Answer:
a.) V = √(mv²/M)
Step-by-step explanation:
As with any "solve for ..." situation, you make use of inverse operations to "undo" what is done to the variable of interest.
Solve
In the given equation ...
MV² = mv²
the variable V is squared and that result is multiplied by M. These operations are dealt with in reverse order.
To undo multiplication by M, we divide both sides of the equation by M.
[tex]MV^2=mv^2\qquad\text{given}\\\\\dfrac{MV^2}{M}=\dfrac{mv^2}{M}\qquad\text{divide by $M$}\\\\V^2=\dfrac{mv^2}{M}\qquad\text{simplify}[/tex]
To undo the squaring of V, we take the square root.
[tex]\sqrt{V^2}=\sqrt{\dfrac{mv^2}{M}}\qquad\text{take the square root}\\\\\boxed{V=\sqrt{\dfrac{mv^2}{M}}}\qquad\text{simplify a bit}[/tex]
This matches the first choice.
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Additional comment
Continued simplification would give you ...
[tex]V=v\sqrt{\dfrac{m}{M}}[/tex]
However, this is not one of the answer choices.
