A mass $M$ located at the origin exerts an attractive force

$$\mathbf{F}(\mathbf{r})=-G \frac{m M}{r^3} \mathbf{r}$$

on a mass $\mathrm{m}$ located at the tip of the radius vector $\mathbf{r}=x \mathbf{i}+$ $y \mathbf{j}+z \mathbf{k}$. Find the flux of $\mathbf{F}$ into the sphere $x^2+y^2+z^2=a^2$.

Write whether you should add a subject (S), verb (V), or a main clause (M), to form a complete sentence. _____ Chief Pontiac the great leader.

Use mathematical induction (with the above definition) to prove that $(\mathrm{n} \cdot a)(\mathrm{m} \cdot b)=(\mathrm{nm}) \cdot a b$ is true for all positive integers n and all elements $a, b \in A$.

In a population of 200,000 people, 40,000 are infected with a virus. After a person becomes infected and then recovers , the person is immune (cannot become infected again). Of the people who are infected, 5% will die each year and the others will recover. Of the people who have never been infected, 25% will become infected each year. How many people will be infected in 4 years?

The distance you are from the band and how loud it sounds to you are related.

Assume ABC Cupcakes of Montana, Inc., completed the following transactions during 2012, the company’s 10th year of operations:

$$\begin{matrix} \text{Feb 3 } & \text{Issued 10,000 shares of common stock (\$3.00 par) for cash of \$280,000.}\\ \text{Mar 19 } & \text{Purchased 2,700 shares of the company’s own common stock at \$24 per share. }\\ \text{Apr 24 } & \text{Sold 1,400 shares of treasury stock for \$26 per share.}\\ \text{Aug 15 } & \text{Declared a cash dividend on the 16,000 shares of \$0.50 no-par preferred stock.}\\ \text{Sep 1 } & \text{Paid the cash dividends. }\\ \text{Nov 22 } & \text{Distributed a 20\\% stock dividend on the 94,000 shares of \$3.00 par common stock outstanding. The market value of the common stock was \$25 per share. }\\ \end{matrix}$$

Analyze each transaction in terms of its effect on the accounting equation of ABC Cupcakes of Montana, Inc.

Base your answers to questions on the following data table. Samples of three different rock materials, $\mathbf{A}, \mathbf{B}$, and $\mathrm{C}$, were placed in different containers of water and shaken vigorously for 20 minutes. At 5-minute intervals, the contents of each container were strained through a sieve screening- The mass of the material remaining in the sieve was measured and recorded as shown in the data table.

Calculate the rate of change in the mass of rock material $\mathrm{C}$ at the end of the 20 minutes. [1]

Fill in the blank with an appropriate word, phrase, or symbol(s). The maximum and minimum values of the objective function occur at the _ of the feasible region.

Choose the letter of the word that is the closest in meaning to the first word.

cleave: (a) depart, (b) grow, (c) adhere

(Practice) For the following declarations, int *xPt, *yAddr; long *dtAddr, *ptAddr; double *ptZ; int a; long b; double c; determine which of the following statements is valid: a. yAddr = &a; h. dtAddr = &b; o. ptAddr = &c; b. yAddr = &b; i. dtAddr = &c; p. ptAddr = a; c. yAddr = &c; j. dtAddr = a; q. ptAddr = b; d. yAddr = a; k. dtAddr = b; r. ptAddr = c; e. yAddr = b; l. dtAddr = c; s. yAddr = xPt; f. yAddr = c; m. ptZ = &a; t. yAddr = dtAddr; g. dtAddr = &a; n. ptAddr = &b; u. yAddr = ptAddr; Copyright

Complete below sentence with the form of the verb indicated in parentheses.
Miners, who __________ with the possibility of catastrophe all their lives, watched in horror as water began pouring into the mine. (present perfect of live)

Twenty-six slips of paper are each marked with a different letter of the alphabet and placed in a basket. A slip is pulled out, its letter recorded (in the order in which the slip was drawn), and the slip is replaced. This is done 5 times. Find the probabilities that the following "words" are formed. A word that starts with "p"

Find the distance from point A to the given line.

A(-3, 2), y = 5x

At January 1, 2016, Canaday Corporation had outstanding the following securities: 600 million common shares 20 million 6% cumulative preferred shares, $50 par 8% convertible bonds,$2,000 million face amount, convertible into 80 million common shares The following additional information is available: - On September 1, 2016, Canaday sold 72 million additional shares of common stock. - Incentive stock options to purchase 60 million shares of common stock after July 1, 2015, at $12 per share were outstanding at the beginning and end of 2016. The average market price of Canaday’s common stock was$18 per share during 2016. - Canaday’s net income for the year ended December 31, 2016, was $1,476 million. The effective income tax rate was 40%. Required: 1. Calculate basic earnings per common share for the year ended December 31, 2016. 2. Calculate the diluted earnings per common share for the year ended December 31, 2016.