Consider the motion of the following objects. Assume the x-axis is horizontal, the positive y-axis is vertical, the ground is horizontal, and only the gravitational force acts on the object. A projectile is launched from a platform $20 \mathrm{ft}$ above the ground at an angle of $60^{\circ}$ above the horizontal with a speed of $250 \mathrm{ft} / \mathrm{s}$. Assume the origin is at the base of the platform. Determine the time of flight and range of the object.

Write the reciprocal of the number. -8

The effect on the graph of $y=\log _{3} x$ if it is transformed to $y=\log _{3} \sqrt{x+7}$ can be described as A. a vertical stretch about the x-axis by a factor of $\frac{1}{2}$ and a vertical translation of 7 units up B. a vertical stretch about the x-axis by a factor of $\frac{1}{2}$ and a horizontal translation of 7 units left C. a horizontal stretch about the y-axis by a factor of $\frac{1}{2}$ and a vertical translation of 7 units up D. a horizontal stretch about the y-axis by a factor of $\frac{1}{2}$ and a horizontal translation of 7 units left

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

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

True or False? Let $r(x)=\frac{x^{2}+x}{(x+1)(2 x-4)}.$ The graph of r has (a) vertical asymptote x = -1. (b) vertical asymptote x = 2. (c) horizontal asymptote y = 1. (d) horizontal asymptote $y=\frac{1}{2}.$

A $1200-\mathrm{kg}$ car rolling on a horizontal surface has speed $v=66 \mathrm{~km} / \mathrm{h}$ when it strikes a horizontal coiled spring and is brought to rest in a distance of $2.2 \mathrm{~m}$. What is the spring constant of the spring?

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

Which of these statements is scientifically correct?
"The mass of the student is $56 \mathrm{~kg}$."
"The weight of the student is $56 \mathrm{~kg}$."

Sketch the level curves $f(x,y)=k$ of the function for the indicated values of $k$.

$$f(x,y)=\ln (x+y);\hspace{6pt}k=-2,-1,0,1,2$$

Write the number as a fraction. 49

(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). $f(x)=3 x^{2}-12 x+4$

Decide whether the following statements are possible for some angle $\theta$, or impossible,

$$\cos \theta=\frac{3}{2}$$

Write pseudocode for Strassen’s algorithm.