In Fig. 20–9, how much inductive reactance, $X_\text{L}$, does the coil have with $S_1$ in position $1$? Explain your answer.

Calculate You push on a desk with a force of $120 N$ to the right. Your friend pushes on the same desk with a force of $90 N$ to left. What is the net force on the desk?

A distance of $38.0 \mathrm{~mm}$ separates two big, parallel metal sheets that are carrying opposing electric charges of equal magnitude. Between them, there is a consistent electric field with a magnitude of $480 \mathrm{~N} / \mathrm{C}$. a) What potential differences could there be between the sheets? b) Which sheet, the one with positive charge or the one with negative charge, has a bigger potential? c) What is the positive sheet's surface charge density, or  $\sigma$ ?

According to Thomson Financial, through last month, the majority of companies reporting profits had beaten estimates. A sample of 162 companies showed that 104 beat estimates, 29 matched estimates, and 29 fell short.

c. How large a sample is needed if the desired margin of error is .05?

On e of Aesop' s fables tells of a race between a tortoise and a hare. Suppose the overconfident hare takes a nap and wakes up to find the tortoise a distance d ahead and a distance L from the finish line. If the hare then begins running with constant speed $v_1$ and the tortoise continues crawling with constant speed $v_2$, it turns out that the tortoise wins the race if the distance L is less than $(v_2 / (v_1 - v_2))d$. Obtain this result by first writing expressions for the times taken by the hare and the tortoise to finish the race, and then noticing that to $t_{\text {tortoise }}<t_{\text {hare }}$. Assume $v_{2}<v_{1}$.

Suppose that you work part-time at a department store, earning a base salary of $\$ 50$ per week plus a $15 \%$ commission on all sales that you make.

$$\begin{array}{|c|c|} \hline \text { Weekly sales, } x & \text { Weekly income, } y \\ \hline 100 & 50+(0.15)(100)=65 \\ \hline 200 & ? \\ \hline 300 & ? \\ \hline 400 & ? \\ \hline x & ? \\ \hline \end{array}$$

$$\text {Find the weekly income, } y \text {, for weekly sales of } \$ 1200 \text {. }$$

A patient is given the drug theophylline intravenously at a rate of 43.2 mg hour to relieve acute asthma. The rate at which the drug leaves the patient's body is proportional to the quantity there, with proportionality constant 0.082 if time, t, is in hours. The patient's body contains none of the drug initially. Write a differential equation satisfied by the quantity of theophylline in the body, Q(t).

Give the oxidation numbers for the underlined atoms in the given molecule: $\underline{\mathrm{I}}\mathrm{F_7}$

Construct the confidence interval estimate of the mean. Consider a sample of 106 body temperatures having a mean of 98.20$^\circ$F and a standard deviation of 0.62$^\circ$F. Construct a 95% confidence interval estimate of the mean body temperature for the entire population. What does the result suggest about the common belief that 98.6$^\circ$F is the mean body temperature?

In quantum mechanics the Dirac matrices are

$$\beta=\left[\begin{array}{rrrr}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & -1 & 0 \\ 0 & 0 & 0 & -1\end{array}\right] . \quad \alpha_1=\left[\begin{array}{llll}0 & 0 & 0 & 1 \\ 0 & 0 & 1 & 0 \\ 0 & 1 & 0 & 0 \\ 1 & 0 & 0 & 0\end{array}\right]$$

.

$$\alpha_y=\left[\begin{array}{rrrr}0 & 0 & 0 & -i \\ 0 & 0 & i & 0 \\ 0 & -i & 0 & 0 \\ i & 0 & 0 & 0\end{array}\right] . \quad \alpha_z=\left[\begin{array}{rrrr}0 & 0 & 1 & 0 \\ 0 & 0 & 0 & -1 \\ 1 & 0 & 0 & 0 \\ 0 & -1 & 0 & 0\end{array}\right]$$

Show that $\beta^2=\alpha_x^2=\alpha_y^2=\alpha_s^2=I$.

Show that the empirical formula given for chrysotile asbestos is consistent with the expected oxidation states of the elements present.

Let $\alpha_{1}>0$, $\alpha_{2}>0$, with $\alpha_{1}+\alpha_{2}=\alpha$. Then $P\left(-z_{\alpha_{1}}<\frac{\bar{X}-\mu}{\sigma / \sqrt{n}}<z_{\alpha_{2}}\right)=1-\alpha$ a. Use this equation to derive a more general expression for a $100(1-\alpha) \%$ CI for $\mu$ of which the interval $\left(\bar{x}-z_{\alpha / 2} \cdot \frac{\sigma}{\sqrt{n}}, \bar{x}+z_{\alpha / 2} \cdot \frac{\sigma}{\sqrt{n}}\right)$ is a special case. b. Let $\alpha=.05$ and $\alpha_{1}=\alpha / 4$, $\alpha_{2}=3 \alpha / 4$. Does this result in a narrower or wider interval than the interval $\left(\bar{x}-z_{\alpha / 2} \cdot \frac{\sigma}{\sqrt{n}}, \bar{x}+z_{\alpha / 2} \cdot \frac{\sigma}{\sqrt{n}}\right)$?

Is the slipper-pad flow of the earlier problem in the creeping flow regime? Discuss. Are the results reasonable?

The time required to fly from one location to another is inversely proportional to the average speed. When the average speed to fly from Québec City to Vancouver is 350 km/h, the flying time is 11 h. a) Write a function to represent the time as a function of the speed. b) Sketch a graph of this function. c) How long would the trip from Québec to Vancouver take at an average speed of 500 km/h? d) Describe the rate of change of the time as the average speed increases.