PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)

8th Edition

ISBN: 9781337904285

Author: Larson

Publisher: CENGAGE L

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Question

Chapter 1.2, Problem 75E

(a)

To determine

To Find: The maximum value.

(a)

Expert Solution

Answer to Problem 75E

Maximum volume is $1024$

Explanation of Solution

Given: An open box of maximum value is to be made from a square piece of material, $24$ cm on a side, by cutting equal squares from the corners and turning up the sides.

PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS), Chapter 1.2, Problem 75E , additional homework tip 1

The table shows the volume of the box for various heights $x$ .

PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS), Chapter 1.2, Problem 75E , additional homework tip 2

The maximum value from the table is $1024$ , corresponding to $x=4$

(b)

To determine

To Plot: The plot the points from the table. Does the relation defined by the ordered pairs represent $V$ as a function of $x$ .

(b)

Expert Solution

Answer to Problem 75E

Yes the relation is a function.

Explanation of Solution

Given: An open box of maximum value is to be made from a square piece of material, $24$ cm on a side, by cutting equal squares from the corners and turning up the sides.

PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS), Chapter 1.2, Problem 75E , additional homework tip 3

The table shows the volume of the box for various heights $x$ .

PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS), Chapter 1.2, Problem 75E , additional homework tip 4

The graph by plotting the points is shown below

PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS), Chapter 1.2, Problem 75E , additional homework tip 5

The relation is a function because for every height there is only one volume.

(c)

To determine

To Find: If $V$ as a function of $x$ , write the function and determine the domain.

(c)

Expert Solution

Answer to Problem 75E

$V=4x(12−x)2$ , $0<x<12$

Explanation of Solution

Given: An open box of maximum value is to be made from a square piece of material, $24$ cm on a side, by cutting equal squares from the corners and turning up the sides.

PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS), Chapter 1.2, Problem 75E , additional homework tip 6

$V=l×w×hV=(24−2x)(24−2x)xV=x(24−2x)2V=4x(12−x)2$

Thus the function is $V=4x(12−x)2$

And

Domain: $0<x<12$

(c)

To determine

To Find: use the graphing utility to plot the points from the table in part (a) with the function from part (c). How closely does the function represent the data?

(c)

Expert Solution

Answer to Problem 75E

The function is a good fit.

Explanation of Solution

Given: An open box of maximum value is to be made from a square piece of material, $24$ cm on a side, by cutting equal squares from the corners and turning up the sides.

PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS), Chapter 1.2, Problem 75E , additional homework tip 7

PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS), Chapter 1.2, Problem 75E , additional homework tip 8

The graph from the table is

PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS), Chapter 1.2, Problem 75E , additional homework tip 9

Function: $V=4x(12−x)2$

The function is good fit.

Chapter 1.2, Problem 74E

Chapter 1.2, Problem 76E

Chapter 1 Solutions

PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)

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Prob. 128E Ch. 1.6 - Prob. 129E Ch. 1.6 - Prob. 130E Ch. 1.6 - Prob. 131E Ch. 1.6 - Prob. 132E Ch. 1.6 - Prob. 133E Ch. 1.6 - Prob. 134E Ch. 1.6 - Prob. 135E Ch. 1.6 - Prob. 136E Ch. 1.6 - Prob. 137E Ch. 1.6 - Prob. 138E Ch. 1.6 - Prob. 139E Ch. 1.6 - Prob. 140E Ch. 1.6 - Prob. 141E Ch. 1.6 - Prob. 142E Ch. 1.6 - Prob. 143E Ch. 1.6 - Prob. 144E Ch. 1.7 - Prob. 1E Ch. 1.7 - Prob. 2E Ch. 1.7 - Prob. 3E Ch. 1.7 - Prob. 4E Ch. 1.7 - Prob. 5E Ch. 1.7 - Prob. 6E Ch. 1.7 - Prob. 7E Ch. 1.7 - Prob. 8E Ch. 1.7 - Prob. 9E Ch. 1.7 - Prob. 10E Ch. 1.7 - Prob. 11E Ch. 1.7 - Prob. 12E Ch. 1.7 - Prob. 13E Ch. 1.7 - Prob. 14E Ch. 1.7 - Prob. 15E Ch. 1.7 - Prob. 16E Ch. 1.7 - Prob. 17E Ch. 1.7 - Prob. 18E Ch. 1.7 - Prob. 19E Ch. 1.7 - Prob. 20E Ch. 1.7 - Prob. 21E Ch. 1.7 - Prob. 22E Ch. 1.7 - Prob. 23E Ch. 1.7 - Prob. 24E Ch. 1.7 - Prob. 25E Ch. 1.7 - Prob. 26E Ch. 1.7 - Prob. 27E Ch. 1.7 - Prob. 28E Ch. 1.7 - Prob. 29E Ch. 1.7 - Prob. 30E Ch. 1.7 - Prob. 31E Ch. 1.7 - Prob. 32E Ch. 1.7 - Prob. 33E Ch. 1.7 - Prob. 34E Ch. 1 - Prob. 1CR Ch. 1 - Prob. 2CR Ch. 1 - Prob. 3CR Ch. 1 - Prob. 4CR Ch. 1 - Prob. 5CR Ch. 1 - Prob. 6CR Ch. 1 - Prob. 7CR Ch. 1 - Prob. 8CR Ch. 1 - Prob. 9CR Ch. 1 - Prob. 10CR Ch. 1 - Prob. 11CR Ch. 1 - Prob. 12CR Ch. 1 - Prob. 13CR Ch. 1 - Prob. 14CR Ch. 1 - Prob. 15CR Ch. 1 - Prob. 16CR Ch. 1 - Prob. 17CR Ch. 1 - Prob. 18CR Ch. 1 - Prob. 19CR Ch. 1 - Prob. 20CR Ch. 1 - Prob. 21CR Ch. 1 - Prob. 22CR Ch. 1 - Prob. 23CR Ch. 1 - Prob. 24CR Ch. 1 - Prob. 25CR Ch. 1 - Prob. 26CR Ch. 1 - Prob. 27CR Ch. 1 - Prob. 28CR Ch. 1 - Prob. 29CR Ch. 1 - Prob. 30CR Ch. 1 - Prob. 31CR Ch. 1 - Prob. 32CR Ch. 1 - Prob. 33CR Ch. 1 - Prob. 34CR Ch. 1 - Prob. 35CR Ch. 1 - Prob. 36CR Ch. 1 - Prob. 37CR Ch. 1 - Prob. 38CR Ch. 1 - Prob. 39CR Ch. 1 - Prob. 40CR Ch. 1 - Prob. 41CR Ch. 1 - Prob. 42CR Ch. 1 - Prob. 43CR Ch. 1 - Prob. 44CR Ch. 1 - Prob. 45CR Ch. 1 - Prob. 46CR Ch. 1 - Prob. 47CR Ch. 1 - Prob. 48CR Ch. 1 - Prob. 49CR Ch. 1 - Prob. 50CR Ch. 1 - Prob. 51CR Ch. 1 - Prob. 52CR Ch. 1 - Prob. 53CR Ch. 1 - Prob. 54CR Ch. 1 - Prob. 55CR Ch. 1 - Prob. 56CR Ch. 1 - Prob. 57CR Ch. 1 - Prob. 58CR Ch. 1 - Prob. 59CR Ch. 1 - Prob. 60CR Ch. 1 - Prob. 61CR Ch. 1 - Prob. 62CR Ch. 1 - Prob. 63CR Ch. 1 - Prob. 64CR Ch. 1 - Prob. 65CR Ch. 1 - Prob. 66CR Ch. 1 - Prob. 67CR Ch. 1 - Prob. 68CR Ch. 1 - Prob. 69CR Ch. 1 - Prob. 70CR Ch. 1 - Prob. 71CR Ch. 1 - Prob. 72CR Ch. 1 - Prob. 73CR Ch. 1 - Prob. 74CR Ch. 1 - Prob. 75CR Ch. 1 - Prob. 76CR Ch. 1 - Prob. 77CR Ch. 1 - Prob. 78CR Ch. 1 - Prob. 79CR Ch. 1 - Prob. 80CR Ch. 1 - Prob. 81CR Ch. 1 - Prob. 82CR Ch. 1 - Prob. 83CR Ch. 1 - Prob. 84CR Ch. 1 - Prob. 85CR Ch. 1 - Prob. 86CR Ch. 1 - Prob. 87CR Ch. 1 - Prob. 88CR Ch. 1 - Prob. 89CR Ch. 1 - Prob. 90CR Ch. 1 - Prob. 91CR Ch. 1 - Prob. 92CR Ch. 1 - Prob. 93CR Ch. 1 - Prob. 94CR Ch. 1 - Prob. 95CR Ch. 1 - Prob. 96CR Ch. 1 - Prob. 97CR Ch. 1 - Prob. 98CR Ch. 1 - Prob. 99CR Ch. 1 - Prob. 100CR Ch. 1 - Prob. 101CR Ch. 1 - Prob. 102CR Ch. 1 - Prob. 103CR Ch. 1 - Prob. 104CR Ch. 1 - Prob. 105CR Ch. 1 - Prob. 106CR Ch. 1 - Prob. 107CR Ch. 1 - Prob. 108CR Ch. 1 - Prob. 109CR Ch. 1 - Prob. 110CR Ch. 1 - Prob. 1CT Ch. 1 - Prob. 2CT Ch. 1 - Prob. 3CT Ch. 1 - Prob. 4CT Ch. 1 - Prob. 5CT Ch. 1 - Prob. 6CT Ch. 1 - Prob. 7CT Ch. 1 - Prob. 8CT Ch. 1 - Prob. 9CT Ch. 1 - Prob. 10CT Ch. 1 - Prob. 11CT Ch. 1 - Prob. 12CT Ch. 1 - Prob. 13CT Ch. 1 - Prob. 14CT Ch. 1 - Prob. 15CT Ch. 1 - Prob. 16CT Ch. 1 - Prob. 17CT Ch. 1 - Prob. 18CT Ch. 1 - Prob. 19CT Ch. 1 - Prob. 20CT

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The maximum value.

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To Find: The maximum value.

Answer to Problem 75E

Explanation of Solution

To Plot: The plot the points from the table. Does the relation defined by the ordered pairs represent V<m:math><m:mi>V</m:mi></m:math> as a function of x<m:math><m:mi>x</m:mi></m:math> .

Answer to Problem 75E

Explanation of Solution

To Find: If V<m:math><m:mi>V</m:mi></m:math> as a function of x<m:math><m:mi>x</m:mi></m:math> , write the function and determine the domain.

Answer to Problem 75E

Explanation of Solution

To Find: use the graphing utility to plot the points from the table in part (a) with the function from part (c). How closely does the function represent the data?

Answer to Problem 75E

Explanation of Solution

Chapter 1 Solutions

To Plot: The plot the points from the table. Does the relation defined by the ordered pairs represent $V$ as a function of $x$ .

To Find: If $V$ as a function of $x$ , write the function and determine the domain.