A volcano erupts in a powerful explosion. The sound from the explosion is heard in all directions for many hundreds of kilometers. The speed of sound is about 340 meters per second.

(a) Fill in the table below showing the distance, $d$, that the sound of the explosion has traveled at time $t$. Write a formula for $d$ as a function of $t$.

Time, $t$	$5 \mathrm{sec}$	$10 \mathrm{sec}$	$1 \mathrm{~min}$	$5 \mathrm{~min}$
Distance, $d(\mathrm{~km})$
Area, $A\left(\mathrm{~km}^2\right)$

(b) How long after the explosion will a person living 200 km away hear the explosion?

(c) Fill in the table below showing the land area, $A$, over which the explosion can be heard as a function of time. Write a formula for $A$ as a function of $t$.

Time, $t$	$5 \mathrm{sec}$	$10 \mathrm{sec}$	$1 \mathrm{~min}$	$5 \mathrm{~min}$
Distance, $d(\mathrm{~km})$
Area, $A\left(\mathrm{~km}^2\right)$

(d) The average population density around the volcano is 31 people per square kilometer. Write a formula for $P$ as function of $t$, where $P$ is the number of people who have heard the explosion at time $t$.

(e) Graph the function $P=f(t)$. How long will it take until 1 million people have heard the explosion?

In the following exercise, simplify, if possible.

$$\frac{(w+2) / 2}{w+2}$$

In the following exercise, split into a sum or difference of reduced fractions.

$$\frac{\frac{1}{3} x-\frac{1}{2}}{2 x}$$

Evaporating water into air cools the air; a swamp cooler works by evaporation. The wet-bulb temperature of air is the temperature that the air would have if it were cooled to saturation ( 100% humidity) by evaporating water into it. The amount of cooling possible with a swamp cooler is proportional to the difference between the actual air temperature, $T$, and the wet-bulb temperature, $W$. A particular swamp cooler can cool air at a temperature of $40^{\circ} \mathrm{Cel}-$ sius to $23^{\circ}$ Celsius if the wet-bulb temperature is $20^{\circ} \mathrm{Ce}$ sius. Determine the lowest temperature that this swamp cooler could achieve:

(a) In Phoenix, where the actual temperature is $48^{\circ} \mathrm{C}$ and the wet-bulb temperature is $22^{\circ} \mathrm{C}$.

(b) In Miami, where the actual temperature is $32^{\circ} \mathrm{C}$ and the wet-bulb temperature is $26^{\circ} \mathrm{C}$.

In the following exercise, simplify, if possible.

$$\frac{1 /(x+y)}{x+y}$$

In the following problem, find a possible formula for the rational functions.

The graph of y=h(x) has two vertical asymptotes: one at x=-2 and one at x=3. It has a horizontal asymptote of y=1. The graph of $h$ touches the x-axis once, at x=5.

Is the statement in the following problem true or false? Give an explanation for your answer.

Rational functions can never cross an asymptote.

Consider the function a(x)=x$^5$+2x$^3$-4x.

(a) Without using a calculator or computer, what can you say about the graph of a?

(b) Use a calculator or a computer to determine the zeros of this function to three decimal places.

(c) Explain why you think that you have all the possible zeros.

(d) What are the zeros of $b(x)=2x^5+4 x^3-8 x$? Does your answer surprise you?

Is the statement in the following problem true or false? Give an explanation for your answer.

In general, the rational function $r(x)=\frac{p(x)}{q(x)}$ must have at least one zero.

Given that a, b, and c are constants, a<b<c, state the domain of

$$y=\sqrt{(x-a)(x-b)(x-c)} .$$

[Hint: Graph y=(x-a)(x-b)(x-c).]

A bird flies 3.0 km due west and then 2.0 km due north. Another bird flies 2.0 km due west and 3.0 km due north. What is the angle between the net displacement vectors for the two birds? A. $23 ^ { \circ }$ B. $34 ^ { \circ }$ C. $56 ^ { \circ }$ D. $90 ^ { \circ }$

Your roommate drops a tennis ball from a third-story balcony. It hits the sidewalk and bounces as high as the second story. Draw a motion diagram, using the particle model, showing the ball's velocity vectors from the time it is released until it reaches the maximum height on its bounce.

Two friends watch a jogger complete a 400 m lap around the track in 100 s. One of the friends states, "The jogger's velocity was 4 m/s during this lap." The second friend objects, saying, "No, the jogger's speed was 4 m/s." Who is correct? Justify your answer.

In the following exercise, split into a sum or difference of reduced fractions.

$$\frac{7+p}{p^2+11}$$