Rom

\(\text{$x$ is the number of lawns mowed, and $y$ is the number of dogs walked}\\ 25x+15y \geq 1975\\ y \leq 4 x\\ y \geq 50\)

I see... the * isn't multiplication....

It would have been far clearer if you had either stated that up front or used a different symbol.

same advice I give for all timed tests.

Go through the entire test answering what you are sure of.

Then go back to the problems you aren't immediately sure of.

Repeat but spend a bit more time on each problem now, if you have no clue move on.

Continue until you have finished the test or run out of time.

deleted

no more ability than you do

Face it.. you're doomed.

DOOOOOOOMED

\(\text{putting this into augmented matrix form}\\ \begin{pmatrix} 1&1&3&|&10\\ -4&2&5&|&7\\ k&0&1&|&3 \end{pmatrix}\)

\(\text{Now we row reduce this a bit}\\ \begin{pmatrix} 1&1&3&|&10\\ 0&6&17&|&47\\ 0&-k&1-3k&|&3-10k \end{pmatrix}\\ \begin{pmatrix} 1&1&3&|&10\\ 0&1&\frac{17}{6}&|&\frac{47}{6}\\ 0&0&1-\frac{k}{6}&|&3-\frac{10k}{6} \end{pmatrix}\)

\(\text{Now we see from the bottom row that if we let $k=6$ we have $0x+0y+0z = -7$}\\ \text{This is clearly impossible and thus $k=6$ is the number we are after}\)

The letters i through n are generally used for integer variables/indices

All other letters generally refer to continuous variables.

This is definitely not a hard and fast rule but you'll find your math writing much easier to understand if you abide by it.

Probability and combinatorics won't really help you at all in calculus.  It just doesn't come up.

Geometry doesn't really come up that much either though it will help with word problems.

You need a solid grounding in trig, that's about it.