On a slow weekday, you spend at least two hours on homework. On a busy weekday, you spend as much as five hours on homework. Write an absolute value inequality that represents the number of hours you spend doing homework on a typical weekday.

Consider the formation of $\mathrm{NO}(\mathrm{g})$ from its elements.

$$\begin{align*} \mathrm{N}_2(\mathrm{~g})+\mathrm{O}_2(\mathrm{~g}) \rightleftharpoons 2 \mathrm{NO}(\mathrm{g}) \end{align*}$$

Calculate $K_{\mathrm{p}}$ at $25^{\circ} \mathrm{C}$. Is the reaction product favored at this temperature?

Suppose that you want to take a photograph of yourself as you look at your image in a mirror $3.1 \mathrm{~m}$ away. For what distance should the camera lens be focused?

Find an equation of the tangent line to the graph of the function at the given point.

$$\begin{matrix} \text{Function} & \text{Point}\\ \text{y=tan 2x} & \text{}{\left(\frac{5 \pi}{8}, 1\right)}\\ \end{matrix}$$

Find all points where the functions defined below have any relative extrema. Find any saddle points. $z=\frac{1}{2} x^{2}+\frac{1}{2} y^{2}+2 x y-5 x-7 y+10$

Using Commas Between Adjectives. In each of the following sentences, two adjectives have been underlined. Add commas between the two adjectives only where necessary $\underline{Slow}$ $\underline{steady}$ rowing soon brought all of the team's boats to shore.

Give a reason for your answer in each. Assume that all variables represent integers. Does 7 | 56?

Determine if the point lies on the unit circle.

$$\left(\frac{\sqrt{10}}{5}, \frac{\sqrt{15}}{5}\right)$$

Set up and evaluate the definite integral for the area of the surface generated by revolving the curve about the x-axis. y=2√x

There is a $50 annual membership fee to join an urban car rental service. Using a car costs$8.50 per hour. Write a verbal model for this situation. Then use the verbal model to write an algebraic expression. How much will it cost to join the service and drive for 20 hours?

Solve the following exercise about tests for positive definiteness.

Test to see if $A^{\mathrm{T}} A$ is positive definite in each case: $A$ needs independent columns.

$$A=\left[\begin{array}{ll} 1 & 2 \\ 0 & 3 \end{array}\right] \text { and } A=\left[\begin{array}{ll} 1 & 1 \\ 1 & 2 \\ 2 & 1 \end{array}\right] \text { and } A=\left[\begin{array}{lll} 1 & 1 & 2 \\ 1 & 2 & 1 \end{array}\right]$$

Find the rectangular coordinates of each point with the given polar coordinates. $\left(14,130^{\circ}\right)$

Simplify the radical expression, if possible. Assume all variables are unrestricted.

$$- \sqrt { 144 t ^ { 4 } }$$

Evaluate the algebraic expression for the given value or values of the variables. $4+5(x-7)^{3}$; x=9