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

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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)   (Show Source): You can put this solution on YOUR website!

The hyperbola in the tower can be modeled by

with as its height.

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

center is at (,)


semimajor axis length |
semiminor axis length |
vertices | (, ) | (, )

the narrowest part in the middle is the distance between vertices or

the width on the top is the distance between points (, ) and (, )
now find when


or


Solved by pluggable solver: Distance Between 2 points
The distance formula is . Plug in the numbers,

The distance is 47.94.



so the width on the top is:


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


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