Answer:
A. V(x)= (50-2x) ( 35-2x)x
Step-by-step explanation:
The volume of a container is the amount of space in it.
The expression for volume is [tex]V(x) = 4x^3 - 110x\² + 750x[/tex]
From the question, we have:
[tex]Length = 30[/tex]
[tex]Width =25[/tex]
When x is removed from the container, the dimension of the box becomes
[tex]Length = 30 -2x[/tex]
[tex]Width = 25 - 2x[/tex]
[tex]Height =x[/tex]
We subtract 2x, because x is removed from both ends
The volume is then calculated as:
[tex]V(x) = Length \times Width \times Height[/tex]
This gives:
[tex]V(x) = (30 -2x) \times (25 -2x) \times x[/tex]
Expand
[tex]V(x) = (30 -2x) \times (25x - 2x^2)[/tex]
Further expand
[tex]V(x) = 750x - 110x\² + 4x^3[/tex]
Rewrite as:
[tex]V(x) = 4x^3 - 110x\² + 750x[/tex]
Hence, the volume expression is [tex]V(x) = 4x^3 - 110x\² + 750x[/tex]
Read more about volumes at:
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