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 10.5, Problem 33E

(a)

To determine

To find: The diameter of the headlight at its opening, if the depth of the headlight is to be 4 inches.

(a)

Expert Solution
Check Mark

Answer to Problem 33E

  The diameter=82

Explanation of Solution

Given information: Automobile: Automobile headlights contain parabolic reflectors, which work on the principle that light placed at the focus of a parabola will reflect off the mirror-like surface in lines parallel to the axis of symmetry. Suppose a bulb is placed at the focus of a headlight’s reflector, which is 2 inches from the vertex.

  Advanced Mathematical Concepts: Precalculus with Applications, Student Edition, Chapter 10.5, Problem 33E , additional homework tip 1

Calculation:

According to the picture we should start at:

  y2=4px

Since, p=2→y2=8x

At a depth of 4 inches, (x=4)

  y2=8xy=32=42

So,

The diameter =2(42)=82

(b)

To determine

To find: The diameter of the headlight at its opening if the depth is increased by 25% .

(b)

Expert Solution
Check Mark

Answer to Problem 33E

  The diameter=±210

Explanation of Solution

Given information: Automobile: Automobile headlights contain parabolic reflectors, which work on the principle that light placed at the focus of a parabola will reflect off the mirror-like surface in lines parallel to the axis of symmetry. Suppose a bulb is placed at the focus of a headlight’s reflector, which is 2 inches from the vertex.

  Advanced Mathematical Concepts: Precalculus with Applications, Student Edition, Chapter 10.5, Problem 33E , additional homework tip 2

Calculation:

Increasing the depth by 25 percent:

  4(1.25)=5 inches

  y2=8x→y=40

  y=±210

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Chapter 10.5, Problem 32E
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Chapter 10.5, Problem 34E

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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