A page that is x inches wide and y inches high contains 34 square inches of print. The margins at the top and bottom are 2 inches deep and the margins on each side are 1 inch wide. (a) Show that the total area A of the page is given by A = 2x(2x + 13) x − 2 We know that A = xy and that x − y − = 34 y = Hence, A = x = (b) Determine the domain of the function based on the physical constraints of the problem. (Enter your answer using interval notation.) (c) Use a graphing utility to graph the area function and approximate the page size such that the minimum amount of paper will be used. Verify your answer numerically using the table feature of the graphing utility. (Round your answers to two decimal places.) x = in y = in
A page that is x inches wide and y inches high contains 34 square inches of print. The margins at the top and bottom are 2 inches deep and the margins on each side are 1 inch wide. (a) Show that the total area A of the page is given by A = 2x(2x + 13) x − 2 We know that A = xy and that x − y − = 34 y = Hence, A = x = (b) Determine the domain of the function based on the physical constraints of the problem. (Enter your answer using interval notation.) (c) Use a graphing utility to graph the area function and approximate the page size such that the minimum amount of paper will be used. Verify your answer numerically using the table feature of the graphing utility. (Round your answers to two decimal places.) x = in y = in
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter4: Polynomial And Rational Functions
Section4.1: Quadratic Functions
Problem 6SC: A company that makes and sells baseball caps has found that the total monthly cost C in dollars of...
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A page that is x inches wide and y inches high contains 34 square inches of print. The margins at the top and bottom are 2 inches deep and the margins on each side are 1 inch wide.
(a) Show that the total area A of the page is given by
We know that
Hence,
(b) Determine the domain of the function based on the physical constraints of the problem. (Enter your answer using interval notation.)
(c) Use a graphing utility to graph the area function and approximate the page size such that the minimum amount of paper will be used. Verify your answer numerically using the table feature of the graphing utility. (Round your answers to two decimal places.)
A =
| 2x(2x + 13) |
| x − 2 |
A = xy
and that|
|
= | 34 | ||||
| y | = |
|
Hence,
| A | = | x
|
||
| = |
|
(b) Determine the domain of the function based on the physical constraints of the problem. (Enter your answer using interval notation.)
(c) Use a graphing utility to graph the area function and approximate the page size such that the minimum amount of paper will be used. Verify your answer numerically using the table feature of the graphing utility. (Round your answers to two decimal places.)
| x = | in |
| y = | in |
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