Precalculus with Limits
Precalculus with Limits
3rd Edition
ISBN: 9781133947202
Author: Ron Larson
Publisher: Cengage Learning
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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
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Chapter 10.2, Problem 62E

(a)

To determine

To write: an equation of the parabola with its vertex at the origin that models the road surface.

(a)

Expert Solution
Check Mark

Answer to Problem 62E

The equation is

  y=x2640 .

Explanation of Solution

Given information:

Roads are often designed with parabolic surface to allow rain to drain off. A particular road is 32 feet wide and 0.4 foot higher in the center than it is on the sides.

  Precalculus with Limits, Chapter 10.2, Problem 62E

Calculation:

Find an equation that models the road surface.

The road is in the shape of a parabola with axis vertical.

We know that the standard equation of a parabola with axis vertical is given as

  (x−h)2=4p(y−k).............(1)

Now, since the vertex is given to be at (0,0) , we have

  h=0k=0

Thus, the equation reduces to

  x2=4py...........(2)

Also, we know that the points (−16,−0.4) and (16,−0.4) lie on the parabola.

Substituting the value of x and y in equation (2), we get

  (−16)2=4p(−0.4)Or p=−16×164×0.4

Thus, substituting the value of p in equation (2), we get

  x2=640yOr  y=x2640............(3)

(b)

To determine

To find: the distance the center of the road.

(b)

Expert Solution
Check Mark

Answer to Problem 62E

The road is 0.1 foot lower than in the middle at a distance of 8 feet from the center.

Explanation of Solution

Given information:

The road surface 0.1 feet lower than the center.

Calculation:

Find the distance from the center of the road where the road surface is 0.1 foot lower than in the middle.

Thus, we need to find the value of x given the value of given the value of y as 0.1

Substituting the value of y in equation (3), we get

Or

  x=±8

Thus, the road is 0.1 foot lower than in the middle at a distance of 8 feet from the center.

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Chapter 10.2, Problem 61E
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Chapter 10.2, Problem 63E

Chapter 10 Solutions

Precalculus with Limits

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Prob. 110ECh. 10.7 - Prob. 111ECh. 10.7 - Prob. 112ECh. 10.7 - Prob. 113ECh. 10.7 - Prob. 114ECh. 10.7 - Prob. 115ECh. 10.7 - Prob. 116ECh. 10.7 - Prob. 117ECh. 10.7 - Prob. 118ECh. 10.7 - Prob. 119ECh. 10.7 - Prob. 120ECh. 10.7 - Prob. 121ECh. 10.7 - Prob. 122ECh. 10.7 - Prob. 123ECh. 10.7 - Prob. 124ECh. 10.7 - Prob. 125ECh. 10.7 - Prob. 126ECh. 10.7 - Prob. 127ECh. 10.7 - Prob. 128ECh. 10.7 - Prob. 129ECh. 10.7 - Prob. 130ECh. 10.7 - Prob. 131ECh. 10.7 - Prob. 132ECh. 10.7 - Prob. 133ECh. 10.7 - Prob. 134ECh. 10.7 - Prob. 135ECh. 10.7 - Prob. 136ECh. 10.8 - Prob. 1ECh. 10.8 - Prob. 2ECh. 10.8 - Prob. 3ECh. 10.8 - Prob. 4ECh. 10.8 - Prob. 5ECh. 10.8 - Prob. 6ECh. 10.8 - Prob. 7ECh. 10.8 - Prob. 8ECh. 10.8 - Prob. 9ECh. 10.8 - Prob. 10ECh. 10.8 - Prob. 11ECh. 10.8 - Prob. 12ECh. 10.8 - Prob. 13ECh. 10.8 - Prob. 14ECh. 10.8 - Prob. 15ECh. 10.8 - Prob. 16ECh. 10.8 - Prob. 17ECh. 10.8 - Prob. 18ECh. 10.8 - Prob. 19ECh. 10.8 - Prob. 20ECh. 10.8 - Prob. 21ECh. 10.8 - Prob. 22ECh. 10.8 - Prob. 23ECh. 10.8 - Prob. 24ECh. 10.8 - Prob. 25ECh. 10.8 - Prob. 26ECh. 10.8 - Prob. 27ECh. 10.8 - Prob. 28ECh. 10.8 - Prob. 29ECh. 10.8 - Prob. 30ECh. 10.8 - Prob. 31ECh. 10.8 - Prob. 32ECh. 10.8 - Prob. 33ECh. 10.8 - Prob. 34ECh. 10.8 - Prob. 35ECh. 10.8 - Prob. 36ECh. 10.8 - Prob. 37ECh. 10.8 - Prob. 38ECh. 10.8 - Prob. 39ECh. 10.8 - Prob. 40ECh. 10.8 - Prob. 41ECh. 10.8 - Prob. 42ECh. 10.8 - Prob. 43ECh. 10.8 - Prob. 44ECh. 10.8 - Prob. 45ECh. 10.8 - Prob. 46ECh. 10.8 - Prob. 47ECh. 10.8 - Prob. 48ECh. 10.8 - Prob. 49ECh. 10.8 - Prob. 50ECh. 10.8 - Prob. 51ECh. 10.8 - Prob. 52ECh. 10.8 - Prob. 53ECh. 10.8 - Prob. 54ECh. 10.8 - Prob. 55ECh. 10.8 - Prob. 56ECh. 10.8 - Prob. 57ECh. 10.8 - Prob. 58ECh. 10.8 - Prob. 59ECh. 10.8 - Prob. 60ECh. 10.8 - Prob. 61ECh. 10.8 - Prob. 62ECh. 10.8 - Prob. 63ECh. 10.8 - Prob. 64ECh. 10.8 - Prob. 65ECh. 10.8 - Prob. 66ECh. 10.8 - Prob. 67ECh. 10.8 - Prob. 68ECh. 10.8 - Prob. 69ECh. 10.8 - Prob. 70ECh. 10.8 - Prob. 71ECh. 10.8 - Prob. 72ECh. 10.8 - Prob. 73ECh. 10.8 - Prob. 74ECh. 10.8 - Prob. 75ECh. 10.8 - Prob. 76ECh. 10.8 - Prob. 77ECh. 10.8 - Prob. 78ECh. 10.8 - Prob. 79ECh. 10.8 - Prob. 80ECh. 10.9 - Prob. 1ECh. 10.9 - Prob. 2ECh. 10.9 - Prob. 3ECh. 10.9 - Prob. 4ECh. 10.9 - Prob. 5ECh. 10.9 - Prob. 6ECh. 10.9 - Prob. 7ECh. 10.9 - Prob. 8ECh. 10.9 - Prob. 9ECh. 10.9 - Prob. 10ECh. 10.9 - Prob. 11ECh. 10.9 - Prob. 12ECh. 10.9 - Prob. 13ECh. 10.9 - Prob. 14ECh. 10.9 - Prob. 15ECh. 10.9 - Prob. 16ECh. 10.9 - Prob. 17ECh. 10.9 - Prob. 18ECh. 10.9 - Prob. 19ECh. 10.9 - Prob. 20ECh. 10.9 - Prob. 21ECh. 10.9 - Prob. 22ECh. 10.9 - Prob. 23ECh. 10.9 - Prob. 24ECh. 10.9 - Prob. 25ECh. 10.9 - Prob. 26ECh. 10.9 - Prob. 27ECh. 10.9 - Prob. 28ECh. 10.9 - Prob. 29ECh. 10.9 - Prob. 30ECh. 10.9 - Prob. 31ECh. 10.9 - Prob. 32ECh. 10.9 - Prob. 33ECh. 10.9 - Prob. 34ECh. 10.9 - Prob. 35ECh. 10.9 - Prob. 36ECh. 10.9 - Prob. 37ECh. 10.9 - Prob. 38ECh. 10.9 - Prob. 39ECh. 10.9 - Prob. 40ECh. 10.9 - Prob. 41ECh. 10.9 - Prob. 42ECh. 10.9 - Prob. 43ECh. 10.9 - Prob. 44ECh. 10.9 - Prob. 45ECh. 10.9 - Prob. 46ECh. 10.9 - Prob. 47ECh. 10.9 - Prob. 48ECh. 10.9 - Prob. 49ECh. 10.9 - Prob. 50ECh. 10.9 - Prob. 51ECh. 10.9 - Prob. 52ECh. 10.9 - Prob. 53ECh. 10.9 - Prob. 54ECh. 10.9 - Prob. 55ECh. 10.9 - Prob. 56ECh. 10.9 - Prob. 57ECh. 10.9 - Prob. 58ECh. 10.9 - Prob. 59ECh. 10.9 - Prob. 60ECh. 10.9 - Prob. 61ECh. 10.9 - Prob. 62ECh. 10.9 - Prob. 63ECh. 10.9 - Prob. 64ECh. 10.9 - Prob. 65ECh. 10.9 - Prob. 66ECh. 10.9 - Prob. 67ECh. 10.9 - Prob. 68ECh. 10.9 - Prob. 69ECh. 10.9 - Prob. 70ECh. 10.9 - Prob. 71ECh. 10.9 - Prob. 72ECh. 10.9 - Prob. 73ECh. 10.9 - Prob. 74ECh. 10.9 - Prob. 75ECh. 10.9 - Prob. 76ECh. 10.9 - Prob. 77ECh. 10.9 - Prob. 78ECh. 10.9 - Prob. 79ECh. 10.9 - Prob. 80ECh. 10 - Prob. 1RECh. 10 - Prob. 2RECh. 10 - Prob. 3RECh. 10 - Prob. 4RECh. 10 - Prob. 5RECh. 10 - Prob. 6RECh. 10 - Prob. 7RECh. 10 - Prob. 8RECh. 10 - Prob. 9RECh. 10 - Prob. 10RECh. 10 - Prob. 11RECh. 10 - Prob. 12RECh. 10 - Prob. 13RECh. 10 - Prob. 14RECh. 10 - Prob. 15RECh. 10 - Prob. 16RECh. 10 - Prob. 17RECh. 10 - Prob. 18RECh. 10 - Prob. 19RECh. 10 - Prob. 20RECh. 10 - Prob. 21RECh. 10 - Prob. 22RECh. 10 - Prob. 23RECh. 10 - Prob. 24RECh. 10 - Prob. 25RECh. 10 - Prob. 26RECh. 10 - Prob. 27RECh. 10 - Prob. 28RECh. 10 - Prob. 29RECh. 10 - Prob. 30RECh. 10 - Prob. 31RECh. 10 - Prob. 32RECh. 10 - Prob. 33RECh. 10 - Prob. 34RECh. 10 - Prob. 35RECh. 10 - Prob. 36RECh. 10 - Prob. 37RECh. 10 - Prob. 38RECh. 10 - Prob. 39RECh. 10 - Prob. 40RECh. 10 - Prob. 41RECh. 10 - Prob. 42RECh. 10 - Prob. 43RECh. 10 - Prob. 44RECh. 10 - Prob. 45RECh. 10 - Prob. 46RECh. 10 - Prob. 47RECh. 10 - Prob. 48RECh. 10 - Prob. 49RECh. 10 - Prob. 50RECh. 10 - Prob. 51RECh. 10 - Prob. 52RECh. 10 - Prob. 53RECh. 10 - Prob. 54RECh. 10 - Prob. 55RECh. 10 - Prob. 56RECh. 10 - Prob. 57RECh. 10 - Prob. 58RECh. 10 - Prob. 59RECh. 10 - Prob. 60RECh. 10 - Prob. 61RECh. 10 - Prob. 62RECh. 10 - Prob. 63RECh. 10 - Prob. 64RECh. 10 - Prob. 65RECh. 10 - Prob. 66RECh. 10 - Prob. 67RECh. 10 - Prob. 68RECh. 10 - Prob. 69RECh. 10 - Prob. 70RECh. 10 - Prob. 71RECh. 10 - Prob. 72RECh. 10 - Prob. 73RECh. 10 - Prob. 74RECh. 10 - Prob. 75RECh. 10 - Prob. 76RECh. 10 - Prob. 77RECh. 10 - Prob. 78RECh. 10 - Prob. 79RECh. 10 - Prob. 80RECh. 10 - Prob. 81RECh. 10 - Prob. 82RECh. 10 - Prob. 83RECh. 10 - Prob. 84RECh. 10 - Prob. 85RECh. 10 - Prob. 86RECh. 10 - Prob. 87RECh. 10 - Prob. 88RECh. 10 - Prob. 89RECh. 10 - Prob. 90RECh. 10 - Prob. 91RECh. 10 - Prob. 92RECh. 10 - Prob. 93RECh. 10 - Prob. 94RECh. 10 - Prob. 95RECh. 10 - Prob. 96RECh. 10 - Prob. 97RECh. 10 - Prob. 98RECh. 10 - Prob. 99RECh. 10 - Prob. 100RECh. 10 - Prob. 101RECh. 10 - Prob. 102RECh. 10 - Prob. 103RECh. 10 - Prob. 104RECh. 10 - Prob. 105RECh. 10 - Prob. 106RECh. 10 - Prob. 107RECh. 10 - Prob. 108RECh. 10 - Prob. 109RECh. 10 - Prob. 110RECh. 10 - Prob. 111RECh. 10 - Prob. 112RECh. 10 - Prob. 113RECh. 10 - Prob. 114RECh. 10 - Prob. 115RECh. 10 - Prob. 116RECh. 10 - Prob. 117RECh. 10 - Prob. 118RECh. 10 - Prob. 119RECh. 10 - Prob. 1CTCh. 10 - Prob. 2CTCh. 10 - Prob. 3CTCh. 10 - Prob. 4CTCh. 10 - Prob. 5CTCh. 10 - Prob. 6CTCh. 10 - Prob. 7CTCh. 10 - Prob. 8CTCh. 10 - Prob. 9CTCh. 10 - Prob. 10CTCh. 10 - Prob. 11CTCh. 10 - Prob. 12CTCh. 10 - Prob. 13CTCh. 10 - Prob. 14CTCh. 10 - Prob. 15CTCh. 10 - Prob. 16CTCh. 10 - Prob. 17CTCh. 10 - Prob. 18CTCh. 10 - Prob. 19CTCh. 10 - Prob. 20CTCh. 10 - Prob. 21CTCh. 10 - Prob. 22CTCh. 10 - Prob. 1PSCh. 10 - Prob. 2PSCh. 10 - Prob. 3PSCh. 10 - Prob. 4PSCh. 10 - Prob. 5PSCh. 10 - Prob. 6PSCh. 10 - Prob. 7PSCh. 10 - Prob. 8PSCh. 10 - Prob. 9PSCh. 10 - Prob. 10PSCh. 10 - Prob. 11PSCh. 10 - Prob. 12PSCh. 10 - Prob. 13PSCh. 10 - Prob. 14PSCh. 10 - Prob. 15PS
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