If the variable x represents the length of a side of the square cutouts in feet,

Question

If the variable x represents the length of a side of the square cutouts in feet, what are the possible values of x in this context? a. x can vary from 0 feet to 2 feet b. x can vary from 0 feet to 4 feet c. x can vary from 0 feet to 6 feet d. x can vary from 0 feet to 8 feet e. x cannot vary-x is an unknown Which the following represents the volume of the toy chest, V, in cubic feet as a function of the length of a side of the square cutout, x, in feet? a. V = f(x) where f(x) = (x - 8)(x - 4)(2x) b. V = f(x) where f(x) = (2x - 8)(2x - 4)(x) c. V = f(x) where f(x) = (8 - 2x)(4 - x)(x) d. V = f(x) where f(x) = (8 - x)(4 - 2x)(2x) e. V = f(x) where f(x) = (8 - 2x)(4 - 2x)(x)

Explanation / Answer

We need the remaining question but i can tell u how its done

Since the original figure dimensions are not known, iam assuming its a rectangle of dimensions 8 and 4. Infact, i am siure this is what it is

Since we are cutting out a square of side length x from each corner,
we can state that the height of the box is : x

The dimensions of the box are 8- 2x
and 4 - 2x

So, volume of the box would be :
x(8 - 2x)(4 - 2x)

Now, we have
8 - 2x > 0
2x < 8
x < 4

Similarly, 4 - 2x < 0
2x < 4
x < 2

So, what satisfies x < 4 and x < 2
and also satisfies x > 0 as height has to be positive?

Clearly the region x lies between 0 and 2

Option A

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28)

Volume = x(8 - 2x)(4 - 2x)

option E

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