find the determinant of the matrix. Expand by cofactors using the indicated row or column. [6 0 -3 5 , 4 13 6 -8 , -1 0 7 4 , 8 6 0 2] Row 2

Solve for

$$\theta , 0 ^ { \circ } \leq \theta < 360 ^ { \circ }$$

, or for x,

$$0 \leq x < 2 \pi$$

.

$$\sin \left( 3 \theta - 25 ^ { \circ } \right) = \frac { \sqrt { 3 } } { 2 }$$

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

Why is the weather in New York State consistently cooler in January than it is in July? (1) Earth is closer to the sun in July (2) Cloudy weather is more common in January (3) The Northern Hemisphere is tilted away from the sun in January. (4) Sunlight is reflected away from Earth by ice and snow during January

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

Solve the equation.

$$( 2 b + 29 ) ^ { 1 / 3 } = 3$$

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

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

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

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 $1+\tan ^{2}(0)=1$

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?