A rectangular piece of cardboard measuring 10 in by 14 in is to be made into a box by cutting equal size squares from each corner and folding up the sides. Let x represent the length of a side of each such square in inches. Answer the following questions. a) Give the restrictions on x. 0

A rectangular piece of cardboard measuring 10 in by 14 in is to be made into a box by cutting equal size squares from each corner and folding up the sides. Let x represent the length of a side of each such square in inches. Answer the following questions. a) Give the restrictions on x. 0

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

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

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

Chapter3: Triangles

Section3.5: Inequalities In A Triangles

Problem 39E

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Question

I do not have a graphing calculator and have no idea how to finish part C of this problem. If someone could help me out that would be great! The second attachment is the instructions but I am a little lost. Any help appreciated.

Part C: For what value of x will volume be a maximum?

Homework: Sections 1.7, 1.8, 3.1, & 3.4
Homework - Applicati
A rectangular piece of cardboard measuring 10 in by 14 in is to be made into a box by cutting equal size squares from
each corner and folding up the sides. Let x represent the length of a side of each such square in inches. Answer the
following questions.
a) Give the restrictions on x.
0<x< 5
(Simplify your answer.)
b) Determine a function V that gives the volume of the box as a function of x.
V(x) = 4x³-48x² +140x
Question 6, 3.4.91-GC
Part 3 of 5
c) For what value of x will the volume be a maximum?
X≈
inches
(Round to the nearest hundredth.)
14
LECHUS
10 inches

ctions 1.7, 1.8, 3.1, & 3.4
pplicati
oard measur
the sides. Let
volume be
t gives the Multiply the factors.
dth.)
View an example | 2 parts remaining
A rectangular piece of cardboard measuring 14 in by 20 in is to be made into a
box by cutting equal size squares from each corner and folding up the sides.
Let x represent the length of a side of each such square in inches. Answer the
following questions.
V(x) = (20-2x)(14-2x)(x)
Question 6. 3.4.91-GC
Print
(...)
View an example Get more help .
Done
GLECHES
20
**
V(x) = 4x³ - 68x²+280x
c) For what value of x will the volume be a maximum? What is this maximum volume?
To determine the maximum volume and the corresponding value for x, use a graphing calculator to graph V(x). Remember to set the window to show the
restrictions on x.
Use the 'calculate maximum' feature of your calculator to calculate the maximum value of the function.
The maximum volume occurs when x is about 2.70 inches (rounded to the nearest hundredth).
The maximum volume is approximately 339.01 cubic inches (rounded to the nearest hundredth).
d) For what values of x will the volume be greater than 200 cubic inches?
To determine the values of x for which the volume will be greater than 200 cubic inches, set V(x) > 200.
14 inches.
MacBook Air
A
HW Score: 35.71%, 5 of 14 poi
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