If a walkway rises 2 ft for every 10 ft on the horizontal, which of the following express its slope (or grade)? (There are several correct choices.) A. 0.2, B. $\frac{2}{10}$, C. $\frac{1}{5}$, D. 20%, E. 5, F. $\frac{20}{100}$, G. 500%, H. $\frac{10}{2}$, I. -5.

A function $y=g(x)$ is described by some geometric property of its graph. Write a differential equation of the form $d y / d x = f ( x , y )$ having the function g as its solution (or as one of its solutions): Every straight line normal to the graph of $g$ passes through the point $(0,1)$. Can you guess what the graph of such a function $g$ might look like?

Let $\alpha \text { and } \beta$ be complex constants and let $z \neq 0$. Show that the following identities hold when each power function is given by its principal branch. a) $z ^ { - \alpha } = 1 / z ^ { \alpha }$ b) $z ^ { \alpha } z ^ { \beta } = z ^ { \alpha + \beta }$ c) $\frac { z ^ { \alpha } } { z ^ { \beta } } = z ^ { \alpha - \beta }$

Match the rational function in Column I with the appropriate description in Column II. Choices in Column II can be used only once.

$$\begin{matrix} \text{I} & \text{II}\\ \text{}{ f(x)=\frac{x+7}{x+1}} & \text{A. The x-intercept is ( - 3, 0).}\\ \text{ } & \text{B. They-intercept is (0, 5).}\\ \text{ } & \text{C. The horizontal asymptote is y = 4.}\\ \text{ } & \text{D. The vertical asymptote is x = - 1.}\\ \text{ } & \text{E. There is a hole in its graph at (- 4, - 8).}\\ \text{ } & \text{F. The graph has an oblique asymptote.}\\ \text{ } & \text{G. The x-axis is its horizontal asymptote, and the y-axis is not its vertical asyn1ptote.}\\ \text{ } & \text{H. The x-axis is its horizontal asymptote, and the y-axis is its vertical asymptote.}\\ \end{matrix}$$

Calculate without using a calculator.

$$\ln \left( \sqrt { e } \cdot e ^ { 7 / 5 } \right)$$

¿Qué hacían tus amigos cuando eran niños? Escribe una oración para cada actividad de tus amigos y sus familias

1. alquilar/ videos/ todos los domingos por la tarde
2. bailar/ en la discoteca/ los sábados por la noche
3. cantar/ en voz alta/ en la ducha
4. cocinar/ para su familia/ una vez por semana
5. escuchar/ música rap/ en el coche

At the north magnetic pole the earth’s magnetic field is vertical and has a strength of 0.62 gauss. The earth’s field at the surface and further out is approximately that of a central dipole. (a) What is the magnitude of the dipole moment in joules/tesla? (b) Imagine that the source of the field is a current ring on the “equator” of the earth’s metallic core, which has a radius of 3000 km, about half the earth’s radius. How large would the current have to be?

Use one of the perspectives on social change to describe social change you have witnesses or about which you have learned.

For each expression in Column I, use an identity to choose an expression from Column II with the same value. $\sin 35^{\circ}$, A. $\sin \left(-35^{\circ}\right)$, B. $\cos 55^{\circ}$, C. $\sqrt{\frac{1+\cos 150^{\circ}}{2}}$, D. $2 \sin 150^{\circ} \cos 150^{\circ}$, E. $\cos 150^{\circ} \cos 60^{\circ}$, F. $\cot \left(-35^{\circ}\right)$, G. $\cos ^{2} 150^{\circ}-\sin ^{2} 150^{\circ}$, H. $\sin 15^{\circ} \cos 60^{\circ}+\cos 15^{\circ} \sin 60^{\circ}$, I. $\cos \left(-35^{\circ}\right)$, J. $\cot 125^{\circ}$

Convert the rectangular equation to polar form and sketch its graph. $x ^ { 2 } + y ^ { 2 } = 16$

Outline the successive stages in the formation of coal.

On a farm, you are pushing on a stubborn pig with a constant horizontal force with magnitude 30.0 N and direction $37.0^{\circ}$ counterclockwise from the +x-axis. How much work does this force do during a displacement of the pig that is (a) $\vec{s}=(5.00 \mathrm{m}) \hat{\imath}$; (b) $\vec{s}=-(6.00 \mathrm{m}) \hat{\jmath}$; (c) $\vec{s}=-(2.00 \mathrm{m}) \hat{\imath}+(4.00 \mathrm{m}) \hat{\jmath}$?

(a) Fill out a plot diagram like the one shown. Identify two key events in the rising action of the story, the event that marks the climax, and one event that is part of the falling action. (b) Citing details from the text, explain the plot's resolution.

Karl bought a pair of jeans for $25 at a store in California, where the sales tax is 6.5%. He was charged$1.45 in sales tax. Is this correct? Explain why or why not.