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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Maximization
Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.
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Chapter 10.4, Problem 46E
To determine

To write: The equation of the hyperbola on which the lightning strike was located, if sound travels at 1100 feet per second.

Expert Solution & Answer
Check Mark

Answer to Problem 46E

  x2(1100)2−y2(5340.55)2=1

Explanation of Solution

Given information: Forestry: Two ranger stations located 4 miles apart observe a lightning strike. A ranger at station A reports hearing the sound of thunder 2 seconds prior to a ranger at station B . place the two ranger stations on the x -axis with the midpoint between the two stations at the origin. The transverse axis is horizontal.

  Advanced Mathematical Concepts: Precalculus with Applications, Student Edition, Chapter 10.4, Problem 46E , additional homework tip 1

Calculation:

  Advanced Mathematical Concepts: Precalculus with Applications, Student Edition, Chapter 10.4, Problem 46E , additional homework tip 2

By the definition of the hyperbola we know the difference of the distances between the towers and the lightning strike = the distance between the vertices (2a) .

The difference was 2 seconds between the towers.

Since sound travels at 1100 feet/sec. The difference would be 2200 feet.

Since we’re centered at the origin, this makes

  a=1100.

We know the distance between the foci is 4 miles.

5280 feet = 1 mile means 21.120 feet.

This means c = 10,560 feet.

If a2+b2=c2→b2=(10560)2−(9110)2b=5340.55

Therefore equation is:

  x2(1100)2−y2(5340.55)2=1

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Chapter 10 Solutions

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition

Ch. 10.1 - Prob. 1CFUCh. 10.1 - Prob. 2CFUCh. 10.1 - Prob. 3CFUCh. 10.1 - Prob. 4CFUCh. 10.1 - Prob. 5CFUCh. 10.1 - Prob. 6CFUCh. 10.1 - Prob. 7CFUCh. 10.1 - Prob. 8CFUCh. 10.1 - Prob. 9CFUCh. 10.1 - Prob. 10CFU
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