Precalculus Examples

$12 r p m$

Use the fact that each revolution is $2 π$ radians and each minute is $60$ seconds to convert from $rpm$ to $\frac{radian}{sec}$

$\frac{12 \cdot round}{min} \cdot \frac{2 π \cdot radian}{round} \cdot \frac{min}{60 \cdot sec}$

Cancel the common units.

$\frac{12 \cdot round}{min} \cdot \frac{2 π \cdot radian}{round} \cdot \frac{min}{60 \cdot sec}$

Reduce the expression by cancelling the common factors.

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Factor $12$ out of $12 \cdot (2 π)$ .

$\frac{12 (2 π)}{60} \cdot \frac{radian}{sec}$

Cancel the common factors.

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Factor $12$ out of $60$ .

$\frac{12 (2 π)}{12 \cdot 5} \cdot \frac{radian}{sec}$

Cancel the common factor.

$\frac{12 (2 π)}{12 \cdot 5} \cdot \frac{radian}{sec}$

Rewrite the expression.

$\frac{2 π}{5} \cdot \frac{radian}{sec}$

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