At $t = 0$, a flywheel has an angular velocity of $4.7\text{~ rad/s}$, a constant angular acceleration of $-0.25\text{~ rad/s}^2$, and a reference line at $\theta_0 = 0$. Graph $\theta$ versus t, and indicate your answers.

Use a calculator to evaluate each function. Round your answers to four decimal places. (Be sure the calculator is in the correct angle mode.) $\cot 11^{\circ} 15^{\prime}$

Write the augmented matrix for each system of equations.

$$\left\{\begin{array}{l}2 x+9 y=10 \\ 3 x-z=8 \\ 5 z+5=13 y\end{array}\right.$$

Break into groups of two or three. Just by looking at patterns in Pascal’s triangle, guess the answers to the following questions. (It is easier to make a conjecture from a pattern than it is to construct a proof!)If p is a prime number, what do all the interior numbers along the pth row have in common?

Solve the absolute value equation.

$$|1-3 b|=-7$$

A prime number is called a Mersenne prime if it can be written in the form $2^p - 1$ for some positive integer p. Write a program that finds all Mersenne primes with $p \le 31$ and displays the output as follows:

p   2^p - 1
2   3
3   7
5   31
...

In this exercise, use a calculator to evaluate each function. Round your answers to four decimal places. (Be sure the calculator is in the correct angle mode.)

$$\sec 42^{\circ} 12^{\prime}$$

Change the Cartesian integral into an equivalent polar integral. Then evaluate the polar integral. \

$$\displaystyle\int_0^2 \int_0^{\sqrt{1-(x-1)^2}} \frac{x+y}{x^2+y^2} d y d x$$

Draw a Venn diagram to represent the following conditional statement. number is an integer if it is a whole number.

Determine whether the statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.

We can immediately tell that $6 x^2-11 x y-10 y^2$ is prime because 11 is a prime number and the polynomial contains two variables.

Find the mean, median, mode, and range of each set of data.

$$\begin{array}{ccccc}{5} & {8} & {11} & {13} & {5} \\ {9} & {2} & {4} & {6}\end{array}$$

Write all classifications that apply to each real number. -12

Calculate the angular momentum of ${ }^7 \mathrm{Li}_2$ in the $J=$ 5 state.

Write all classifications that apply to each real number. -32