Solve the equation $$ M=\frac{17 r^{2} h}{13} $$ for $$ r $$ in terms of $$ M $$ and $$ h $$. Assume $$ r, M $$ and $$ h $$ are all positive. $$ \begin{aligned} ext { Or } & =\sqrt{\frac{13 M}{17 h}} \ ext { Or } & =\frac{13 M}{17 h} \ ext { Or } & =\sqrt{\frac{17 M}{13 h}} \ O r & =\frac{17 M}{13 h} \ O r & =\sqrt{\frac{17 h}{13 M}}\end{aligned} $$

Question

Solve the equation $$ M=\frac{17 r^{2} h}{13} $$ for $$ r $$ in terms of $$ M $$ and $$ h $$. Assume $$ r, M $$ and $$ h $$ are all positive. $$ \begin{aligned} 	ext { Or } & =\sqrt{\frac{13 M}{17 h}} \ 	ext { Or } & =\frac{13 M}{17 h} \ 	ext { Or } & =\sqrt{\frac{17 M}{13 h}} \ O r & =\frac{17 M}{13 h} \ O r & =\sqrt{\frac{17 h}{13 M}}\end{aligned} $$

UpStudy AI · Accepted Answer

Given the equation

$$
M = \frac{17r^2h}{13},
$$

we want to solve for $$ r $$.

**Step 1. Isolate $$ r^2 $$:**

Multiply both sides by $$ \frac{13}{17h} $$ (assuming $$ h > 0 $$):

$$
\frac{13M}{17h} = r^2.
$$

**Step 2. Solve for $$ r $$:**

Take the square root of both sides (and use the positive square root since $$ r > 0 $$):

$$
r = \sqrt{\frac{13M}{17h}}.
$$

Thus, the solution is

$$
r = \sqrt{\frac{13M}{17h}}.
$$
$$ r = \sqrt{\frac{13M}{17h}} $$

Solve the equation for in terms of and . Assume and are all positive.

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