(a)
Draw a diagram that illustrates the problem
(a)
Explanation of Solution
Given:
A page that is
The diagram for the problem given is as shown:
(b)
To show: Total area
(b)
Explanation of Solution
Given information:
A page that is
Formula used:
Area of a rectangle
Proof:
Consider the figure shown above,
Total area of page (
Print area
Taking y as a subject,
Substituting Equation 2 in Equation 1:
Hence proved.
(c)
The domain of the function
(c)
Explanation of Solution
Given:
Concept used:
Domain of a function: It refers to the values that the independent variable (
For example:
In this equation,
Hence,
Calculation:
Width of the page (
Also, total area of a page (
As
Further, for
Hence the domain of the function
Conclusion:
The domain of the function
(d)
To graph:
Find the approximate page size such that the minimum amount of paper will be used.
(d)
Explanation of Solution
Given information:
Graph:
In order to plot the graph, various data points need to be plotted which are then joined to draw a smooth graph.The data points are shown in the table below.
Width (inches) | Total Area (square inches) |
5 | 170 |
10 | 90 |
15 | 100.91 |
20 | 117.5 |
25 | 135.71 |
30 | 154.615 |
Here,
Interpretation:
To use minimum amount of paper, the total area
From the graph, the point having smallest value of
Substituting
Chapter 2 Solutions
Precalculus with Limits: A Graphing Approach
- 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