Determine the value of the literal numbers in each of the given matrix equalities. If the matrices cannot be equal, explain why.

$$\begin{bmatrix} x & 2y & z \\ r/4 & -s & -5t \end{bmatrix} = \begin{bmatrix} -2 & 10 & -9 \\ 12 & -4 & 5 \end{bmatrix}$$

The _ of a plane wave is perpendicular to the direction of motion of this wave.

Write each English phrase as an algebraic expression. Then simplify the expression. Let x represent the number. The difference between the product of six and a number and negative two times the number

Find the indefinite integral.

$$\int \sqrt[3]{\tan x} \sec ^{2} x d x$$

Find $\mathcal L^{-1}\left\{ F(s)\right\}$ for the function $F$ defined below.

$$F(s)=\frac{e^{-2 s}-2 e^{-5 s}}{s^{3}}$$

Suppose we have a sinusoidal current i(t) that has an rms value of 5 A, has a period of 10 ms, and reaches a positive peak at t = 3 ms. Write an expression for i(t).

For problem

$$\overrightarrow{\textbf{x}}'=\begin{bmatrix}1&4\\2&3\end{bmatrix}\overrightarrow{\textbf{x}}+\begin{bmatrix}t\\2t\end{bmatrix}$$

, construct appropriate diagonalizing matrices, decouple the linear system, then solve the nonhomogeneous system.

Tell how you know whether each number is prime or composite. 29

A court decision has stated that the enrollment of each high school in Metropolis must be at least 20 percent black, the numbers of black and white high school students in each of the city’s five school districts are shown in Table 90. The distance (in miles) that a student in each district must travel to each high school is shown in Table 91. School board policy requires that all the students in a given district attend the same school. Assuming that each school must have an enrollment of at least 150 students, formulate an IP that will minimize the total distance that Metropolis students must travel to high school. TABLE 90:

$$\begin{matrix} \text{District} & \text{Whites} & \text{Blacks}\\ \text{1} & \text{80} & \text{30}\\ \text{2} & \text{70} & \text{5}\\ \text{3} & \text{90} & \text{10}\\ \text{4} & \text{50} & \text{40}\\ \text{5} & \text{60} & \text{30}\\ \end{matrix}$$

TABLE 91:

$$\begin{matrix} \text{District} & \text{High School 1} & \text{High School 2}\\ \text{1} & \text{1} & \text{2}\\ \text{2} & \text{0.5} & \text{1.7}\\ \text{3} & \text{0.8} & \text{0.8}\\ \text{4} & \text{1.3} & \text{0.4}\\ \text{5} & \text{1.5} & \text{0.6}\\ \end{matrix}$$

The normal strain in the $45^{\circ}$ direction on the surface of a circular tube is $880 \times 10^{-6}$ when the torque $T=750 \mathrm{lb}-\mathrm{in}$. The tube is made of copper alloy with $G=6.2 \times 10^{6} \mathrm{psi.}$ If the outside diameter $d_{2}$ of the tube is 0.8 in., what is the inside diameter $d_{1}$?

Compare. Write <, >, or =.

$$2 m \square 275 cm$$

Predict whether each of the following molecules is polar or nonpolar:

$$PCl_3$$

Find each unknown number. Check your work. 365+P=653

Draw the circuit symbol and give the truth table for a positive-edge- triggered D flip-flop.