SOLUTION: natural draft cooling tower are shaped like hyperbola for more efficient cooling of power plants. The hyperbola in the tower can be modeled by x^2 over 25 minus y^2 over 256 equals

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: natural draft cooling tower are shaped like hyperbola for more efficient cooling of power plants. The hyperbola in the tower can be modeled by x^2 over 25 minus y^2 over 256 equals      Log On


   

Question 1198410: natural draft cooling tower are shaped like hyperbola for more efficient cooling of power plants. The hyperbola in the tower can be modeled by x^2 over 25 minus y^2 over 256 equals to 1 with 150m as its height. Find the width of the tower at the top and its narrowest part in the middle.
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

The hyperbola in the tower can be modeled by
x%5E2%2F25+-+y%5E2%2F256+=1+
with 150m as its height.

Capture11-20-2022-5-05-35-PM

center is at (0,+0)
a=5
b=16
semimajor axis length | 5
semiminor axis length | 16
vertices | (-5, 0) | (5, 0)

the narrowest part in the middle is the distance between vertices or
2a=2%2A5=10m
the width on the top is the distance between points (-x, 75) and (x, 75)
now find x+ when y=75
x%5E2%2F25+-+75%5E2%2F256+=1+
x+=+%285+sqrt%285881%29%29%2F16=23.97
or
x+=+%285+sqrt%285881%29%29%2F16=-23.97

Solved by pluggable solver: Distance Between 2 points
The distance formula is sqrt%28%28%28x%5B2%5D-x%5B1%5D%29%5E2%29%2B%28%28y%5B2%5D-y%5B1%5D%29%5E2%29%29. Plug in the numbers,
sqrt%28%28%2823.97-%28-23.97%29%29%5E2%29%2B%28%2875-%2875%29%29%5E2%29%29
sqrt%2847.94%5E2%2B0%5E2%29 The distance is 47.94.



so the width on the top is: 47.94m


answer:
the width of the tower at the top is 47.94m
and
its narrowest part in the middle is 10m