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Dmitry_Shevchenko [17]
2 years ago
14

A rectangular box has the dimensions shown in the diagram. The volume of the box is given by the function V(x) = x3 – 4x, where

x is the height in inches.
What is the height of the box if the volume is 15 in.3?


There is a rectangular box with length x+2 in. , width x-2 in. , and height x in.


height = in.

Mathematics
1 answer:
marta [7]2 years ago
3 0

Answer:

Height =3

Step-by-step explanation:

Given

Length = x + 2

Width = x - 2

Height = x

Volume = 15

Required

Find the height

The volume is calculated as thus:

Volume = Length * Width * Height

This gives

15 = (x + 2) * (x - 2) * x

Apply difference of two squares

15 =(x^2 - 4 ) * x

15 = x^3 - 4x

Subtract 15 from both sides

x^3 - 4x - 15 = 0

Using a calculator to factorize, we have:

(x-3)(x^2+3x+5) = 0

Split

x - 3 = 0 or x^2 + 3x + 5 = 0

x = 3 or  x^2 + 3x + 5 = 0

x has complex roots for x^2 + 3x + 5 = 0

Hence:

x = 3

Recall that:

Height = x

Height =3

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