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A square of x inches is cut out of each corner of a 8x11 piece of cardboard and the sides are folded up to form an open-top box. Complete the following: a) The dimensions of the box, in terms of x. (length, width, height) b) Write a function V(x) in standard form to represent the volume of the box. c) Find the domain and range of V(x). What are the zeros? d) e) Graph the function- only on the interval of the domain. f) Use the graph over the domain to find the maximum volume your box could hold. g) What size cut-outs would produce that maximum volume? h) What are the dimensions of your box?

A square of x inches is cut out of each corner of a 8x11 piece of cardboard and the sides are folded up to form an open-top box. Complete the following: a) The dimensions of the box, in terms of x. (length, width, height) b) Write a function V(x) in standard form to represent the volume of the box. c) Find the domain and range of V(x). What are the zeros? d) e) Graph the function- only on the interval of the domain. f) Use the graph over the domain to find the maximum volume your box could hold. g) What size cut-outs would produce that maximum volume? h) What are the dimensions of your box?

Advanced Engineering Mathematics
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 square of x inches is cut out of each corner of a 8x11 piece of cardboard and the sides are folded up to form an open-top box. Complete the following: a) The dimensions of the box, in terms of x. (length, width, height) b) Write a function V(x) in standard form to represent the volume of the box. What are the zeros? d) Find the domain and range of V(x). e) Graph the function- only on the interval of the domain. f) Use the graph over the domain to find the maximum volume your box could hold. g) What size cut-outs would produce that maximum volume? h) What are the dimensions of your box?
Transcribed Image Text:A square of x inches is cut out of each corner of a 8x11 piece of cardboard and the sides are folded up to form an open-top box. Complete the following: a) The dimensions of the box, in terms of x. (length, width, height) b) Write a function V(x) in standard form to represent the volume of the box. What are the zeros? d) Find the domain and range of V(x). e) Graph the function- only on the interval of the domain. f) Use the graph over the domain to find the maximum volume your box could hold. g) What size cut-outs would produce that maximum volume? h) What are the dimensions of your box?
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