Precalculus with Limits
Precalculus with Limits
3rd Edition
ISBN: 9781133947202
Author: Ron Larson
Publisher: Cengage Learning
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Chapter 10.4, Problem 47E

a.

To determine

To find:The equation that models the curve sides of the sculpture.

a.

Expert Solution
Check Mark

Answer to Problem 47E

The equation of the curved sides of the sculpture is x21−3y2169=1 .

Explanation of Solution

Given information:

The given sculpture of hyperbolic cross section is shown in figure (1).

  Precalculus with Limits, Chapter 10.4, Problem 47E , additional homework tip 1

Figure (1)

Calculation:

The curved part of sculpture is having the shape of a hyperbola.

From the figure (1), the vertices of the hyperbola are (−1,0) and (1,0) .

And the transverse axis is horizontal, and the hyperbola passes through (2,13) .

The equation of the hyperbola in the given as.

  (x−h)2a2−(y−k)2b2=1

The center of the hyperbola is given by the midpoint of the line segment joining the vertices.

Calculate the midpoint between the (−1,0) and (1,0) .

  ((−1)+12,0+02)=(0,0)

The center is at (0,0) .

Calculate the value of a for the vertex (1,0) and (0,0) .

  a=(1−0)2+(0+0)2=1

The hyperbola passes through the point (2,13) .

Substitute value of a for calculate the value of b .

  (2−0)212−(13−0)2b2=1169b2=3b=133

Calculate the standard form of the hyperbola.

  (x−0)212−(y−0)2(133)2=1x21−3y2169=1

Therefore, the equation of the curved sides of the sculptureis x21−3y2169=1 .

b.

To determine

To find: The width of the sculpture at height of the 5 feet .

b.

Expert Solution
Check Mark

Answer to Problem 47E

The width of the sculpture at height of the 5 feet is 2.4 feet .

Explanation of Solution

Given information:

Each unit is equal to 1 foot .

The given sculpture of hyperbolic cross section is shown in figure (1).

  Precalculus with Limits, Chapter 10.4, Problem 47E , additional homework tip 2

Figure (1)

Calculation:

Let b be the width.

Calculate the x− coordinate by using the equation of the curved, with y - coordinate as 5 units.

  x31−3×52169=1x2=244169x=1.2

The sculpture is symmetric about y - axis the width b is given as.

  b=2x=2×1.2=2.4

Therefore, the width of the sculpture at height of the 5 feet is 2.4 feet .

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Chapter 10.4, Problem 46E
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Chapter 10.4, Problem 48E

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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