Use the letters A, B, C, D, E, and F. Write all possible selections of three letters that can be formed from the letters. (The order of the three letters is not important.)

Solve the inequality. Graph your solution. -6y < -36

Find dy/dx amd d²y/dx² at the given point without eliminating the parameter.

$$x = \theta + \cos \theta , y = 1 + \sin \theta ; \theta = \pi / 6$$

Describe how to find the inverse function of a one-to-one function given by an equation in x and y. Give an example.

Taylor's gross monthly pay is $2,500. How much does Taylor pay for Social Security, which is 6.2% of his monthly salary? (A)$130.82 (B) $155 (C)$2,240.82 (D) $2,655

Mobile telephones perform handoffs as they move from cell to cell. During a call, a telephone either performs zero handoffs $\left(H_{0}\right)$, one handoff $\left(H_{1}\right)$, or more than one handoff $\left(H_{2}\right)$. In addition, each call is either long (L), if it lasts more than three minutes, or brief (B). The following table describes the probabilities of the possible types of calls.

$$\begin{matrix} & \text{}{H_{0}} & \text{}{H_{1}} & \text{}{H_{2}}\\ \text{L} & \text{0.1} & \text{0.1} & \text{0.2}\\ \text{B} & \text{0.4} & \text{0.1} & \text{0.1}\\ \end{matrix}$$

(a) What is the probability that a brief call will have no handoffs? (b) What is the probability that a call with one handoff will be long? (c) What is the probability that a long call will have one or more handoffs?

Prove the identity.

$$cos3x+cosx=2cos2xcox$$

For what type of variable does it makes sense to construct a confidence interval about a population mean?

Solve each system of equations.

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

Find values of x, y, and $\lambda$ that satisfy the system. These systems arise in certain optimization problems in calculus. ($\lambda$ is called a Lagrange multiplier.)

$$\left\{\begin{array}{r}{y+\lambda=0} \\ {x+\lambda=0} \\ {x+y-10=0}\end{array}\right.$$

Complete the table for the set of parametric equations. Plot the points (x, y) and sketch a graph of the parametric equations.

$$\begin{array}{l}{x=\sqrt{t}} \\ {y=8-t}\end{array}$$

.

$$\begin{matrix} \text{t} & \text{0} & \text{1} & \text{2} & \text{3} & \text{4}\\ \text{x}\\ \text{y}\\ \end{matrix}$$

Use the Chain Rule to find the derivative of the following functions. y=

$$\left( 1 - e ^ { x } \right) ^ { 4 }$$

Graph the polar equation over the given interval. Use the integration capabilities of the graphing utility to approximate the length of the curve accurate to two decimal places. Polar Equation: r = e^θ Interval: 0 ≤ θ ≤ π

A hydraulic jump occurs in a 4-m-wide rectangular channel at a point where the slope changes from 3 m per 100 m upstream of the jump to h m per 100 m downstream of the jump. The depth and velocity of the uniform flow upstream of the jump are 0.5 m and 8 m/s, respectively. Determine the value of h if the flow downstream of the jump is to be uniform flow.