A piece of cardboard is 2.8 times as long as it is wide. It is to be made into a box with an open top by cutting 3-inch squares from each corner and folding up the sides. Let x represent the width (in inches) of the original piece of cardboard. a.) Represent the length of the original piece of cardboard in terms of x.b) Give the restrictions on x. What will be the dimensions of the bottom rectangular base of the box? c) Determine a function V that represents the volume of the box in terms of x.d) For what dimensions of the bottom of the box will the volume be 520in.^3? e) Find the values of x if such a box is to have a volume between 600 and 800 in.^3
A piece of cardboard is 2.8 times as long as it is wide. It is to be made into a box with an open top by cutting 3-inch squares from each corner and folding up the sides. Let x represent the width (in inches) of the original piece of cardboard. a.) Represent the length of the original piece of cardboard in terms of x.b) Give the restrictions on x. What will be the dimensions of the bottom rectangular base of the box? c) Determine a function V that represents the volume of the box in terms of x.d) For what dimensions of the bottom of the box will the volume be 520in.^3? e) Find the values of x if such a box is to have a volume between 600 and 800 in.^3
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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A piece of cardboard is 2.8 times as long as it is wide. It is to be made into a box with an open top by cutting 3-inch squares from each corner and folding up the sides. Let x represent the width (in inches) of the original piece of cardboard.
a.) Represent the length of the original piece of cardboard in terms of x.
b) Give the restrictions on x. What will be the dimensions of the bottom rectangular base of the box?
c) Determine a function V that represents the volume of the box in terms of x.
d) For what dimensions of the bottom of the box will the volume be 520in.^3?
e) Find the values of x if such a box is to have a volume between 600 and 800 in.^3
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