A mountain lion is a(n) a. omnivore. b. herbivore. c.detritivore d. carnivore.

Cable car route As shown in the figure on the next page, a cable car carries passengers from a point $A$, which is $1.2$ miles from a point $B$ at the base of a mountain, to a point $P$ at the top of the mountain. The angles of elevation of $P$ from $A$ and $B$ are $21^{\circ}$ and $65^{\circ}$, respectively.

Approximate the height of the mountain. Tutorial available at www.thomsonedu.com/login

Use a calculator to evaluate each expression. Round answers to two decimal places. $7^{0.39}$

The surface of a mountain can be thought of as the graph of what function?

What are the subcategories of the ANS?

If you climbed a mountain carrying a mercury barometer, would the level of the mercury column in the glass tube of the barometer increase or decrease (compared to the mercury reservoir) as you climb the mountain? Explain

The switchbacks of a trail up the side of a mountain are an example of a/an____

Height of a mountain When a mountaintop is viewed from the point $P$ shown in the figure, the angle of elevation is $\alpha$. From a point $\bar{Q}$, which is $d$ miles closer to the mountain, the angle of elevation increases to $\beta$.

If $d=2 \mathrm{mi}, \alpha=15^{\circ}$, and $\beta=20^{\circ}$, approximate the height of the mountain.

Suppose that X, Y, and Z are independent Poisson random variables, each with a mean 1 . Find

a) $P(X+Y=4)$;

b) $E\left[(X+Y)^2\right]$

c) $P(X+Y+Z=4)$.

Why are temperatures in the thermosphere not strictly comparable to those experienced near Earth’s surface?

A woman stands at a horizontal distance $x$ from a mountain and measures the angle of elevation of the mountaintop above the horizontal as $\theta$. After walking a distance $d$ closer to the mountain on level ground, she finds the angle to be $\phi$. Find a general equation for the height $y$ of the mountain in terms of $d, \phi$, and $\theta$, neglecting the height of her eyes above the ground.

Find the solutions of the equation in the interval $[0,2 \pi)$. $\cos \left(x+\frac{\pi}{4}\right)-\cos \left(x-\frac{\pi}{4}\right)=1$

The surface of a mountain is modeled by the equation h(x, y) = 5000 - 0.001x$^2$ - 0.004y$^2$. A mountain climber is at the point $(500,300,4390)$. In what direction should the climber move in order to ascend at the greatest rate?

The surface of a mountain is modeled by the equation h(x, y) = 5000 - 0.001x² - 0.004y². A mountain climber is at the point (500, 300, 4390). In what direction should the climber move in order to ascend at the greatest rate?