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3 years ago

9

A manufacturer cuts squares from the corners of a rectangular plece of sheet metal that measures 2 inches by 7 inches (see Figur

e 1). The manufacturer then
folds the metal upward to make an open-topped box (see Figure 2). Letting x represent the side-lengths (in inches) of the squares, use the ALEKS graphing
calculator to find the value of x that maximizes the volume enclosed by this box. Then give the maximum volume. Round your responses to two decimal places.

1 answer:

Vladimir79 [104]3 years ago

8 0

Answer:

The value of x that maximizes the volume enclosed by this box is 0.46 inches

The maximum volume is 3.02 cubic inches

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

The volume of the open-topped box is equal to

$V=LWH$

where

$L=(7-2x)\ in\\W=(2-2x)\ in\\H=x\ in$

substitute

$V=(7-2x)(2-2x)x$

Convert to expanded form

$V=(7-2x)(2-2x)x\\V=(14-14x-4x+4x^{2})x\\V=14x-14x^2-4x^2+4x^{3}\\V=4x^{3}-18x^{2} +14x$

using a graphing tool

Graph the cubic equation

Remember that

The domain for x is the interval -----> (0,1)

Because

If x>1

then

the width is negative (W=2-2x)

so

The maximum is the point (0.46,3.02)

see the attached figure

therefore

The value of x that maximizes the volume enclosed by this box is 0.46 inches

The maximum volume is 3.02 cubic inches

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<u>Solution:</u>

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Read 2 more answers

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Step-by-step explanation:

We need to solve the inequality: $-3q+12\geq 4q-30$ and find value of q

Solving:

$-3q+12\geq 4q-30\\Adding\,\,-12\,\,on\,\,both\,\,sides:\\-3q+12-12\geq 4q-30-12\\-3q\geq 4q-42\\Adding\,\,-4q\,\,on\,\,both\,\,sides:\\-3q-4q\geq 4q-42-4q\\-7q\geq -42\\Divide\,\,both\,\,sides\,\,by\,\,7\\\frac{-7q}{7}\geq \frac{-42}{7}\\ -q\geq -6\\Multiply\,\,both\,\,sides\,\,by\,\,-1\,\,and\,\,reverse\,\,the\,\,inequality:\\q\leq 6$

So, solving the inequality $-3q+12\geq 4q-30$ the value of q is $q\leq 6$

Keywords: Solving inequality

Learn more about solving inequality at:

#learnwithBrainly

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