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) Responses in.=in. in. equals in. in.3in.2=in. Start Fraction in. cubed over in. squared End Fraction equals in. in.3in.2=in.3in.2 Start Fraction in. cubed over in. squared End Fraction equals Start Fraction in. cubed over in. squared End Fraction in.3=in.3
Answers
GPT-4o mini
To solve for the width (w) in the volume formula \( V = lwh \), we can rearrange the equation as follows:
\[
w = \frac{V}{lh}
\]
Now, to justify this rearrangement in terms of units:
The volume \( V \) is measured in cubic inches (in³), while the length \( l \) and height \( h \) are measured in square inches (in²).
Thus, the units on the right side of the equation would be:
\[
w = \frac{\text{in}^3}{\text{in}^2}
\]
When you divide cubic inches by square inches, the units simplify as follows:
\[
w = \text{in}^{3-2} = \text{in}^1 = \text{in}
\]
Therefore, the equation that best represents the remaining units when justifying the rearrangement to solve for the width is:
\[
\text{in}^3 \div \text{in}^2 = \text{in}^1
\]
This shows that dividing cubic inches by square inches results in inches, which is consistent with what we expect for the width.
\[
w = \frac{V}{lh}
\]
Now, to justify this rearrangement in terms of units:
The volume \( V \) is measured in cubic inches (in³), while the length \( l \) and height \( h \) are measured in square inches (in²).
Thus, the units on the right side of the equation would be:
\[
w = \frac{\text{in}^3}{\text{in}^2}
\]
When you divide cubic inches by square inches, the units simplify as follows:
\[
w = \text{in}^{3-2} = \text{in}^1 = \text{in}
\]
Therefore, the equation that best represents the remaining units when justifying the rearrangement to solve for the width is:
\[
\text{in}^3 \div \text{in}^2 = \text{in}^1
\]
This shows that dividing cubic inches by square inches results in inches, which is consistent with what we expect for the width.