# Question #02852

Dec 15, 2014

Example: convert $\left(\text{x centimeters")/("1 second") -> ("Kilometers")/("year}\right)$

$\frac{x c m}{1 \sec} \cdot \frac{1 m}{100 c m} \cdot \frac{1 K m}{1000 m} \cdot \frac{60 \sec}{1 \min} \cdot \frac{60 \min}{\text{1 hour") * ("24 hour")/("1 day") *("365 day")/("1 year}}$

$= \frac{x \cdot 60 \cdot 60 \cdot 24 \cdot 365 K m}{100 \cdot \text{1000 year}}$

Calculus:

Derivative calculation, second derivative calculation, using those to find the local maximum, local minimum, and points of inflection (example: titrations)

Algebraic equation manipulation:

Example: combined gas law

If $\frac{{P}_{1} \cdot {V}_{1}}{T} _ 1 = \frac{{P}_{2} \cdot {V}_{2}}{T} _ 2$ you could imagine that a certain piece were x to solve for it individually:

If ${V}_{1} = x$, then solving for x would look like $x = \frac{{P}_{2} \cdot {V}_{2}}{T} _ 2 \cdot \frac{{T}_{1}}{{P}_{1}}$