A change of state is a ________ change.

a. Simplify $(-1+i \sqrt{2})^{3}.$ b. Write $5+i \sqrt{2}$ in the form $a^{3} \operatorname{cis} \theta$ stating the exact values of a and $\theta.$ c. Find the exact solutions of $z^{3}=5+i \sqrt{2}.$ d. Hence, show that $\arctan \left(\frac{\sqrt{2}}{5}\right)+2 \pi=3 \arccos \left(\frac{-1}{\sqrt{3}}\right) .$

Many firms that offer franchise opportunities promote their organizations on the Internet. Identify a particular franchise business that exists in your community. Search the Internet for information about this franchise. What does the organization offer its members? What is the cost of becoming a franchisee? Would you ever consider starting this type of business yourself?

Peanuts are sold in 8-ounce and 12 -ounce packages. What is the fewest number of ounces you can buy of each package to have equal amounts of each package size?

An object attached to a horizontal spring is oscillating back and forth along a friction less surface . The maximum speed of the object is 1.25 m/s, and its maximum acceleration is $6.89 \mathrm{m} / \mathrm{s}^{2}$. How much time elapses between an instant when the object's speed is at a maximum and the next instant when its acceleration is at a maximum?

Find the amplitude of a symmetrical square wave of period T that provides the same power as a sine wave of peak amplitude $\hat{V}$ and the same frequency. Does this result depend on equality of the frequencies of the two waveforms?

Graph the following by hand.

$$y=\left(\frac{1}{2}\right)^{x-1}$$

Find the derivative of the function.

$$f ( x ) = 3 x ^ { 2 } ( x - 1 )$$

If

$$\pi < t < \frac { 3 \pi } { 2 },$$

which of the following is true?

$$\left. \begin{array} { l } a.{ \sin t > 0 \text { and tan } t > 0 .} \\ b.{ \sin t < 0 \text { and tan } t < 0 .} \\ c.{ \tan t > 0 \text { and } \cot t > 0 .} \\ d.{ \tan t < 0 \text { and cot } t < 0 .} \end{array} \right.$$

Why is Earth called the "blue planet"?

The equation of a surface in spherical coordinates is given. Find the equation of the surface in rectangular coordinates. Identify and graph the surface. $\rho = 4 \csc \varphi$

Why did the growth of civilization make government necessary?

Find the limits.

$$\lim _ { t \rightarrow - 2 } \frac { t ^ { 3 } + 8 } { t + 2 }$$

Write an equation for each translation of y = -|x|. 2.25 units left