$m = r\sqrt\frac{x}{a}$. Make $x$ the subject of the formula. [closed]

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Make $x$ the subject of the formula $$m = r\sqrt\frac{x}{a}$$

I don't know how to approach this question. Thank you and help is appreciated

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2 Answers

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The question is asking you to solve for $x$ in terms of everything else ($x=\cdots$). You can do so by reversing the operations you are performing onto $x$.

\begin{align}m&=r\sqrt{\frac{x}{a}}\\\frac{m}{r}&=\sqrt{\frac{x}{a}}\\\bigg(\frac{m}{r}\bigg)^2&=\frac{x}{a}\\a\bigg(\frac{m}{r}\bigg)^2&=x\end{align}

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The basic concept in any "make $x$ the subject" or "solve for $x$" is "undo" whatever has been done to $x$. That is what Andrew Chin did!

Here, we have $m= r\sqrt{\frac{x}{a}}$. If you were given $x$ and asked to find $m$ you would

1) Divide $x$ by $a$.

2) Take the square root.

3) Multiply by $r$.

To "undo" that, do the opposite (inverse) of each step in the opposite order.

To undo "multiply by $r$", divide by r (and, of course, do that on both sides of the equation). That gives $\frac{m}{r}= \sqrt{\frac{x}{a}}$.

To undo "take the square root", square. That gives $\left(\frac{m}{r}\right)= \frac{m^2}{r^2}= \frac{x}{a}$.

To undo "divide by $a$", multiply by $a$. That gives $\frac{am^2}{r^2}= x$.

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