A slender rod, $0.240 \mathrm{~m}$ long, rotates with an angular speed of $8.80 \mathrm{rad} / \mathrm{s}$ about an axis through one end and perpendicular to the rod. The plane of rotation of the rod is perpendicular to a uniform magnetic field with a magnitude of $0.650 \mathrm{~T}$. What is the potential difference between its ends?

In Fig. we saw earlier a conducting rod of length $L=30.0 \mathrm{~cm}$ moves in a magnetic field $\overrightarrow{\boldsymbol{B}}$ of magnitude $0.450 \mathrm{~T}$ directed into the plane of the figure. The rod moves with speed $v=5.00 \mathrm{~m} / \mathrm{s}$ in the direction shown.What is the potential difference between the ends of the rod?

Selected balance sheet and income statement information from Siemens, AG, for 2015 through 2017 follows(Euro in millions).

What is your overall assessment of the company's liquidity and solvency? Explain.

a) Let $\mathrm{Q}[\sqrt{2}]=(\mathrm{a}+\mathrm{b} \sqrt{2} | \mathrm{a}, \mathrm{b} \in \mathrm{Q}).$ Prove that $(Q[\sqrt{2}],+, \cdot)$ is a subring of the field $(R,+, \cdot).$ (Here the binary operations in R and $\mathrm{Q}[\sqrt{2}]$ are those of ordinary addition and multiplication of real numbers.) b) Prove that $\mathrm{Q}[\sqrt{2}]$ is a field and that Q[x]/(x2 – 2) is isomorphic to $\mathrm{Q}[\sqrt{2}].$

Figure $18.31$ showed how a circle at the origin can be linearly separated by mapping from the features $\left(x_1, x_2\right)$ to the two dimensions $\left(x_1^2, x_2^2\right)$. But what if the circle is not located at the origin? What if it is an ellipse, not a circle? The general equation for a circle (and hence the decision boundary) is $\left(x_1-a\right)^2+\left(x_2-b\right)^2-r^2=0$, and the general equation for an ellipse is $c\left(x_1-a\right)^2+d\left(x_2-b\right)^2-1=0$.

• a. Expand out the equation for the circle and show what the weights $w_i$ would be for the decision boundary in the four-dimensional feature space $\left(x_1, x_2, x_1^2, x_2^2\right)$. Explain why this means that any circle is linearly separable in this space.
• b. Do the same for ellipses in the five-dimensional feature space $\left(x_1, x_2, x_1^2, x_2^2, x_1 x_2\right)$.

Solve the open sentence. Then graph the solution set. $|5 c-8|=12$

An $8-\mathrm{kg}$ cylinder $C$ rests on a $4-\mathrm{kg}$ platform $A$ supported by a cord which passes over the pulleys $D$ and $E$ and is attached to a $4-\mathrm{kg}$ block $B$. Knowing that the system is released from rest, determine (a) the velocity of block $B$ after $0.8 \mathrm{~s}$, (b) the force exerted by the cylinder on the platform.

In March 2009, 100 registered voters were asked to rate the effectiveness of President Obama. In March 2010, these same people were again asked to make the same assessment. Seventy percent of the second ratings were lower than the first ratings and $30 \%$ were higher.

a. Using the sign test, specify the competing hypotheses to determine whether the president's rating had significantly declined.

b. Calculate the value of the test statistic.

c. Calculate the $p$-value.

d. At the $5 \%$ significance level, do the data suggest that the president's rating had significantly declined?

Classify each of the quadratic forms as positive definite, positive semidefinite, negative definite, negative semidefinite, or indefinite.

$$x _ { 1 } ^ { 2 } + x _ { 2 } ^ { 2 } - x _ { 3 } ^ { 2 } + 4 x _ { 1 } x _ { 2 }$$

When consumers respond more positively to ground beef described as "75 percent lean" than to the same product labeled "25 percent fat," they have been influenced by __________ .

Kyle bought a candle in the shape of a right cone. The candle has a height of 7 inches and a base radius of 1 inch. What is the volume of the candle to the nearest hundredth?

A ruba has the same thickness as a modern U.S. penny (about 0.06 inch). Suppose the king had been able to reward the peasant by using Plan 1 (doubling the number of rubas in each square). What would be the height of the stack of rubas on square 64 ?

The financial statements for Castile Products, Inc., are given below:

$$\begin{array}{c} \textbf{Castile Products, Inc.}\\ \textbf{Balance sheet}\\ \textbf{December 31}\\ \end{array}$$

$$\begin{array}{lr} \textbf{Assets}\\ \text{Current Assets:}\\ \text{\ \ \ \ \ Cash}&\$\ 6,500\\ \text{\ \ \ \ \ Accounts Receivable, net}&35,000\\ \text{\ \ \ \ \ Merchandise Inventory}&70,000\\ \text{\ \ \ \ \ Prepaid Expenses}&\underline{3,500}\\ \text{Total Current Assets}& 115,000\\ \\ \text{Property and Equipment, net}&185,000\\\hline \textbf{Total Assets}&\textbf{\underline{\underline{\$\ 300,000}}}\\\hline \\ \textbf{Liabilities and Stockholders' Equity}\\ \text{Liabilities:}\\ \text{\ \ \ \ \ Current Liabilities}&\$\ 50,000\\ \text{\ \ \ \ \ Bonds Payable, 10\\\%}&\underline{ 80,000}\\ \text{Total Liabilities}&\text{\underline{\underline{\$\ 130,000}}}\\ \\ \text{Stockholder's Equity:}\\ \text{Common Stock, \$5 par value }&\$\ 30,000\\ \text{Retained Earnings}&\underline{140,000}\\ \text{Total Stockholder's Equity}&\text{\underline{\underline{\$\ 170,000}}}\\\hline \textbf{Total Liabilities and }\\ \textbf{Stockholder's Equity}&\textbf{\underline{\underline{\$\ 300,000}}}\\\hline \end{array}$$

$$\begin{array}{c} \textbf{Castile Products, Inc.}\\ \textbf{Income Statement}\\ \textbf{For the Year Ended December 31}\\ \end{array}$$

$$\begin{array}{lrrrr} \text{Sales}& \$\ 420,000\\ \text{Cost of Goods Sold}&\underline{ 292,500}\\ \text{Gross Margin}& \$\ 127,500\\ \text{Selling and Administrative Expenses}&\underline{ 89,500}\\ \text{Net Operating Income}& \$\ 38,000\\ \text{Interest Expense}&\underline{ 8,000}\\ \text{Net Income Before Taxes}& \$\ 30,000\\ \text{Income Taxes (30\\\%)}&\underline{ 9,000}\\\hline \textbf{Net Income }&\textbf{ \$\ 21,000}\\\hline \end{array}$$

Account balances at the beginning of the year were: accounts receivable, $25,000; and inventory,$60,000. All sales were on account.

Assume that Castile Products, Inc., paid dividends of $2.10 per share during the year. Also assume that the company’s common stock had a market price of$42 at the end of the year and there was no change in the number of outstanding shares of common stock during the year. Required: Compute financial ratios as follows:

1. Earnings per share. (Round your answer to 2 decimal places.)
2. Dividend payout ratio. (Round your intermediate calculations to 2 decimal places. Round your percentage final answer to nearest whole number (i.e., 0.1234 should be entered as 12).)
3. Dividend yield ratio. (Round your intermediate calculations to 2 decimal places. Round your percentage final answer to nearest whole number (i.e., 0.1234 should be entered as 12).)
4. Price-earnings ratio. (Round your intermediate calculations to 2 decimal places. Round your answer to nearest whole number.)
5. Book value per share. (Round your answer to 2 decimal places.)

What does amenorrhea in female athletes suggest about the relationship between body fat and menstruation?