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? in.=in., in^3/in^2=in^3/in^2, in^3=in^3, or in^3/in^2=in
Answers
GPT-4o mini
To rearrange the formula for the volume of a box, \( V = lwh \), to solve for the width \( w \), we can isolate \( w \) as follows:
1. Start with \( V = lwh \).
2. To solve for \( w \), divide both sides by \( lh \):
\[
w = \frac{V}{lh}
\]
Now, let's analyze the units in this equation.
Given:
- Volume \( V \) is measured in cubic inches (\( \text{in}^3 \)).
- Length \( l \) and height \( h \) are both measured in inches (\( \text{in} \)).
When you divide the volume by the product of length and height, the units are:
\[
w = \frac{\text{in}^3}{\text{in} \cdot \text{in}} = \frac{\text{in}^3}{\text{in}^2} = \text{in}
\]
So, the equation that best represents the remaining units when justifying your rearrangement to solve for the width \( w \) is:
\[
\frac{\text{in}^3}{\text{in}^2} = \text{in}
\]
This confirms that the width \( w \) is expressed in inches (\( \text{in} \)), which is the unit of measurement for width in this context.
1. Start with \( V = lwh \).
2. To solve for \( w \), divide both sides by \( lh \):
\[
w = \frac{V}{lh}
\]
Now, let's analyze the units in this equation.
Given:
- Volume \( V \) is measured in cubic inches (\( \text{in}^3 \)).
- Length \( l \) and height \( h \) are both measured in inches (\( \text{in} \)).
When you divide the volume by the product of length and height, the units are:
\[
w = \frac{\text{in}^3}{\text{in} \cdot \text{in}} = \frac{\text{in}^3}{\text{in}^2} = \text{in}
\]
So, the equation that best represents the remaining units when justifying your rearrangement to solve for the width \( w \) is:
\[
\frac{\text{in}^3}{\text{in}^2} = \text{in}
\]
This confirms that the width \( w \) is expressed in inches (\( \text{in} \)), which is the unit of measurement for width in this context.