The following data are the equilibrium vapor pressure of limonene, $C _{10} H _{10}$, at various temperatures. (Limonene is used as a scent in commercial products.)

$$\begin{array}{cc} \text { Temperature }\left({ }^{\circ} C \right) & \text { Vapor Pressure }( mm Hg ) \\ \hline 14.0 & 1.0 \\ 53.8 & 10 . \\ 84.3 & 40 . \\ 108.3 & 100 . \\ 151.4 & 400 . \\ \hline \end{array}$$

Plot these data as $\ln P$ versus $1 / T$ so that you have a graph resembling the one in

What kinds of salts hydrolyze water?

In banking circles. the "Rule of 70 " states that the time (in years) required for the value of an account to double in value can be approximated by dividing 70 by the annual interest rate (as a percentage, not a decimal). What is the reasoning behind this rule?

If $10$ grams of salt is added to a quantity of water, then the amount $q(t)$ that is undissolved after $t$ minutes is given by $q(t) = 10\left(\dfrac{4}{5}\right)^t$. Sketch a graph that shows the value $q(t)$ at any time from $t = 0$ to $t = 10$.

Explain why the $\mathrm{pH}$ does not change significantly when a small amount of an acid or a base is added to a solution that contains equal amounts of the acid $\mathrm{H}_3 \mathrm{PO}_4$ and a salt of its conjugate base $\mathrm{NaH}_2 \mathrm{PO}_4$.

A car rounds a banked curve where the radius of curvature of the road is R, the banking angle is $\theta$, and the coefficient of static friction is $\mu$. Determine the range of speeds the car can have without slipping up or down the road.

Find the integral by using the simplest method. Not all problems require integration by parts. $\int ( \ln x ) ^ { 2 } d x$

Use the traditional square of opposition to find the answers to these problems. When a statement is given as false, simply enter an “F” into the square of opposition and compute (if possible) the other truth values. If “All fashion fads are products of commercial brainwashing” is false, what is the truth value of the following statements? a. No fashion fads are products of commercial brainwashing. b. Some fashion fads are products of commercial brainwashing. c. Some fashion fads are not products of commercial brainwashing.

Find the integral by using the simplest method. Not all problems require integration by parts. $\int x ^ { 2 } \cos x d x$

What tissue is calcified by mineral salts?

A marker buoy consisting of a cylinder and cone has the dimensions shown and weighs 625 lb when out of the water. Determine the protrusion h when the buoy is floating in salt water. The buoy is weighted so that a low center of mass ensures stability.

Rewrite the equation in slope intercept form. Then determine whether the lines are parallel. Explain.

$$\begin{aligned} 2 y &=x+15 \\ x &=2 y+5 \end{aligned}$$

In given problem, perform indicated integration.

$$\int \frac{\sin \left(\ln 4 x^2\right)}{x} d x$$

Foci: (0,0), (0,8), major axis of length 16