Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)
Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)
4th Edition
ISBN: 9780133178579
Author: Ross L. Finney
Publisher: PEARSON
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Concept explainers

Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear re…
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
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Chapter 5, Problem 51RE

a.

To determine

To write a formula V(x) for the volume of box.

a.

Expert Solution
Check Mark

Answer to Problem 51RE

The required formula is V(x)=2x3−25x2+75x .

Explanation of Solution

Given information: A piece of cardboard measures 10 in. by 15 in. Two equal sides are removed from the corners of a 15 in. sides.

  Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy), Chapter 5, Problem 51RE , additional homework tip 1

Calculation: The required formula is obtained as,

Refer to the diagram exercise 18 of the sction 4.4, but imagine the vertical side as 15” and the horizontal side as 10” .

The length of box be 15−2x .

The width of box be 10−2x2=5−x .

The height of box be x .

  V(x)=x(15−2x)(5−x)        =2x3−25x2+75x

Hence, the required formula is V(x)=2x3−25x2+75x .

b.

To determine

To find the domain of V for the problem situation and graph V over this domain.

b.

Expert Solution
Check Mark

Answer to Problem 51RE

The domain is: 0 < x< 5 and graph below,

  Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy), Chapter 5, Problem 51RE , additional homework tip 2

Explanation of Solution

Given information: A piece of cardboard measures 10 in. by 15 in. Two equal sides are removed from the corners of a 15 in. sides.

  Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy), Chapter 5, Problem 51RE , additional homework tip 3

Calculation: The required solution is obtained as,

  x must be > 0 since you have to cut something. x must be less than the smaller of 15/2 = 7.5 and 10/2 = 5, so that you don’t cut away more material than you actually have.

Hence, the domain is: 0 < x< 5 and graph below,

  Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy), Chapter 5, Problem 51RE , additional homework tip 4

c.

To determine

To find the maximum volume and the value of x that gives it, by using a graphical method.

c.

Expert Solution
Check Mark

Answer to Problem 51RE

The maximum is at approximately x=1.96 and V=66.02 .

Explanation of Solution

Given information: A piece of cardboard measures 10 in. by 15 in. Two equal sides are removed from the corners of a 15 in. sides.

  Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy), Chapter 5, Problem 51RE , additional homework tip 5

Calculation: The required solution is obtained as,

From the graph, the maximum is at approximately x=1.96 and V=66.02 .

d.

To determine

To confirm your result in part (C) analytically.

d.

Expert Solution
Check Mark

Answer to Problem 51RE

The required solution is 1.96.

Explanation of Solution

Given information: A piece of cardboard measures 10 in. by 15 in. Two equal sides are removed from the corners of a 15 in. sides.

  Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy), Chapter 5, Problem 51RE , additional homework tip 6

Calculation: The required solution is obtained as,

Find V’ and where it is = 0.

  V'(x)=6x2−50x+75       0=6x2−50x+75       x=−b±b2−4ac2a        =−(−50)±(−50)2−4(6)(75)2(6)        =50±70012        =50±10712        =25±576        =25+576≈6.37        =25−576≈1.96

Hence the required solution is 1.96.

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Chapter 5, Problem 52RE

Chapter 5 Solutions

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

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