Question
Given the formula for the volume of a box, V = lwh , which equation best represents the remaining units when justifying your rearrangement to solve for the width? (1 point) in.^ 3 in^ 2 = in.^ 3 in.^ 2; in.=in.; (i * n ^ 2)/(i * n ^ 2) = in; in.^ 3 =in.^ 3
Answers
Answered by
GPT-4o mini
To rearrange the formula for the volume of a box, \( V = lwh \), to solve for the width \( w \), you divide both sides by the product of the length \( l \) and the height \( h \):
\[
w = \frac{V}{lh}
\]
In this rearrangement, let's analyze the units of \( V \), \( l \), \( h \), and \( w \):
- Volume \( V \) is measured in cubic inches (in³).
- Length \( l \) is measured in inches (in).
- Height \( h \) is measured in inches (in).
Thus, the units for \( lh \) (length times height) are:
\[
l \times h = \text{in} \times \text{in} = \text{in}^2
\]
When you divide \( V \) (in³) by \( lh \) (in²), the units become:
\[
\frac{V}{lh} = \frac{\text{in}^3}{\text{in}^2} = \text{in}
\]
This means that the width \( w \) is measured in inches (in).
To justify our rearrangement with regard to units, we can express the relationship in a simple equation:
\[
\frac{\text{in}^3}{\text{in}^2} = \text{in}
\]
Among the given options, the best representation of the remaining units when justifying the rearrangement to solve for the width would be:
\[
\frac{i \cdot n^3}{i \cdot n^2} = in
\]
Thus, the conclusion is that the remaining units result in \( \text{in} \), which matches the units for width \( w \).
\[
w = \frac{V}{lh}
\]
In this rearrangement, let's analyze the units of \( V \), \( l \), \( h \), and \( w \):
- Volume \( V \) is measured in cubic inches (in³).
- Length \( l \) is measured in inches (in).
- Height \( h \) is measured in inches (in).
Thus, the units for \( lh \) (length times height) are:
\[
l \times h = \text{in} \times \text{in} = \text{in}^2
\]
When you divide \( V \) (in³) by \( lh \) (in²), the units become:
\[
\frac{V}{lh} = \frac{\text{in}^3}{\text{in}^2} = \text{in}
\]
This means that the width \( w \) is measured in inches (in).
To justify our rearrangement with regard to units, we can express the relationship in a simple equation:
\[
\frac{\text{in}^3}{\text{in}^2} = \text{in}
\]
Among the given options, the best representation of the remaining units when justifying the rearrangement to solve for the width would be:
\[
\frac{i \cdot n^3}{i \cdot n^2} = in
\]
Thus, the conclusion is that the remaining units result in \( \text{in} \), which matches the units for width \( w \).