clare wants to make an open-top box by cutting out corners of a 30 inch by 25 inch piece of poster board and then folding up the sides. The volume V(x) in cubic inches of the open-top is a function of the side lengh x in inches of the square cutouts. Write an expression for V(x).

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imeldamatias08 imeldamatias08 · Answer 1 · 2020-09-24T19:01:59+02:00

Answer:

A. V(x)= (50-2x) ( 35-2x)x

Step-by-step explanation:

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MrRoyal MrRoyal · Answer 2 · 2021-10-01T23:34:03+02:00

The volume of a container is the amount of space in it.

The expression for volume is [tex]V(x) = 4x^3 - 110x\² + 750x[/tex]

From the question, we have:

[tex]Length = 30[/tex]

[tex]Width =25[/tex]

When x is removed from the container, the dimension of the box becomes

[tex]Length = 30 -2x[/tex]

[tex]Width = 25 - 2x[/tex]

[tex]Height =x[/tex]

We subtract 2x, because x is removed from both ends

The volume is then calculated as:

[tex]V(x) = Length \times Width \times Height[/tex]

This gives:

[tex]V(x) = (30 -2x) \times (25 -2x) \times x[/tex]

Expand

[tex]V(x) = (30 -2x) \times (25x - 2x^2)[/tex]

Further expand

[tex]V(x) = 750x - 110x\² + 4x^3[/tex]

Rewrite as:

[tex]V(x) = 4x^3 - 110x\² + 750x[/tex]

Hence, the volume expression is [tex]V(x) = 4x^3 - 110x\² + 750x[/tex]