Determine the amplitude of each function. Then graph the function and y = sin x in the same rectangular coordinate system for

$$0 \leq x \leq 2 \pi.$$

y = 5 sin x

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

$$\begin{array} { l } { \text { Show that the correspondence } x \rightarrow 5 x \text { from } Z _ { 5 } \text { to } Z _ { 10 } \text { does not pre- } } \\ { \text { serve addition. } } \end{array}$$

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 $A=PDP^{-1}$.

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

The coordination number for $Mg^{2+}$ ion is usually six. Assuming this assumption holds, determine the anion coordination number in the following compounds: MgO

Solve the system using the elimination method.

$$\left. \begin{array} { l } { 5 x + y - z = 6 } \\ { x + y + z = 2 } \\ { 12 x + 4 y = 10 } \end{array} \right.$$

Graph the function. Compare the graph to the graph of

$$f ( x ) = | x + 3 | - 2$$

.

$$b ( x ) = | x + 3 | + 3$$

What aldehyde is needed to synthesize each amino acid by the Strecker synthesis: (a) valine; (b) leucine; (c) phenylalanine?

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?

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?

(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. $x=\sqrt{t}, y=1-t$