A $45.0-\mathrm{kg}$ crate is dragged at constant velocity $8.20 \mathrm{~m}$ across a horizontal floor with a rope making a $30^{\circ}$ angle above the horizontal. The coefficient of kinetic friction is $0.250$. Find the work done (a) by friction.

"A $5.00\text{-kg}$ object on a frictionless horizontal surface is attached to one end of a horizontal spring that has a force constant $k=700 \text{~N/m}$. The spring is stretched $8.00 \text{~cm}$ from equilibrium and released. What are $(b)$ the period, "

(a) Find the points, if any, at which the graph of each function f has a horizontal tangent line. (b) Find an equation for each horizontal tangent line. (c) Solve the inequality $f^{\prime}(x)>0$. (d) Solve the inequality $f^{\prime}(x)<0$. (e) Graph f and any horizontal lines found in (b) on the same set of axes. (f) Describe the graph of for the results obtained in parts (c) and (d). $f(x)=x^{3}-3 x+2$

(a) Find the points, if any, at which the graph of each function f has a horizontal tangent line. (b) Find an equation for each horizontal tangent line. (c) Solve the inequality $f^{\prime}(x)>0$. (d) Solve the inequality $f^{\prime}(x)<0$. (e) Graph f and any horizontal lines found in (b) on the same set of axes. (f) Describe the graph of f for the results obtained in (c) and (d). $f(x)=(x+1)\left(x^{2}-x-11\right)$

Write the reciprocal of the number. -8

Find the exact values of the six trigonometric functions of $\theta$ if the terminal side of $\theta$ in the standard position contains the given point.

$$(-3,-4)$$

Sum the series (if they converge).

$$\sum_{k=1}^{\infty} \frac{3^{2 k}+1}{27^k}$$

State the properties that graphs of the form $y=e^{k x}$ have in common when k is positive. When k is negative.

Write the prime factorization of 360.

(a) Find the points, if any, at which the graph of each function f has a horizontal tangent line. (b) Find an equation for each horizontal tangent line. (c) Solve the inequality $f^{\prime}(x)>0$. (d) Solve the inequality $f^{\prime}(x)<0$. (e) Graph f and any horizontal lines found in (b) on the same set of axes. (f) Describe the graph of f for the results obtained in (c) and (d). $f(x)=\frac{x^{2}-3}{e^{x}}$

Write an example of a cubic trinomial.

Write the number as a fraction. 49

A baseball is hit from a height of 3 feet at a $60^{\circ}$ angle above the horizontal. Its initial velocity is 64 feet per second.

Determine the horizontal distance traveled by the ball in the air. Assume that the ground is level.

Show that $\lim _{k \rightarrow \infty}\left(1+\frac{r}{k}\right)^{k}=e^{r}.$