Convert the polar equation to rectangular form and sketch its graph.

r=3

In the following symbolized arguments, derive the line needed to obtain the conclusion (last line), and supply the justification for both lines. $1. H \supset(\sim C \vee R) \\ 2. \text{\_\_\_\_\_\_ \_\_\_\_} \\ 3. (H \cdot C) \supset R \text{\_\_\_\_\_\_}$

For each of the following lists of premises, derive the conclusion and supply the justification for it. There is only one possible answer for each problem. $1. \ \sim C \supset \sim F \\ 2. \ L \supset F \\ 3. \ \sim \sim F \\ 4. \ F \vee \sim L \\ {\text{ 5. \_\_\_\_\_\_ \_\_\_\_} }$

In the following symbolized arguments, derive the line needed to obtain the conclusion (last line ), and supply the justification for both lines. $1. K \vee C \\ 2. \sim C \\ 3. \text{\_\_\_\_\_ \_\_\_\_} \\ 4. K \text{\_\_\_\_}$

Solve the absolute value inequality. Write solutions in interval notation. Check solutions by back substitution, or using a calculator. $|2-3 u|+5 \leq 4$

Determine whether the statement is true or folse. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.

If $f(x, y)$ has two local maxima, then $f$ must have a local minimum.

Convert the given equation to polar coordinates and then sketch the graph.

$$x^2+y^2=25$$

Sketch the graph of each polar equation. $r=5 \cos 3 \theta$

Smiling Cow Dairy can sell all the milk it wants for $4 a gallon, and it can rent all the robots it wants to milk the cows at a capital rental price of$100 a day. It faces the following production schedule:

$$\begin{array}{cc} \begin{array}{c} \text { Number of } \\ \text { Robots } \end{array} & \begin{array}{c} \text { Total } \\ \text { Product } \end{array} \\ \hline 0 & 0 \text { gallons } \\ 1 & 50 \\ 2 & 85 \\ 3 & 115 \\ 4 & 140 \\ 5 & 150 \\ 6 & 155 \end{array}$$

Calculate the marginal product and the value of the marginal product for each additional robot.

Write the given equation in polar coordinates. Then isolate the variable $r$ when possible.

$$y=-x$$

The mean for a particular test is 1200 and the standard deviation is 150. Find the z-value for each score:

a. 1150

b. 1430

c. 1560

d. 1090

e. 850

Choose the word that could be substituted for the italicized word or phrase in the sentence below. Wounded soldiers were seen falling back all over the battlefield.

What evolutionary advances are seen in the phyla of bilaterally symmetrical worms?

Find the inverse of f(x) algebraically. Hint: After swapping variables make a substitution: $u=e^y$. Solve for u then back-substitute to find y.

$$f(x)=\dfrac{e^x-e^{-x}}{2}$$