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Answer :
Sure, let's solve the problem step by step!
We are given the dimensions of Box 2 as:
- Length: [tex]\( x \)[/tex]
- Width: [tex]\( 4x - 1 \)[/tex]
- Height: [tex]\( x^3 \)[/tex]
To find the volume of the box, we need to multiply these dimensions together. The formula for the volume [tex]\(V\)[/tex] is:
[tex]\[ V = \text{Length} \times \text{Width} \times \text{Height} \][/tex]
Substituting the given dimensions into the formula, we get:
[tex]\[ V = x \times (4x - 1) \times x^3 \][/tex]
Now, let's simplify this step by step:
1. Multiply the length and width together:
[tex]\[ x \times (4x - 1) = 4x^2 - x \][/tex]
2. Now, multiply the result by the height:
[tex]\[ (4x^2 - x) \times x^3 \][/tex]
This can be further expanded as:
[tex]\[ 4x^2 \times x^3 - x \times x^3 \][/tex]
[tex]\[ 4x^5 - x^4 \][/tex]
So, the volume of Box 2 is:
[tex]\[ 4x^5 - x^4 \][/tex]
Let's match this with the given choices:
1. [tex]\( 4x^5 - x^4 \)[/tex]
2. [tex]\( 4x^6 - x^3 \)[/tex]
3. [tex]\( 4x^5 + x^4 \)[/tex]
4. [tex]\( x^3 + 5x - 1 \)[/tex]
The correct choice corresponds to [tex]\( 4x^5 - x^4 \)[/tex].
Therefore, the volume of Box 2 is:
[tex]\[ 4x^5 - x^4 \][/tex]
And the correct choice is 1.
We are given the dimensions of Box 2 as:
- Length: [tex]\( x \)[/tex]
- Width: [tex]\( 4x - 1 \)[/tex]
- Height: [tex]\( x^3 \)[/tex]
To find the volume of the box, we need to multiply these dimensions together. The formula for the volume [tex]\(V\)[/tex] is:
[tex]\[ V = \text{Length} \times \text{Width} \times \text{Height} \][/tex]
Substituting the given dimensions into the formula, we get:
[tex]\[ V = x \times (4x - 1) \times x^3 \][/tex]
Now, let's simplify this step by step:
1. Multiply the length and width together:
[tex]\[ x \times (4x - 1) = 4x^2 - x \][/tex]
2. Now, multiply the result by the height:
[tex]\[ (4x^2 - x) \times x^3 \][/tex]
This can be further expanded as:
[tex]\[ 4x^2 \times x^3 - x \times x^3 \][/tex]
[tex]\[ 4x^5 - x^4 \][/tex]
So, the volume of Box 2 is:
[tex]\[ 4x^5 - x^4 \][/tex]
Let's match this with the given choices:
1. [tex]\( 4x^5 - x^4 \)[/tex]
2. [tex]\( 4x^6 - x^3 \)[/tex]
3. [tex]\( 4x^5 + x^4 \)[/tex]
4. [tex]\( x^3 + 5x - 1 \)[/tex]
The correct choice corresponds to [tex]\( 4x^5 - x^4 \)[/tex].
Therefore, the volume of Box 2 is:
[tex]\[ 4x^5 - x^4 \][/tex]
And the correct choice is 1.
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