Minimizing Surface Area United Parcel Service has contracted you to design a closed box with a square base that has a volume of 10,000 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 a closed box with a square base that has a volume of 10,000 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 a closed box with a square base that has a volume of 10,000 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?
According to Newton's law of universal gravitation, the force F between two bodies of constant mass
GmM
m and M is given by the formula F =
, where G is the gravitational constant and d is the
d²
distance between the bodies.
a. Suppose that G, m, and M are constants. Find the rate of change of force F with respect to
distance d.
F' (d)
2GmM
b. Find the rate of change of force F with gravitational constant G = 6.67 × 10-¹¹ Nm²/kg², on
two bodies 5 meters apart, each with a mass of 250 kilograms. Answer in scientific notation,
rounding to 2 decimal places.
-6.67x10
N/m syntax incomplete.
Chapter 4 Solutions
Precalculus Enhanced with Graphing Utilities (7th Edition)
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