Minimizing Surface Area United Parcel Service has contracted you to design an open box with a square base that has a volume of 5000 cubic inches. See the illustration. (a) Express the surface area S of the box as a function of x . (b) Using a graphing utility, graph the function found in part (a). (c) What is the minimum amount of cardboard that can be used to construct the box? (d) What are the dimensions of the box that minimize the surface area? (e) Why might UPS be interested in designing a box that minimizes the surface area?
Minimizing Surface Area United Parcel Service has contracted you to design an open box with a square base that has a volume of 5000 cubic inches. See the illustration. (a) Express the surface area S of the box as a function of x . (b) Using a graphing utility, graph the function found in part (a). (c) What is the minimum amount of cardboard that can be used to construct the box? (d) What are the dimensions of the box that minimize the surface area? (e) Why might UPS be interested in designing a box that minimizes the surface area?
Solution Summary: The author explains that UPS would like to design a box that has the largest volume with the least amount of surface area.
Minimizing Surface Area United Parcel Service has contracted you to design an open box with a square base that has a volume of 5000 cubic inches. See the illustration.
(a) Express the surface area
of the box as a function of
.
(b) Using a graphing utility, graph the function found in part (a).
(c) What is the minimum amount of cardboard that can be used to construct the box?
(d) What are the dimensions of the box that minimize the surface area?
(e) Why might UPS be interested in designing a box that minimizes the surface area?
The fox population in a certain region has an annual growth rate of 8 percent per year. It is estimated that the
population in the year 2000 was 22600.
(a) Find a function that models the population t years after 2000 (t = 0 for 2000).
Your answer is P(t)
=
(b) Use the function from part (a) to estimate the fox population in the year 2008.
Your answer is (the answer should be an integer)
r
The solutions are 1
where x1 x2-
● Question 11
Solve: x 54
Give your answer as an interval.
Question 12
Chapter 4 Solutions
Precalculus Enhanced with Graphing Utilities Plus MyLab Math with Pearson eText - Access Card Package (7th Edition) (Sullivan & Sullivan Precalculus Titles)
Elementary Statistics: Picturing the World (7th Edition)
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