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\left(x\right),` in cubic inches of the open-top box is a function of the side length, `x,`in inches, of the square cutouts.

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oladayoademosu oladayoademosu · Answer 1 · 2020-11-26T06:09:53+01:00

Answer:

V(x) = 4x³ - 110x² + 750x

Step-by-step explanation:

For each side of the base of the open-top box, since x inches is cut out from each side, we have 2x inches removed from each sides dimension.

Since the dimensions of the poster are 30 inches by 25 inches, the area of the base of the open-top box is thus

A(x) = (30 - 2x)(25 - 2x) since we remove 2x inches from each dimension.

Now, the height of the open-top box is x. So, its volume is V(x) = Ax

V(x) = (30 - 2x)(25 - 2x)x

V(x) = (750 - 60x - 50x + 4x²)x

V(x) = (750 - 110x + 4x²)x

Expanding the bracket, we have

V(x) = 750x - 110x² + 4x³

Re-arranging, we have

V(x) = 4x³ - 110x² + 750x