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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Question

Chapter 10.4, Problem 45E

(a)

To determine

To write: An equation of the hyperbola used to generate the hyperboloid, if the cooling tower is 150 feet wide at its narrowest point.

(a)

Expert Solution

Answer to Problem 45E

x2752−y21002=1

Explanation of Solution

Given information: Nuclear Power: A nuclear cooling tower is a hyperboloid , that is, a hyperbola rotated around its conjugate axis. Suppose the hyperbola used to generate the hyperboloid modeling the shape of the cooling tower has an eccentricity of 53 .

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition, Chapter 10.4, Problem 45E , additional homework tip 1

Calculation:

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition, Chapter 10.4, Problem 45E , additional homework tip 2

If its 150 feet wide at the narrowest point (conjugate axis), then a = 75.

And,

e=c75=53→c=125

If: a2+b2=c2→b2=1252−752=10,000

This gives us:

x2752−y21002=1

(b)

To determine

To find: The radius of the top and the base of the tower, if the tower is 450 feet tall, the top is 100 feet above the center of the hyperbola and the base is 350 feet below the center.

(b)

Expert Solution

Answer to Problem 45E

Top radius=106.06 feetBase radius=273.004 feet

Explanation of Solution

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition, Chapter 10.4, Problem 45E , additional homework tip 3

Calculation:

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition, Chapter 10.4, Problem 45E , additional homework tip 4

Given:

(r1)2752−10021001=1→(r1)2752=2r1=2×752=752=106.06 feet

(r2)2752−(−350)21001=1→(r2)2752=1+494(r2)2752=534r2=75532r2=273.004 feet

Chapter 10.4, Problem 44E

Chapter 10.4, Problem 46E

Chapter 10 Solutions

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition

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