a)
To express: the volume
a)
Answer to Problem 22RE
Explanation of Solution
Given information:
A small shelter for delicate plants is to be constructed of thin plastic material. It will have square ends and a rectangular top and back, with an open bottom and front, as shown in the figure. The total area of the four plastic sides is to be
Calculation:
Consider the diagram:
In this diagram, there are four plastic sides. Two sides are rectangular and two are square.
Area of the four plastic sides is
That is,
Here
To express this equation in terms of
To express the volume
Here,
b)
To draw: a graph of
b)
Explanation of Solution
Given information:
A small shelter for delicate plants is to be constructed of thin plastic material. It will have square ends and a rectangular top and back, with an open bottom and front, as shown in the figure. The total area of the four plastic sides is to be
Calculation:
Consider the diagram:
To draw a graph of a function
c)
To find: the dimensions will maximize the volume of the shelter.
c)
Answer to Problem 22RE
The dimensions of the shelter is
Explanation of Solution
Given information:
A small shelter for delicate plants is to be constructed of thin plastic material. It will have square ends and a rectangular top and back, with an open bottom and front, as shown in the figure. The total area of the four plastic sides is to be
Calculation:
Consider the diagram:
Consider the function
Taking the derivative with respect to
To maximize the volume of the shelter, equate the derivative zero.
To find the value of
Therefore, the dimensions of the shelter is
Chapter 3 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning