Match the term with the correct synonym.

initially

a. major change, transformation b. altered, revised c. stipulation, provision d. originally, in the beginning e. situation, condition f. purpose, duty

Something most likely to be desolate a. Mars b. a town c. a huge skyscraper d. a busy highway

In the following exercise, find the slope of the line passing through the origin which satisfies the given additional condition.

The line forms an angle of $6 \pi / 7$ with the positive $x$-axis.

Use a graph to estimate the critical numbers of $f(x)=\left|x^3-3 x^2+2\right|$ correct to one decimal place.

You will explore functions to identify their local extrema. Use a CAS to perform the following steps:

Calculate the function’s first partial derivatives and use the CAS equation solver to find the critical points. How do the critical points relate to the level curves? Which critical points, if any, appear to give a saddle point? Give reasons for your answer.

$$f(x, y)=2 x^{4}+y^{4}-2 x^{2}-2 y^{2}+3, \quad -3 / 2 \leq x \leq 3 / 2, \quad -3 / 2 \leq y \leq 3 / 2$$

Kyle says the radian angle measure

$$\frac{5\pi}{2}$$

is between

$$180^\circ$$

and

$$360^\circ.$$

Is he correct? Explain your thinking. How many degrees is

$$\frac{5\pi}{2}$$

radians?

Find the general solution. If an initial condition is given, find the solution that passes through it. $y^{\prime \prime}-2 y^{\prime}-8 y=4 e^{2 x}-21 e^{-3 x}$

Plutonium 239 has a half-life of 24,400 years. How fast is a lump of 10 grams decaying after 100 years?

Use the binomial formula to expand each binomial See the mentioned example.

$$(b+c)^6$$

What is a solution? What are the solute and solvent?

Find the value(s) of c guaranteed by the Mean Value Theorem for Integrals for the function over the given interval.

$$f(x)=3 x^{2}, \quad[1,3]$$

A block has acceleration a when pulled by a string. If two identical blocks are glued together and pulled with twice the original force, their acceleration will be A. (1/4)a B. (1/2)a C. a D. 2a E. 4a

An aluminum block slides along a horizontal surface. The block has an initial speed of $10 \mathrm{~m} / \mathrm{s}$ and an initial temperature of $10^{\circ} \mathrm{C}$. The block eventually slides to rest due to friction. It is likely that at least a little bit of the heat energy will go toward heating the horizontal surface on which the block slides. Will this effect make the final temperature of the block larger or smaller?

Solve each differential equation with the given initial condition. $\frac{d y}{d x}=\frac{y+1}{x-1}, \text { with } y_{0}=5 \text { if } x_{0}=2$