Construct the constraints and graph the feasible regions for the following situations. See the earlier example.

A plane carrying relief food and water can carry a maximum of 50,000 pounds, and is limited in space to carrying no more than 6000 cubic feet. Each container of water weighs 60 pounds and takes up 1 cubic foot, and each container of food weighs 50 pounds and takes up 10 cubic feet. What is the region of constraint for the number of containers of food and water that the plane can carry?

Write the form of the partial fraction decomposition of the following rational function. In this case, assume the degree of the numerator is less than the degree of the denominator. See the earlier examples.

$$f(x)=\dfrac{p(x)}{x^2-x-6}$$

Let

$$A=\left[\begin{array}{cc}4 & -1 \\ 0 & 3 \\ 9 & -5\end{array}\right]$$

. Determine the following, if possible:

a. The order of $A$.

b. The value of $a_{12}$.

c. The value of $a_{23}$.Let

$$C=\left[\begin{array}{cc}1 & 0 \\ 5 & -3 \\ 2 & 9 \\ \pi & e \\ 10 & -7\end{array}\right]$$

. Determine the following, if possible:

a. The order of $C$.

b. The value of $c_{23}$.

c. The value of $c_{51}$.

Write each of the following systems of equation as a single matrix equation. See the earlier example.

$$\left\{\begin{array}{r}14 x-5 y=7 \\ x+9 y=2\end{array}\right.$$

Let

$$A=\left[\begin{array}{cc}4 & -1 \\ 0 & 3 \\ 9 & -5\end{array}\right]$$

. Determine the following, if possible:

a. The order of $A$.

b. The value of $a_{12}$.

c. The value of $a_{23}$.Let

$$C=\left[\begin{array}{cc}1 & 0 \\ 5 & -3 \\ 2 & 9 \\ \pi & e \\ 10 & -7\end{array}\right]$$

. Determine the following, if possible:

a. The order of $C$.

b. The value of $c_{23}$.

c. The value of $c_{51}$.

Let

$$A=\left[\begin{array}{cc}4 & -1 \\ 0 & 3 \\ 9 & -5\end{array}\right]$$

. Determine the following, if possible:

a. The order of $A$.

b. The value of $a_{12}$.

c. The value of $a_{23}$.Let

$$C=\left[\begin{array}{cc}1 & 0 \\ 5 & -3 \\ 2 & 9 \\ \pi & e \\ 10 & -7\end{array}\right]$$

. Determine the following, if possible:

a. The order of $C$.

b. The value of $c_{23}$.

c. The value of $c_{51}$.

Use the following equation for problems 1-6:

$$\mathrm{N}_2 \mathrm{O}_5+\mathrm{H}_2 \mathrm{O} \rightarrow \ldots \mathrm{HNO}_3$$

What is the percent yield of the last reaction if $24.25 \mathrm{~g}$ nitric acid are actually produced?

What is meant by “delocalized charge”?

Three point charges are arranged on a line. Charge $q _ { 3 } = + 5.00 n C$ and is at the origin. Charge $q _ { 2 } = - 3.00 n C$ and is at x = +4.00 cm. Charge $q_1$ is at x = +2.00 cm. What is $q_1$ (magnitude and sign) if the net force on $q_3$ is zero?

Use the applet Simulating the Probability of a Head with a Fair Coin to explore the relationship between the proportion of heads on several flips of a coin and the theoretical probability of getting heads on one flip of a fair coin. Based on your results for part a, do you believe that we could justifiably conclude that a coin is unfair because we flipped it 10 times and didn't get any heads? Explain.

Presented here are liability items for Desmond Inc. at December 31, 2014. Prepare the liabilities section of Desmond’s balance sheet.

Accounts payable                    $157,000 
Notes payable (due May 1, 2015)       20,000
Bonds payable (due 2018)             900,000 
Unearned rent revenue                240,000
Discount on bonds payable             41,000
FICA taxes payable                     7,800
Interest payable                      40,000
Notes payable (due 2016)              80,000
Income taxes payable                   3,500
Sales taxes payable                    1,700

Use Table discussed before and the information on page $680 to find the total annual renters insurance permises. Duke Schmidt has a renters insurance policy for$$20,000$ of household goods, has selected $\$ 300,000$ liability with $\$ 1,000$ deductible. and his credit is rated as occasional payments past $30$ days. If Duke also adds an endorsement of $\$ 12.500$ to insure his gun collection and $\$ 3.500$ to insure the jewelry he keeps at his condo, how much is his annual premium?

You charge a $5- \mu \mathrm{F}$ capacitor to $150 \mathrm{~V}$. Your lab partner then momentarily places a resistor across its terminals and bleeds off enough charge that its voltage falls to $84 \mathrm{~V}$. What is the final charge on the capacitor?

When $50.0$ g of silicon dioxide is heated with an excess of carbon, $32.2$ g of silicon carbide is produced.

SiO$_2$(s) + 3C(s) $\longrightarrow$ SiC(s) + 2CO(g)

a. What is the percent yield of this reaction?

b. How many grams of CO gas are made?