Concept explainers
a.
To write: A polynomial function for the volume of the box.
The polynomial function for the volume of the box would be
Given information:
You want to make an open box from a piece of cardboard to hold your school supplies. The original piece of cardboard is 20 inches by 30 inches.
Formula used:
Volume of rectangular box is length times width times the height of the box.
Calculation:
The box will be formed by making the cuts of
The length of the box would be
Therefore, the polynomial function for the volume of the box would be
b.
To graph: The function in part (a).
Given information:
You want to make an open box from a piece of cardboard to hold your school supplies. The original piece of cardboard is 20 inches by 30 inches.
Formula used:
Volume of rectangular box is length times width times the height of the box.
Calculation:
Upon graphing the volume function, the required graph would like as shown below:
c.
To determine: What are the dimensions of the box with the maximum volume?
The dimensions of the box will be about
Given information:
You want to make an open box from a piece of cardboard to hold your school supplies. The original piece of cardboard is 20 inches by 30 inches.
Calculation:
It is visible from the graph in part (a) that the maximum volume is about
Length of the box would be:
Width of the box would be:
Therefore, the dimensions of the box will be about
d.
To determine: What is the maximum volume of the box?
The maximum volume of the box will be approximately
Given information:
You want to make an open box from a piece of cardboard to hold your school supplies. The original piece of cardboard is 20 inches by 30 inches.
Formula used:
Volume of rectangular box is length times width times the height of the box.
Calculation:
The volume would be the maximum when
Therefore, the maximum volume of the box will be approximately
Chapter 2 Solutions
Holt Mcdougal Larson Algebra 2: Student Edition 2012
- Algebra and Trigonometry (6th Edition)AlgebraISBN:9780134463216Author:Robert F. BlitzerPublisher:PEARSONContemporary Abstract AlgebraAlgebraISBN:9781305657960Author:Joseph GallianPublisher:Cengage LearningLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
- Algebra And Trigonometry (11th Edition)AlgebraISBN:9780135163078Author:Michael SullivanPublisher:PEARSONIntroduction to Linear Algebra, Fifth EditionAlgebraISBN:9780980232776Author:Gilbert StrangPublisher:Wellesley-Cambridge PressCollege Algebra (Collegiate Math)AlgebraISBN:9780077836344Author:Julie Miller, Donna GerkenPublisher:McGraw-Hill Education