Match the trigonometric expression with its simplified form. (a) sec x, (b) -1 (c) cot x, (d) 1, (e) -tan x, (f) sin x. $\frac{\sin (-x)}{\cos (-x)}$

Describe and correct the error in solving the equation.

$$\left.\begin{aligned} 5 c - 6 & = 4 - 3 c \\ 2 c - 6 & = 4 \\ 2 c & = 10 \\ c & = 5 \end{aligned} \right.$$

Does a higher rate of saving lead to higher growth temporarily or indefinitely?

Use a graphing utility to graph the sales function over 1 year, where S is the sales (in thousands of units) of a seasonal product, and t is the time (in months), with t = 1 corresponding to January. Determine the months of maximum and minimum sales. $S=56.25+9.50 \sin \frac{\pi t}{6}$

Find the product. Write your answer using exponents. (0.5) • (0.5)²

An assumption inherent in capital budgeting is that all positive net cash flows are reinvested at the MARR from the time they are realized until: (a) The end of the shortest-lived project (b) The end of the longest-lived project (c) The end of the respective project that generated the cash flow (d) The average of the lives of the projects included in the bundle

Determine whether the statement is true or false. Justify your answer. The equation $\sin ^{2} \theta+\cos ^{2} \theta=1+\tan ^{2} \theta$ is an identity, because $\sin ^{2}(0)+\cos ^{2}(0)=1$ and $1+\tan ^{2}(0)=1$

Use complex numbers to find an invertible matrix $P$ and a diagonal matrix $D$ such that $A=PDP^{-1}$.

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

Alana was working with dilations. She wondered, "What would happen if I multiplied each coordinate of a shape by 1/3?" Graph and connect the points below to form her dilated shape. Be sure to connect them in the order given. A (-1, -1) B (-1, 1) C (1, 2) D (2, -1) a. Alana graphed this shape by multiplying each of her original coordinates by 1/3. What do you think Alana's shape looked like before the dilation? Make a prediction. b. On the same graph, undo the dilation to show Alana's original shape. List the coordinates of the vertices of Alana's original shape. c. What did you do to each coordinate to undo the dilation? How did the shape change? d. Why do you think the shape changed in this way?

Zeke ran 4 miles in 45 minutes. If he keeps running at the same pace, how long will it take him to run 10 miles? What is his unit rate in miles per hour?

(a) sketch the curve represented by the parametric equations (indicate the orientation of the curve). Use a graphing utility to confirm your result. (b) Eliminate the parameter and write the corresponding rectangular equation whose graph represents the curve. Adjust the domain of the resulting rectangular equation, if necessary. $x=\sqrt{t}, y=1-t$

The times from a 100 meter race in seconds were: 12.5, 13.1, 11.9, 12.4, 12.7, 13.1, 12.6, and 12.2. What measure of center best represents the data? Explain.

Determine whether each relation is a function. $\{(1,1),(2,2),(3,5),(4,10),(5,15)\}$

Which contains more chemical energy, 1 kmol of $\mathrm{H}_{2}$ or 1 kmol of $\mathrm{H}_{2} \mathrm{O}$?