Evaluate $\int_{\mathbf{c}} f\, ds$, where $f (x, y, z) = z$ and $\mathbf{c}(t) = (t \cos t, t \sin t, t)$ for $0 \leq t \leq t_0$.

Multiply. $m^{2}(2 m-5)(3 m+8)$ _____.

Solve any pair of the system equation $2x-y=4,\text{ } 3x+y=1, \text{ and } x-2y=5$. Show that the solution is valid for any pair chosen. What conclusions can be drawn about the graphs of the three equations.

A farmer’s fruit storage cellar is unheated. To prevent the fruit from freezing, the farmer places a barrel of water in the cellar. Explain why this helps prevent the fruit from freezing.

Solve and check. $7 = m \div 21$

Find the average $y$ coordinate of the points on the semicircle parametrized by $\mathbf{c}: [0, \pi]\to \mathbb{R}^3, \theta\mapsto (0, a \sin \theta, a \cos \theta); a > 0$.

Explain the differences between each set of vocabulary words given below. Then explain how the words are related. pH—buffer

The weight of a radioactive isotope remaining after t weeks is given by $W_{t}=8000 \times e^{-\frac{t}{20}}$ grams. Find the time for the weight to: reach 0.1% of its original value.

A solution of $\mathrm{KClO}_{3}$ is prepared using 75 grams of the solute in enough water to make 0.250 liters of solution. The gram-formula mass of $\mathrm{KClO}_{3}$ is 122 grams per mole. Assuming the solution is saturated, determine the temperature of the solution.

Determine whether the given expression is a polynomial ll it is, write it in standard form. $2 x ^ { 2 } - \sqrt { 3 } x + 4$

Write equivalent expression. $35x+30$

Solve.

$$\begin{array} { l } { \text { a) } 3 x ^ { 2 } + 28 x + 9 = 0 } \\ { \text { b) } 4 k ^ { 2 } + 19 k + 15 = 0 } \\ { \text { c) } 8 y ^ { 2 } - 22 y + 15 = 0 } \\ { \text { d) } 16 b ^ { 2 } - 1 = 0 } \\ { \text { e) } 10 m ^ { 2 } + 30 m = 0 } \\ { \text { f) } 4 x ^ { 2 } - 12 x + 9 = 0 } \end{array}$$

Use your book or dictionary to define ganglion.

If possible, compute the matrix products using paper and pencil.

$$\begin{bmatrix} 1 & 0 & -1\\0 & 1 & 1 \\ 1 & -1 & -2 \end{bmatrix} \begin{bmatrix} 1 & 2 & 3\\ 3 & 2 & 1\\ 2 & 1 & 3 \end{bmatrix}$$