.Elena is making an open-top box by cutting squares out of the corners of a piece of paper that is 11 inches wide and 17 inches long, and then folding up the sides. If the side lengths of her square cutouts are x inches, then the volume of the box is given by V(x)=x(11-2x)(17-2x). Elena graphs the volume of the box along with the function B(x)=140. YA y = V(x) 200 150 y B(x) 100 + 50 ++++++ 6 7 8 9 10 11 12 13 14 * ++++ -4-3-2-1 2. 5. -50 -100 1. What is a reasonable domain for V(x)? 2. Approximately which value of x will give her a box with the greatest volume? 3. For approximately which values of x is the volume of the box increasing?
.Elena is making an open-top box by cutting squares out of the corners of a piece of paper that is 11 inches wide and 17 inches long, and then folding up the sides. If the side lengths of her square cutouts are x inches, then the volume of the box is given by V(x)=x(11-2x)(17-2x). Elena graphs the volume of the box along with the function B(x)=140. YA y = V(x) 200 150 y B(x) 100 + 50 ++++++ 6 7 8 9 10 11 12 13 14 * ++++ -4-3-2-1 2. 5. -50 -100 1. What is a reasonable domain for V(x)? 2. Approximately which value of x will give her a box with the greatest volume? 3. For approximately which values of x is the volume of the box increasing?
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Transcribed Image Text:.Elena is making an open-top box by cutting squares out of the corners of a
piece of paper that is 11 inches wide and 17 inches long, and then folding up
the sides. If the side lengths of her square cutouts are x inches, then the volume
of the box is given by
V(x)=x(11-2x)(17-2x).
Elena graphs the volume of the box along with the function B(x)=140.
YA
y V(x)
200
150
y B(x)
100 +
50
++++
7 89 10 11 12 13 14 X
++++
-4-3-2-1
2.
-50
-100
1. What is a reasonable domain for V(x)?
2. Approximately which value of x will give her a box with the greatest volume?
3. For approximately which values of x is the volume of the box increasing?
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