Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)

4th Edition

ISBN: 9780133178579

Author: Ross L. Finney

Publisher: PEARSON

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Question

Chapter 5.4, Problem 19E

To determine

Write a formula for the volume of the box.

Expert Solution

Answer to Problem 19E

The volume of the box is 8x3−168x2+864x

Explanation of Solution

Calculation:

The height of the box is 2x and the dimensions of the base are 18−2x and 24−2x .

Volume of box is

V=lwh =(18−2x)(24−2x)(2x) =(432−48x−36x+4x2)(2x) =8x3−168x2+864x

Thus, the volume of the box is 8x3−168x2+864x

To determine

Find the domain of V .

Expert Solution

Answer to Problem 19E

Explanation of Solution

Calculation:

volume from part (a)

V=2x(24−2x)(18−2x)

Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy), Chapter 5.4, Problem 19E , additional homework tip 1

Domain is 0<x<9

To determine

Find the maximum volume and value of x .

Expert Solution

Answer to Problem 19E

Explanation of Solution

Calculation:

Examine the graph; the maximum occurs at about x=3.4 with volume slightly over 1300

Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy), Chapter 5.4, Problem 19E , additional homework tip 2

Thus, the value is x≈3.4inches, volume a bit over1300in3

To determine

Support the result in part (c) graphically.

Expert Solution

Answer to Problem 19E

Explanation of Solution

Calculation:

Multiply it out to avoid product rule before find V′

V=(18−2x)(24−2x)(2x) =4x(12−x)(18−2x) =8(x3−21x2+108x)V′=8(3x2−14x+36) =24(x2−14x+36)Find whereV′=00=(x2−14x+36)x=−b±b2−4ac2a =−(−14)±(−14)2−4(1)(36)2(1) =14±4⋅132(1) =14±2132(1) =7+13≈10.61 =7−13≈3.39

Thus, the values are 7−13 and volume ≈1309.95in3

To determine

Find value of x that yields a volume of 1120in3 .

Expert Solution

Answer to Problem 19E

Explanation of Solution

Calculation:

Multiply it out to avoid product rule before find V′

V=(36−4x)∗(24−2x)∗x1120=2(18−2x)∗(12−x)∗x280=216x−24x2−18x2+2x3280=2x3−42x2+216xx3−21x2+108x−140=0 cancel 2 from bothsides(x−14)(x−5)(x−2)=0 x=2.5

To determine

Write a paragraph describe the issues that arise in part (b)

Expert Solution

Answer to Problem 19E

Explanation of Solution

Calculation:

Must be careful to restrict the size of x so that one square on a corner does not overlap a square on another corner. If they did overlap then there would be miss sides for the box or nothing left.

Chapter 5.4, Problem 18E

Chapter 5.4, Problem 20E

Chapter 5 Solutions

Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)

Ch. 5.1 - Prob. 1QR Ch. 5.1 - Prob. 2QR Ch. 5.1 - Prob. 3QR Ch. 5.1 - Prob. 4QR Ch. 5.1 - Prob. 5QR Ch. 5.1 - Prob. 6QR Ch. 5.1 - Prob. 7QR Ch. 5.1 - Prob. 8QR Ch. 5.1 - Prob. 9QR Ch. 5.1 - Prob. 10QR

Ch. 5.1 - Prob. 11QR Ch. 5.1 - Prob. 12QR Ch. 5.1 - Prob. 1E Ch. 5.1 - Prob. 2E Ch. 5.1 - Prob. 3E Ch. 5.1 - Prob. 4E Ch. 5.1 - Prob. 5E Ch. 5.1 - Prob. 6E Ch. 5.1 - Prob. 7E Ch. 5.1 - Prob. 8E Ch. 5.1 - Prob. 9E Ch. 5.1 - Prob. 10E Ch. 5.1 - Prob. 11E Ch. 5.1 - Prob. 12E Ch. 5.1 - Prob. 13E Ch. 5.1 - Prob. 14E Ch. 5.1 - Prob. 15E Ch. 5.1 - Prob. 16E Ch. 5.1 - Prob. 17E Ch. 5.1 - Prob. 18E Ch. 5.1 - Prob. 19E Ch. 5.1 - Prob. 20E Ch. 5.1 - Prob. 21E Ch. 5.1 - Prob. 22E Ch. 5.1 - Prob. 23E Ch. 5.1 - Prob. 24E Ch. 5.1 - Prob. 25E Ch. 5.1 - Prob. 26E Ch. 5.1 - Prob. 27E Ch. 5.1 - Prob. 28E Ch. 5.1 - Prob. 29E Ch. 5.1 - Prob. 30E Ch. 5.1 - Prob. 31E Ch. 5.1 - Prob. 32E Ch. 5.1 - Prob. 33E Ch. 5.1 - Prob. 34E Ch. 5.1 - Prob. 35E Ch. 5.1 - Prob. 36E Ch. 5.1 - Prob. 37E Ch. 5.1 - Prob. 38E Ch. 5.1 - Prob. 39E Ch. 5.1 - Prob. 40E Ch. 5.1 - Prob. 41E Ch. 5.1 - Prob. 42E Ch. 5.1 - Prob. 43E Ch. 5.1 - Prob. 44E Ch. 5.1 - Prob. 45E Ch. 5.1 - Prob. 46E Ch. 5.1 - Prob. 47E Ch. 5.1 - Prob. 48E Ch. 5.1 - 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