Advanced Mathematical Concepts: Precalculus with Applications, Student Edition
Advanced Mathematical Concepts: Precalculus with Applications, Student Edition
1st Edition
ISBN: 9780078682278
Author: McGraw-Hill, Berchie Holliday
Publisher: Glencoe/McGraw-Hill
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Chapter 12.8, Problem 39E
To determine

To find: the equation of the hyperbola used to generate the hyperboloid of the cooling tower.

Expert Solution & Answer
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Answer to Problem 39E

The equation of the hyperbola is x24225+y22704=1 .

Explanation of Solution

Given:

The cooling tower is 130feet .

Eccentricity is 75 .

Concept:

The equation of hyperbola

  x2a2+y2b2=1.

  b2=a2(e21) .

Length of transverse axis =2a .

Calculation:

To find the equation of the hyperbola having the length of the transverse axis is 130 Feet and the eccentricity is 75 .

The equation of hyperbola having the transverse axis 2a and the length of the conjugate axis 2b and eccentricity e can be taken as:

  x2a2+y2b2=1.

Here,

  b2=a2(e21) .

Since, the length of the transverse axis is 130 feet.

  2a=130.a=65.a2=(65)2.a2=4225.

To get the value of b ,substitute a=65 and e=75 in the equation:

  b2=4225(49251).4225(1625).2704.

Therefore, the equation of the hyperbola used to generate the hyperboloid of the cooling tower is:

  x24225+y22704=1 .

Hence, the equation of the hyperbola is x24225+y22704=1 .

Chapter 12 Solutions

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition

Ch. 12.1 - Prob. 11CFUCh. 12.1 - Prob. 12CFUCh. 12.1 - Prob. 13CFUCh. 12.1 - Prob. 14CFUCh. 12.1 - Prob. 15CFUCh. 12.1 - Prob. 16CFUCh. 12.1 - Prob. 17ECh. 12.1 - Prob. 18ECh. 12.1 - Prob. 19ECh. 12.1 - Prob. 20ECh. 12.1 - Prob. 21ECh. 12.1 - Prob. 22ECh. 12.1 - Prob. 23ECh. 12.1 - Prob. 24ECh. 12.1 - Prob. 25ECh. 12.1 - Prob. 26ECh. 12.1 - Prob. 27ECh. 12.1 - Prob. 28ECh. 12.1 - Prob. 29ECh. 12.1 - Prob. 30ECh. 12.1 - Prob. 31ECh. 12.1 - Prob. 32ECh. 12.1 - Prob. 33ECh. 12.1 - Prob. 34ECh. 12.1 - Prob. 35ECh. 12.1 - Prob. 36ECh. 12.1 - Prob. 37ECh. 12.1 - Prob. 38ECh. 12.1 - Prob. 39ECh. 12.1 - Prob. 40ECh. 12.1 - Prob. 41ECh. 12.1 - Prob. 42ECh. 12.1 - Prob. 43ECh. 12.1 - Prob. 44ECh. 12.1 - Prob. 45ECh. 12.1 - Prob. 46ECh. 12.1 - Prob. 47ECh. 12.1 - Prob. 48ECh. 12.1 - Prob. 49ECh. 12.1 - Prob. 50ECh. 12.1 - Prob. 51ECh. 12.1 - Prob. 52ECh. 12.1 - Prob. 53ECh. 12.1 - Prob. 54ECh. 12.1 - Prob. 55ECh. 12.1 - Prob. 56ECh. 12.1 - Prob. 57ECh. 12.1 - Prob. 58ECh. 12.1 - Prob. 59ECh. 12.1 - 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Prob. 13CFUCh. 12.5 - Prob. 14ECh. 12.5 - Prob. 15ECh. 12.5 - Prob. 16ECh. 12.5 - Prob. 17ECh. 12.5 - Prob. 18ECh. 12.5 - Prob. 19ECh. 12.5 - Prob. 20ECh. 12.5 - Prob. 21ECh. 12.5 - Prob. 22ECh. 12.5 - Prob. 23ECh. 12.5 - Prob. 24ECh. 12.5 - Prob. 25ECh. 12.5 - Prob. 26ECh. 12.5 - Prob. 27ECh. 12.5 - Prob. 28ECh. 12.5 - Prob. 29ECh. 12.5 - Prob. 30ECh. 12.5 - Prob. 31ECh. 12.5 - Prob. 32ECh. 12.5 - Prob. 33ECh. 12.5 - Prob. 34ECh. 12.5 - Prob. 35ECh. 12.5 - Prob. 36ECh. 12.5 - Prob. 37ECh. 12.5 - Prob. 38ECh. 12.5 - Prob. 39ECh. 12.5 - Prob. 40ECh. 12.5 - Prob. 41ECh. 12.5 - Prob. 42ECh. 12.5 - Prob. 43ECh. 12.5 - Prob. 44ECh. 12.5 - Prob. 45ECh. 12.5 - Prob. 46ECh. 12.5 - Prob. 47ECh. 12.5 - Prob. 48ECh. 12.5 - Prob. 49ECh. 12.5 - Prob. 50ECh. 12.5 - Prob. 51ECh. 12.5 - Prob. 52ECh. 12.5 - Prob. 53ECh. 12.5 - Prob. 54ECh. 12.5 - Prob. 55ECh. 12.5 - Prob. 56ECh. 12.5 - Prob. 57ECh. 12.5 - Prob. 58ECh. 12.5 - Prob. 59ECh. 12.6 - Prob. 1CFUCh. 12.6 - Prob. 2CFUCh. 12.6 - Prob. 3CFUCh. 12.6 - 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Prob. 2CFUCh. 12.8 - Prob. 3CFUCh. 12.8 - Prob. 4CFUCh. 12.8 - Prob. 5CFUCh. 12.8 - Prob. 6CFUCh. 12.8 - Prob. 7CFUCh. 12.8 - Prob. 8CFUCh. 12.8 - Prob. 9CFUCh. 12.8 - Prob. 10CFUCh. 12.8 - Prob. 11ECh. 12.8 - Prob. 12ECh. 12.8 - Prob. 13ECh. 12.8 - Prob. 14ECh. 12.8 - Prob. 15ECh. 12.8 - Prob. 16ECh. 12.8 - Prob. 17ECh. 12.8 - Prob. 18ECh. 12.8 - Prob. 19ECh. 12.8 - Prob. 20ECh. 12.8 - Prob. 21ECh. 12.8 - Prob. 22ECh. 12.8 - Prob. 23ECh. 12.8 - Prob. 24ECh. 12.8 - Prob. 25ECh. 12.8 - Prob. 26ECh. 12.8 - Prob. 27ECh. 12.8 - Prob. 28ECh. 12.8 - Prob. 29ECh. 12.8 - Prob. 30ECh. 12.8 - Prob. 31ECh. 12.8 - Prob. 32ECh. 12.8 - Prob. 33ECh. 12.8 - Prob. 35ECh. 12.8 - Prob. 36ECh. 12.8 - Prob. 37ECh. 12.8 - Prob. 38ECh. 12.8 - Prob. 39ECh. 12.8 - Prob. 40ECh. 12.8 - Prob. 41ECh. 12.8 - Prob. 42ECh. 12.8 - Prob. 43ECh. 12.8 - Prob. 44ECh. 12.9 - Prob. 1CFUCh. 12.9 - Prob. 2CFUCh. 12.9 - Prob. 3CFUCh. 12.9 - Prob. 4CFUCh. 12.9 - Prob. 5CFUCh. 12.9 - Prob. 6CFUCh. 12.9 - Prob. 7CFUCh. 12.9 - Prob. 8CFUCh. 12.9 - 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