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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Concept explainers

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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Question

Chapter 10.3, Problem 49E

(a)

To determine

To write: An equation modeling the shape of the room. Assume that is centered at the origin and the major axis is horizontal.

(a)

Expert Solution

Answer to Problem 49E

x22304+y2529=1

Explanation of Solution

Given information: History: A whispering gallery is designed using an elliptical ceiling. It operates on the principle that sound projected from one focus of an ellipse reflects off the ceiling and back to the other focus. The United States Capitol contains such an elliptical room. The room is 96 feet in length, 46 feet in width and has a ceiling that is about 23 feet high.

Calculation:

Take ½ of each measurement for ( a and b ) and then squared.

x22304+y2529=1

(b)

To determine

To describe: Two possible places where Adams might have stood to overhear, as John Quincy Adams is known to have overheard conversations being held at the opposite party leader’s desk by standing in a certain spot in this room.

(b)

Expert Solution

Explanation of Solution

Calculation:

He could stand at either foci, with the desk at the other foci.

(c)

To determine

To find: The distance did Adams stand from the desk.

(c)

Expert Solution

Answer to Problem 49E

84.26 feet

Explanation of Solution

Calculation:

Since the foci are:

a2−b2=c2→c2=2304−529=1775c=42.13 feet

Adams will be at one the same distance from the room’s center as the desk so,

2×(42.13)⇒84.26 feet

Chapter 10.3, Problem 48E

Chapter 10.3, Problem 50E

Chapter 10 Solutions

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition

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

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