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Allisa [31]
3 years ago
8

Devon made a box with length x+1, width x+3, and height x-3. What is the volume of Devon's box as a function of x?

Mathematics
1 answer:
erica [24]3 years ago
8 0

Answer:

(a)

V=x^3+x^2-9x-9

(b)

x=10

(c)

x=\frac{7}{2}

Step-by-step explanation:

we are given

length is x+1

L=x+1

width is x+3

W=x+3

height is x-3

H=x-3

(a)

we can use volume formula

V=L\times W\times H

now, we can plug it

V=(x+1)\times (x+3)\times (x-3)

now, we can simplify it

V=x^3+x^2-9x-9

(b)

we are given volume =1001

so, we can set V=1001

and then we can solve for x

V=x^3+x^2-9x-9=1001

now, we can factor it

\left(x-10\right)\left(x^2+11x+101\right)=0

x-10=0

x=10

(b)

we are given volume

so, we can set

V=14\frac{5}{8}=\frac{14\times 8+5}{8}

V=\frac{117}{8}

and then we can solve for x

V=x^3+x^2-9x-9=\frac{117}{8}

now, we can factor it

8x^3+8x^2-72x-189=0

\left(2x-7\right)\left(4x^2+18x+27\right)=0

2x-7=0

x=\frac{7}{2}

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