Make the indicated pressure conversions.
d. $99,436 \mathrm{~Pa}$ to kilopascals

If $R$ denotes the reaction of the body to some stimulus of strength $x$, the sensitivity $S$ is defined to be the rate of change of the reaction with respect to $x$. A particular example is that when the brightness $x$ of a light source is increased, the eye reacts by decreasing the area $R$ of the pupil. The experimental formula

$$R=\frac{40+24 x^{0.4}}{1+4 x^{0.4}}$$

describes the dependence of $R$ on $x$ when $R$ is measured in square millimeters and $x$ is measured in appropriate units of brightness.

Find the sensitivity.

Illustrate above part by graphing both $R$ and $S$ as functions of $x$. Comment on the values of $R$ and $S$ at low levels of brightness. Is this what you would expect?

Suggest why $\mathrm{Be}^{2+}$ has a higher affinity for $\mathrm{H}_2 \mathrm{O}$ molecules than $\mathrm{Mg}^{2+}$.

For each of the following reactions, give the substitution products; if the products can exist as stereoisomers, show what stereoisomers are obtained: a. (R)-2-bromopentane + high concentration of $\mathrm{CH}_3 \mathrm{O}^{-}$ d. (R)-3-bromo-3-methylhexane $+\mathrm{CH}_3 \mathrm{OH}$ b. trans-1-bromo-4-methylcyclohexane $+$ high concentration of $\mathrm{CH}_3 \mathrm{O}^{-}$ e. 1-bromo-1-methylcyclohexane $+\mathrm{CH}_3 \mathrm{OH}$ c. 3-bromo-3-methylpentane $+\mathrm{CH}_3 \mathrm{OH}$

Select the best choice for each of the following:

a. Higher $\mathrm{N}-\mathrm{O}$ stretching frequency:

$$\left[\mathrm{Fe}(\mathrm{NO})(\mathrm{mnt})_2\right]^{-}\left[\mathrm{Fe}(\mathrm{NO})(\mathrm{mnt})_2\right]^{2^{-}}$$

b. Longest $\mathrm{N}-\mathrm{N}$ bond:

$$\mathrm{N}_2$$

$$(\mathrm{CO})_5 \mathrm{Cr}: \mathrm{N} \equiv \mathrm{N}$$

$$(\mathrm{CO})_5 \mathrm{Cr}: \mathrm{N} \equiv \mathrm{N}: \mathrm{Cr}(\mathrm{CO})_5$$

c. Shorter $\mathrm{Ta}-\mathrm{C}$ distance in $\left(\eta^5-\mathrm{C}_5 \mathrm{H}_5\right)_2 \mathrm{Ta}\left(\mathrm{CH}_2\right)\left(\mathrm{CH}_3\right):$

$$\mathrm{Ta}-\mathrm{CH}_2$$

$$\mathrm{Ta}-\mathrm{CH}_3$$

d. Shortest $\mathrm{Cr}-\mathrm{C}$ distance: $\mathrm{Cr}(\mathrm{CO})_6$ $\mathrm{Cr}-\mathrm{CO}$ in trans $-\mathrm{Cr}(\mathrm{CO})_4 \mathrm{I}\left(\mathrm{CCH}_3\right)$ $\mathrm{Cr}-\mathrm{CCH}_3$ in trans $-\mathrm{Cr}(\mathrm{CO})_4 \mathrm{I}\left(\mathrm{CCH}_3\right)$

e. Lowest $\mathrm{C}-\mathrm{O}$ stretching frequency:

$$\mathrm{Ni}(\mathrm{CO})_4$$

$$\left[\mathrm{Co}(\mathrm{CO})_4\right]^{-}$$

$$\left[\mathrm{Fe}(\mathrm{CO})_4\right]^{2-}$$

By calculating numerical quantities for a multiparticle system, one can get a concrete sense of the meaning of the relationships $\vec{p}_\text{sys} =M_\text{tot}\vec{v}_\text{CM}$ and $K_\text{tot}=K_\text{trans} + K_\text{rel}$. Consider an object consisting of two balls connected by a spring, whose stiffness is 400 N/m. The object has been thrown through the air and is rotating and vibrating as it moves. At a particular instant the spring is stretched 0.3 m, and the two balls at the ends of the spring have the following masses and velocities:

$$\begin{align*} &\text{1: 5 kg, } \left\langle 8,14,0\right\rangle \text{ m/s} \\ &\text{2: 3 kg, } \left\langle -5,9,0\right\rangle \text{ m/s} \end{align*}$$

Calculate $\vec{v}_\text{CM}.$

Steam enters the turbine of a simple vapor power plant with a pressure of 12 MPa and a temperature of $600^{\circ} \mathrm{C}$ and expands adiabatically to condenser pressure, p. Saturated liquid exits the condenser at pressure p. The isentropic efficiency of both the turbine and the pump is 84%. a. For p = 30 kPa, determine the turbine exit quality and the cycle thermal efficiency. b. Plot the quantities of part (a) versus p ranging from 6 kPa to 100 kPa.

On the said page of Physics: Calculus by Eugene Hecht (Pacific Grove, CA: Brooks/Cole, 1996), in the course of deriving the formula $T=2 \pi \sqrt{L / g}$ for the period of a pendulum of length L, the author obtains the equation $a_T=-g \sin \theta$ for the tangential acceleration of the bob of the pendulum. He then says, "for small angles, the value of $\theta$ in radians is very nearly the value of $\sin \theta$; they differ by less than 2% out to about 20 degrees."

Use a graphing device to determine the values of x for which sin x and x differ by less than 2%. Then verify Hecht's statement by converting from radians to degrees.

Sketch the region of integration for the iterated integral, and reverse the order of integration.

$$\int_{-1}^{1} \int_{x^2}^{3-2x62} f(x,y)\ dy\ dx$$

HERE COME THE CLOWNS! is the name of a traveling circus. The ledger accounts as of the business at June 30, 2011, are listed here in alphabetical order:

$$\begin{array}{|cc} \text { Accounts Payable } & \$ 26,100 & \text{Notes Payable} & \$180,000 \\ \text { Accounts Receivable } & 7,450 & \text{Notes Receivable} & 9,500 \\ \text { Animals } & 189,060 & \text{ Props and Equipment} &89,580\\ \text {Cages } & 24,630 & \text {Retained Earnings} & 27,230\\ \text { Capital Stock } & 310,000 & \text{Salaries Payable} & 9,750 \\ \text {Cash } & ? & \text{Tents} &63,000 \\ \text { Costumes } & 31,500 & \text{Trucks and Wagons} & 105,840 \\ \end{array}$$

Instructions
a. Prepare a balance sheet by using these items and computing the amount of Cash at June 30, 2011. Organize your balance sheet similar to the one illustrated in Exhibit 2-10. (After "Accounts Receivable," you may list the remaining assets in any order.) Include a proper balance sheet heading.

Sketch the region of integration and write an equivalent integral with the order of integration reversed.

$$\int_{0}^{1} \int_{x}^{2-x} f(x, y) d y \ d x$$

Following is an incomplete current-year income statement.

$$\begin{array}{c} \textbf{Income Statement} \end{array}$$

$$\begin{array}{lcc} \text{Net sales}&\text{\$\hspace{5pt}(a)}\\ \text{Cost of goods sold}&\text{\hspace{11pt}(b)}\\ \text{Selling, general, and administrative expenses}&\text{\hspace{1pt}7,000}\\ \text{Income tax expense}&\underline{\text{\hspace{1pt}2,000}}\\ \text{Net income}&\underline{\underline{\text{\hspace{6pt}(c)\hspace{6pt}}}}\\ \end{array}$$

Determine amounts a, b, and c. Additional information follows:

• Return on total assets is 16% (average total assets is $68,750).
• Inventory turnover is 5 (average inventory is$6,000).
• Accounts receivable turnover is 8 (average accounts receivable is $6,250).

Refer to the example below.

a. Which outcome do you think is most likely?

b. Describe the three outcomes using the words likely and unlikely.

c. Use the number of times each event occurred to calculate the probability of each event.

d. What do you think would happen if you performed more trials?

$$\begin{array}{|l|c|} \hline {}{}{ Outcome } & Experimental Probability \\ \hline Open-end up & \frac{\text { open }-\text { end up }}{30}=\frac{}{30} \\ \hline Open-end down & \frac{\text { open }-\text { end down }}{30}=\frac{}{30} \\ \hline On its side & \frac{\text { on its side }}{30}=\frac{}{30} \\ \hline \end{array}$$

e. What is the sum of the three probabilities in question 1c?

Example:

You can toss a paper cup to demonstrate experimental probability.

Consider tossing a paper cup. What are the three different ways the cup could land?

Toss a paper cup thirty times. Record your observations in the table.

$$\begin{array}{|l|l|} \hline {}{}{\text { Outcome }} & \text { Number of Times } \\ \hline \text { Open-end up } & \\ \hline \text { Open-end down } & \\ \hline \text { On its side } & \\ \hline \end{array}$$

Give the total number of valence electrons in each of the following molecules.
c. $\mathrm{C}_2 \mathrm{H}_6 \mathrm{O}$