2%2Fb%5E2=1
50^2/24^2-1=(-84)^2/b^2
3.34=7056/b^2
b^2=7056/3.34=2112.57
Equation: x%5E2%2F24%5E2-y%5E2%2F2112.57=1
solve for x-coordinate of right corner of top
x%5E2%2F24%5E2-36%5E2%2F2112.57=1
x%5E2%2F576-1296%2F2112.57=1
x%5E2%2F576-.6135=1
x%5E2%2F576=1.6135
x^2=576*1.6135=929.38
x=√929.38=30.48
Diameter at the top=2x≈61 ft
Please check my arithmetic