To solve the equation [tex]\( p = m \cdot v \)[/tex] for [tex]\( m \)[/tex], follow these steps:
1. Start with the given equation:
[tex]\[
p = m \cdot v
\][/tex]
2. Our goal is to isolate [tex]\( m \)[/tex]. To do this, we need to get [tex]\( m \)[/tex] by itself on one side of the equation.
3. Since [tex]\( m \)[/tex] is multiplied by [tex]\( v \)[/tex], we can isolate [tex]\( m \)[/tex] by performing the opposite operation, which is division. Divide both sides of the equation by [tex]\( v \)[/tex]:
[tex]\[
\frac{p}{v} = \frac{m \cdot v}{v}
\][/tex]
4. On the right-hand side, [tex]\( v \)[/tex] in the numerator and denominator will cancel out:
[tex]\[
\frac{p}{v} = m
\][/tex]
5. Now, the equation is simplified to:
[tex]\[
m = \frac{p}{v}
\][/tex]
So, the solution for [tex]\( m \)[/tex] in terms of [tex]\( p \)[/tex] and [tex]\( v \)[/tex] is:
[tex]\[
m = \frac{p}{v}
\][/tex]
This is the required formula for [tex]\( m \)[/tex].
