How do L$\acute{o}$pe$\={z}$ de C$\acute{a}$rdenas's experiences with the rough Grand Canyon terrain influence which details he includes in his narrative?

If a cup of coffee has a temperature $95^{\circ} C$ in a room where the temperature is $20^{\circ} C$, then, according to Newton's Law of Cooling, the temperature of the coffee after $t$ minutes is $T(t)=20+75 e^{-t / 50}$. What is the average temperature of the coffee during the first half hour?

Solve. The product of two numbers is 1, and the difference of their square is

$$\frac { 15 } { 4 }$$

. Find the numbers.

(a) Find all the critical numbers of f where $f(x)=-2 x^{3}-3 x^{2}-4$. (b) Use the equation and a rough sketch of the graph of f to find the values of x at which f attains local maximum or minimum values.

Deuterium makes up 0.0115% of natural hydrogen on average. Make a rough estimate of the total deuterium in the Earth's oceans and estimate the total energy released if all of it were used in fusion reactors.

A cup of coffee is removed from a microwave oven with a temperature of $80^{\circ} \mathrm{C}$ and allowed to cool in a room with a temperature of $25^{\circ} \mathrm{C}$. Five minutes later, the temperature of the coffee is $60^{\circ} \mathrm{C}$. When does the temperature of the coffee reach $50^{\circ} \mathrm{C}$ ?

Figure 8-33 shows a $1.75-\mathrm{kg}$ block at rest on a ramp of height h. When the block is released, it slides without friction to the bottom of the ramp, and then continues across a surface that is frictionless except for a rough patch of width $10.0 \mathrm{~cm}$ that has a coefficient of kinetic friction $\mu_{\mathrm{k}}=0.640$. Find $h$ such that the block's speed after crossing the rough patch is $3.50 \mathrm{~m} / \mathrm{s}$.

Which bone forms the anterior portion of the pelvic bone?

For this exercise, find a pair of factors for the given number below by using the difference of two squares.

224

Use a graph to give a rough estimate of the area of the region that lies beneath the given curve. Then find the exact area.

$$y = \sec ^ { 2 } x , 0 \leqslant x \leqslant \pi / 3$$

Consider a wall made of brick 10 cm thick, which separates a room in a house from the outside. The room is kept at $20^{\circ}$. (a) Originally the outside temperature is $10^{\circ} \mathrm{C}$ and the temperature in the wall has reached steady state. What is the temperature in the wall at this point? (b) There is a sudden.cold snap and the outside temperature drops to $-10^{\circ} \mathrm{C}$. Find the temperature in the wall as a function of position and time.

In each part, make a rough sketch of the graph using asymptotes and appropriate limits but no derivatives. Compare your graph to that generated with a graphing utility.

$$y = \frac { x ^ { 2 } } { x ^ { 2 } - x - 2 }$$

Use Newton’s Law of Cooling, $T = C + (T_0 - C)e^{kt}$, to solve this exercise. You are served a cup of coffee that has a temperature of $185^{\circ}\mathrm{F}$. The room temperature is $65^{\circ}\mathrm{F}$. After $2$ minutes, the temperature of the coffee is $155^{\circ}\mathrm{F}$.

a. Write a model for the temperature of the coffee, $T$, after $t$ minutes.

b. When will the temperature of the coffee be $105^{\circ}\mathrm{F}$?

Categorize each of the following as a specular or a diffuse reflecting surface: paper, polished metal, window glass, rough metal, plastic milk jug, smooth water surface, and ground glass.