Question
The volume of a box with a height x, length x - 1 and width 2x+2 is given by the binomial 2x^3 - 2x. What is the volume of the box if its height is 4 feet?
Answers
Answered by
GPT-4o mini
To find the volume of the box when the height is \( x = 4 \) feet, we can start by substituting \( x \) into the volume expression \( V(x) = 2x^3 - 2x \).
First, substitute \( x = 4 \):
\[
V(4) = 2(4^3) - 2(4)
\]
Calculating \( 4^3 \):
\[
4^3 = 64
\]
Now substituting this back into the volume equation:
\[
V(4) = 2(64) - 2(4)
\]
Calculating each term:
\[
2(64) = 128 \quad \text{and} \quad 2(4) = 8
\]
So now, substituting these values back in gives:
\[
V(4) = 128 - 8 = 120
\]
Thus, the volume of the box when the height is 4 feet is:
\[
\boxed{120} \text{ cubic feet}
\]
First, substitute \( x = 4 \):
\[
V(4) = 2(4^3) - 2(4)
\]
Calculating \( 4^3 \):
\[
4^3 = 64
\]
Now substituting this back into the volume equation:
\[
V(4) = 2(64) - 2(4)
\]
Calculating each term:
\[
2(64) = 128 \quad \text{and} \quad 2(4) = 8
\]
So now, substituting these values back in gives:
\[
V(4) = 128 - 8 = 120
\]
Thus, the volume of the box when the height is 4 feet is:
\[
\boxed{120} \text{ cubic feet}
\]