Need help with C D E and F Consider the following problem: A box with an open top is to be constructed from a square piece of cardboard, 3 ft wide, by cutting out a square from each of the four corners and bending up the sides. Find the largest volume that such a box can have.(a) Draw several diagrams to illustrate the situation, some short boxes with large bases and some tall boxes with small bases. Find the volumes of several such boxes.(b) Draw a diagram illustrating the general situation. Let x denote the length of the side of the square being cut out. Let y denote the length of the base.(c) Write an expression for the volume V in terms of both x and y.V =(d) Use the given information to write an uation that relates the variables x and y.(e) Use part (d) to write the volume as a function of only x.V(x) =(f) Finish solving the problem by finding the largest volume that such a box can have.V=ft3

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Answered: (d) Use the given information to write…

Math

Calculus

(d) Use the given information to write an Lauation that relates the variables x and y.

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter9: Surfaces And Solids

Section9.1: Prisms, Area And Volume

Problem 40E: As in Exercise 39, find the volume of the box if four congruent squares with sides of length 6 in....

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Question

Need help with C D E and F

Consider the following problem: A box with an open top is to be constructed from a square piece of cardboard, 3 ft wide, by cutting out a square from each of the four corners and bending up the sides. Find the largest volume that such a box can have.
(a) Draw several diagrams to illustrate the situation, some short boxes with large bases and some tall boxes with small bases. Find the volumes of several such boxes.
(b) Draw a diagram illustrating the general situation. Let x denote the length of the side of the square being cut out. Let y denote the length of the base.
(c) Write an expression for the volume V in terms of both x and y.
V =
(d) Use the given information to write an uation that relates the variables x and y.
(e) Use part (d) to write the volume as a function of only x.
V(x) =
(f) Finish solving the problem by finding the largest volume that such a box can have.
V=
ft3

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