Solution Found!

Precalculus with Limits | 3rd Edition | ISBN: 9781133947202 | Authors: Ron Larson
Change Question

Numerical and Graphical Analysis You plan to construct an open box from a square piece

Chapter 2, Problem 97

(choose chapter or problem)

Get Unlimited Answers
QUESTION:

Numerical and Graphical Analysis You plan to construct an open box from a square piece of material, 36 inches on a side, by cutting equal squares with sides of length from the corners and turning up the sides (see figure). (a) Write a function that represents the volume of the box. (b) Determine the domain of the function (c) Use a graphing utility to construct a table that shows the box heights and the corresponding volumes Use the table to estimate the dimensions that will produce a maximum volume. (d) Use the graphing utility to graph and use the graph to estimate the value of for which is a maximum. Compare your result with that of part (c).

Questions & Answers

QUESTION:

Numerical and Graphical Analysis You plan to construct an open box from a square piece of material, 36 inches on a side, by cutting equal squares with sides of length from the corners and turning up the sides (see figure). (a) Write a function that represents the volume of the box. (b) Determine the domain of the function (c) Use a graphing utility to construct a table that shows the box heights and the corresponding volumes Use the table to estimate the dimensions that will produce a maximum volume. (d) Use the graphing utility to graph and use the graph to estimate the value of for which is a maximum. Compare your result with that of part (c).

ANSWER:

Step 1 of 4

An open box is constructed from a square piece of material, 36 inches on a side, by cutting equal squares with sides of length   from the corners and turning up the sides.

The length of the box is inches and the width of the box is   inches.

Since, the open box is constructed from a square piece of materials, therefore, height of the ox is also   inches.

Thus, the volume of the box is

                                                   

Hence, the volume of the box can be expressed by the function  

                                                   

 

Add to cart

Study Tools You Might Need

Chapter: 2 Problem: 48P

Organic Chemistry 7
Which is a stronger base? a. \(H S^{-} \text {or } H O^{-}\) c. \(\mathrm{CH}_{3} \mathrm{OH} \text { or } \mathrm{CH}_{3} \mathrm{O}^{-}\) e. \(\mathrm{CH}_{3} \mathrm{COO}^{-} \text {or } \mathrm{CF}_{3} \mathrm{COO}^{-}\) b. \(\mathrm{CH}_{3} \mathrm{O}^{-} \text {o

Chapter: 0 Problem: 5

Biology 8
The reactivity of an atom arises from a. the average distance of the outermost electron shell from the nucleus. b. the existence of unpaired electrons in the valence shell. c. the sum ofthe potential energies of all the electron shells. d. the potential energy of the valence shell. e. the energy diff

Chapter: 0 Problem: 7.2

Biology 8
Aquaporins exclude passage of hydronium ions (H30+). But recent research has revealed a role for some aquaporins in fat metabolism, in which they allow passage of glycerol, a three-carbon alcohol (see Figure 5.11), as well as H20. Since H30+ is much closer in size to water than is glycerol, what do y

Chapter: 1 Problem: 10

Campbell Biology in Focus - Standalone book 1
A typical prokaryotic cell has about 3,000 genes in its DNA, while a human cell has about 20,500 genes. About 1,000 of these genes are present in both types of cells. Based on your understanding of evolution, explain how such different organisms could have this same subset of genes. What sorts of fun

Chapter: 23 Problem: 2

Campbell Biology in Focus - Standalone book 1
Adaptive radiations can be a direct consequence of four of the following five factors. Select the exception. a. vacant ecological niches b. genetic drift c. colonization of an isolated region that contains suitable habitat and few competitor species d. evolutionary innovation e. an adaptive radiation

Chapter: 27 Problem: 9

Principles of Economics 1
What is the double-coincidence of wants?

Chapter: 5 Problem: 6

Psychology 5
Which explanation of dreams proposes that they are produced when the mind attempts to make sense of random neural activity that occurs in the brain during sleep? a. Freuds psychoanalytic theory b. the activationsynthesis model c. the cognitive unconscious model d. the manifest content framework

Chapter: 53 Problem: 7

Biology: The Dynamic Science 5
The change in the species composition of a terrestrial community from bare and lifeless rock to climax vegetation is called: a. disturbance. b. competition. c. secondary succession. d. primary succession. e. facilitation.

Not The Solution You Need? Search for Your Answer Here:

×

Login

Login or Sign up for access to all of our study tools and educational content!

Forgot password?
Register Now

×

Register

Sign up for access to all content on our site!

Or login if you already have an account

×

Reset password

If you have an active account we’ll send you an e-mail for password recovery

Or login if you have your password back