A rectangular package sent by a delivery service can have a maximum combined length and girth (perimeter of a cross section) of 120 inches (see figure). (a) Determine which of the following functions gives the volume of the package. (Assume the volume is measured in cubic inches.) O v(x) = 30x2(4 - x) O v(x) = 4x²(30 - x) O V(x) = 30x²(120-x) Ov(x) = 120x2(4 - x) O v(x) = 4x²(120-x) (b) Use a graphing utility to graph the function. V 15 000 10 000 O 5000 5 10 15 20 25 30 X A 15 000 10 000 5000 5 10 15 20 25 30 x
A rectangular package sent by a delivery service can have a maximum combined length and girth (perimeter of a cross section) of 120 inches (see figure). (a) Determine which of the following functions gives the volume of the package. (Assume the volume is measured in cubic inches.) O v(x) = 30x2(4 - x) O v(x) = 4x²(30 - x) O V(x) = 30x²(120-x) Ov(x) = 120x2(4 - x) O v(x) = 4x²(120-x) (b) Use a graphing utility to graph the function. V 15 000 10 000 O 5000 5 10 15 20 25 30 X A 15 000 10 000 5000 5 10 15 20 25 30 x
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:A rectangular package sent by a delivery service can have a maximum combined length and girth (perimeter of a cross section) of 120 inches (see figure).
47°F
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(a) Determine which of the following functions gives the volume of the package. (Assume the volume is measured in cubic inches.)
O V(x) = 30x²(4- x)
4
O V(x) = 4x² (30 - x)
O V(x)= 30x2(120 - x)
O v(x) = 120x²(4 - x)
O V(x) = 4x²(120 - x)
(b) Use a graphing utility to graph the function.
V
15 000
15 000
MEA
10 000
5000
10 000
O
1X1
5000
V
15 000
5
10
15
20
25 30
X
V
O
V
15 000
Q Search
5
10
15 20
25
30
X
Transcribed Image Text:47°F
Sunny
X =
y =
5
X =
X =
V
15 000
10 000
5000
5
Need Help?
10
R
15 20
Read It
3
25
30
30
X
O
V
15 000
10 000
5000
O
Approximate the dimensions of the package that yield a maximum volume. (Round your values to the nearest inch.)
in
in
▬▬
5
(c) Find the values of x such that V = 13,500 cubic inches. (Round your answers to two decimal places.)
X =
in (smallest value)
in
in (largest value)
10
Which of these values is a physical impossibility in the construction of the package? Explain.
O The smallest value is physically impossible because it is greater than the corresponding y value.
15 20 25 30
5 10 15 20
O The smallest value is physically impossible because a length cannot be negative.
The middle value is physically impossible because it is equivalent to the x value that maximizes the volume.
The largest value is physically impossible because it is greater than the corresponding y value.
O The largest value is physically impossible because it is greater than the total volume.
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30
X
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