A box is formed by cutting squares from the four corners of a 11"-wide by 13"- long sheet of paper and folding up the sides.

Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter9: Polynomial And Rational Functions
Section9.4: Graphing Polynomial Functions
Problem 43PS
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A box is formed by cutting squares from the four corners of a 11"-wide by 13"-
long sheet of paper and folding up the sides.
Let x represent the length of the side of the square cutout (in inches), let w
represent the width of the base of the box (in inches), let l represent the length of
the base of the box (in inches), let h represent the height of the box (in inches), and
let V represent the volume of the box (in cubic inches).
Complete the table of values below. If an entry cannot be completed, enter "DNE".
h
V
11
13
0.5
11.5
13.5
0.5
.5
2.25
11
5.5
11
13
5.5
Transcribed Image Text:A box is formed by cutting squares from the four corners of a 11"-wide by 13"- long sheet of paper and folding up the sides. Let x represent the length of the side of the square cutout (in inches), let w represent the width of the base of the box (in inches), let l represent the length of the base of the box (in inches), let h represent the height of the box (in inches), and let V represent the volume of the box (in cubic inches). Complete the table of values below. If an entry cannot be completed, enter "DNE". h V 11 13 0.5 11.5 13.5 0.5 .5 2.25 11 5.5 11 13 5.5
A box is formed by cutting squares from the four corners of a sheet of paper and folding up the
sides. The graph below shows how the volume of the box in cubic inches, V, is related to the
length of the side of the square cutout in inches, x.
V
(1.3, 36.61)
a. The point (1, 35) is on the graph. This means that when the volume of the box is 1.3
* cubic inches, the cutout length is 36.61
* inches.
b. When the cutout length is 2.5 inches, the volume of the box is 20 cubic inches. This means
that the point 40
|* is on the graph above.
c. Suppose the largest possible cutout length is 3.5 inches. Over what interval of x does the
volume of the box decrease as the cutout length gets larger? (Enter your answer as an
interval.)
80
Preview
Transcribed Image Text:A box is formed by cutting squares from the four corners of a sheet of paper and folding up the sides. The graph below shows how the volume of the box in cubic inches, V, is related to the length of the side of the square cutout in inches, x. V (1.3, 36.61) a. The point (1, 35) is on the graph. This means that when the volume of the box is 1.3 * cubic inches, the cutout length is 36.61 * inches. b. When the cutout length is 2.5 inches, the volume of the box is 20 cubic inches. This means that the point 40 |* is on the graph above. c. Suppose the largest possible cutout length is 3.5 inches. Over what interval of x does the volume of the box decrease as the cutout length gets larger? (Enter your answer as an interval.) 80 Preview
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