From the list below, supply the words needed to complete [he paragraph. Some words will not be used. Laggard, entice, gambit, obsequy, denizen, fealty, gratify. The king knew that his plan for a surprise attack would be a[n] ______ that would test the _____ of his soldiers, but it was the only chance he had of thwarting the invading fleet. Speed would be the key to success; one ______ in the ranks could jeopardize the entire operation if the soldier were not in place at the right time, As an incentive to fight well, the king promised to each soldier with twenty acres of land after the battle. The promise was unprecedented, but on the other hand, if the army should fail, then the soldiers would be lucky to receive proper _____ because the invaders did not plan to take prisoners.

Complete the given tables.

$$\begin{matrix} \text{Exponential Form} & \text{}{10^{4}=10,000} & \text{}{4^{2}=16} & \text{}{3^{3}=27} & \text{}{5^{1}=5} & \text{}{7^{0}=1} & \text{}{4^{-2}=\frac{1}{16}}\\ \text{Logarithmic Form} & \text{} & \text{} & \text{} & \text{} & \text{} & \text{}\\ \end{matrix}$$

Write the first five terms of the sequence defined recursively. $a_{0}=-1, a_{1}=5, a_{k}=a_{k-2}+a_{k-1}$

a. Draw a graph to verify that $0 \leq x^{2} \sec x^{2} \leq x^{4}+x^{2}$ for x near 0. b. Use the Squeeze Theorem to determine $\lim _{x \rightarrow 0} x^{2} \sec x^{2}$.

Complete the sentence in a way that shows you understand the meaning of the italicized vocabulary word. Uncle Phil was admittedly a male chauvinist who believed that...

Factor the expression.

$$p^{2}+3 p-54$$

Each branch of $y=\sec x$ and $y=\csc x$ is a curve. Explain why these curves cannot be parabolas.

Find the degree of the polynomial.

$$-3p^4r^5t^2$$

Find the eccentricities of the ellipses and hyperbolas. Sketch each conic section. Include the foci, vertices, and asymptotes (as appropriate) in your sketch.

$$16 x ^ { 2 } + 7 y ^ { 2 } = 112$$

The revenues R (in millions of dollars) for Priceline Group from 2004 through 2013 can be approximated by the model $R=86.727 t^{2}-839.83 t+2967.9,4 \leq t \leq 13$ where t is the year, with t = 4 corresponding to 2004. (a) Use a graphing utility to graph the model in an appropriate viewing window. (b) Use the zoom and trace features of the graphing utility to estimate when the revenue reached 4 billion dollars. (c) Algebraically find when the revenue reached 4 billion dollars. (d) Use the model to predict when the revenue will reach 10 billion dollars.

Use a graphing utility to graph the first 10 terms of the sequence. $a_{n}=20(0.85)^{n-1}$

Complete the statement with always, sometimes, or never. Explain your reasoning. Two lines that are not parallel _ intersect.

Omar has $84 and Calina has$12. How much money must Omar give to Calina so that Calina will have three times as much as Omar? a. Solve the problem above by setting up an equation. b. In your opinion, is this problem easier to solve using an equation or using a tape diagram? Why?

The endpoints of the diameter of a circle are (−3, 4) and (1, −8). (a) Find the coordinates of the endpoints when the circle is shifted 5 units to the left. (b) Write the standard form of the equation of the circle following the translation in part (a).