Find the exact value of each expression, if it exists. $\cos ^{-1}\left(-\frac{\sqrt{3}}{2}\right)$

Express the following in completed square form. (a) $x^{2}+2 x+2$ (b) $x^{2}-8 x-3$ (c) $x^{2}+3 x-7$ (d) $5-6 x+x^{2}$ (e) $x^{2}+14 x+49$ (f) $2 x^{2}+12 x-5$ (g) $3 x^{2}-12 x+3$ (h) $7-8 x-4 x^{2}$ (i) $2 x^{2}+5 x-3$

Find the determinant of each matrix. than find the inverse of the matrix, if it exists.

$$\left[\begin{array}{rr} -4 & -7 \\ 6 & 9 \end{array}\right]$$

A one-to-one function is given. Write an equation for the inverse function. $g(x)=b(x+a)^{3}+c$

Use the graph of f(x) to describe the transformation that results in the graph of g(x). than sketch the graphs of f(x) and g(x). $f(x)=\ln x ; g(x)=\ln (-x)$

The nth term of a sequence is given. Write the first four terms of the sequence. $b_{n}=\sqrt{n-1}$

The function g is defined by $g(x) = 2f(x+3) - 4$. Explain how the behavior of function g compares to the behavior of function f.

The motion of an object traveling along a straight path is given by $s(t)=\frac{1}{2} a t^{2}+v_{0} t+s_{0},$ where s(t) is the position relative to the origin at time t. For this exercise, three observed data points are given. Find the yalues of a, $\(v_{0},\) and \(s_{0}\).$ $s(1)=-7, s(2)=12, s(3)=37$

A spider is slowly climbing up a wall. Brianna is standing 6 feet away from the wall watching the spider. Let d be the distance Brianna is from the spider and $\theta$ be the angle of elevation of the spider from Brianna. Approximately how far away is the spider from Brianna when the angle of elevation is $32^{\circ} ?$

Solve each equation. $\frac{4}{x3}-\frac{2}{x 1}=\frac{2}{15}$

A lab received a sample of an isotope of cobalt in 1999. The amount of cobalt in grams remaining per year is shown in the table below.

$$\begin{array}{|l|c|c|c|c|c|c|c|c|} \hline \text { Teals } & 2000 & 2001 & 2002 & 2003 & 2004 & 2005 & 2006 & 2007 \\ \hline \text { Cobalt }(\mathrm{g}) & 877 & 769 & 674 & 591 & 518 & 454 & 398 & 349 \\ \hline \end{array}$$

Find a logarithmic function to model the data. Let x=1 represent 2000.

What is the basic idea behind the PageRank algorithm?

Evaluate each expression. $\log _{\sqrt[7]{4}} 64$

Determine the standard form of an equation of a hyperbola with eccentricity $\frac{5}{4}$ and vertices (- 1, 1) and (7, - 1).