To solve the equation [tex]\( d = \frac{m}{V} \)[/tex] for [tex]\( V \)[/tex], follow these steps:
1. Start with the given equation:
[tex]\[
d = \frac{m}{V}
\][/tex]
2. Our goal is to isolate [tex]\( V \)[/tex]. To do this, multiply both sides of the equation by [tex]\( V \)[/tex] to get rid of the fraction:
[tex]\[
d \cdot V = m
\][/tex]
3. Now, to isolate [tex]\( V \)[/tex], divide both sides of the equation by [tex]\( d \)[/tex]:
[tex]\[
V = \frac{m}{d}
\][/tex]
So, the equation [tex]\( d = \frac{m}{V} \)[/tex] solved for [tex]\( V \)[/tex] is:
[tex]\[
V = \frac{m}{d}
\][/tex]
Among the given options:
- [tex]\( dm = V \)[/tex] is incorrect because it does not correctly isolate [tex]\( V \)[/tex].
- [tex]\( \frac{d}{m} = V \)[/tex] is incorrect because it does not have the correct relationship between [tex]\( d \)[/tex], [tex]\( m \)[/tex], and [tex]\( V \)[/tex].
- [tex]\( \frac{m}{d} = V \)[/tex] is correct and matches our derived equation.
- [tex]\( m - d = V \)[/tex] is incorrect as it does not come from rearranging the original equation properly.
Therefore, the correct equivalent equation solved for [tex]\( V \)[/tex] is:
[tex]\[
\frac{m}{d} = V
\][/tex]
