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A manufacturer uses a 17 x 42 metal sheet to construct
an open box by cutting out squares from each corner.
What length square should be cut out to maximize the
volume?
Round your answer to two decimal places.

Respuesta :

jaydentechy

Answer:

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

where

substitute

Convert to expanded form

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

Step-by-step explanation:

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