Methyl alcohol $(CH_3OH)$ burns with 200% theoretical air, yielding $CO_2, H_2O, O_2,$ and $N_2.$ Determine the a. balanced reaction equation. b. air-fuel ratio on a mass basis. c. molar analysis of the products.

Find the following matrices: 3A + 2B.

$$A = \left[ \begin{array} { l l } { 4 } & { 1 } \\ { 3 } & { 2 } \end{array} \right] , \quad B = \left[ \begin{array} { l l } { 5 } & { 9 } \\ { 0 } & { 7 } \end{array} \right]$$

Methyl alcohol $(CH_3OH)$ is burned with 100 percent excess air. During the combustion process, 60 percent of the carbon in the fuel is converted to $\mathrm{CO}_{2}$ and 40 percent is converted to CO. Write the balanced reaction equation and determine the air-fuel ratio.

The Fibonacci sequence models the number of pairs of rabbits after a certain number of months. The sequence begins 1, 1, . . ., and each term after that is the sum of the two terms before it. Find the first 12 terms of the Fibonacci sequence. How many pairs of rabbits are produced under ideal circumstances at the end of one year?

In the book Of Mice and Men by John Steinbeck, two good friends named Lenny and George dream of raising rabbits and living off the land. What if their dream came true? Suppose Lenny and George started with two rabbits and during the first month those rabbits have two babies. Also suppose that every month thereafter, each pair of rabbits has two babies. With your team: Determine how many rabbits Lenny and George would have after one year (12 months). Represent this situation with a written description of the pattern of growth, a diagram, and a table. State the assumptions you made when you modeled the number of rabbits raised. Compare any patterns you find to other patterns that you have investigated previously. What strategies can help us keep track of the total number of rabbits? What patterns can we see in the growth of the rabbit population? How can we predict the total number of rabbits after many months have passed?

Only 4% of people have Type AB blood. What's the probability that we won't find a Type AB donor before the 10th person?

What percentage of an iron anchor's weight will be supported by buoyant force when submerged in salt water?

Consider the sequence defined by the recursive formula

$$A _ { N } = A _ { N - 1 } - 2 A _ { N - 2 }$$

and starting with

$$A _ { 1 } = 1 , A _ { 2 } = - 1$$

. (a) List the next four terms of the sequence. (b) Find

$$A_8$$

.

Let

$$f(x, y, z)=x ^ { 2 } + y ^ { 2 } - z$$

. Find an equation of the level surface that passes through the point (1, -2, 0).

Write each equation in logarithmic form.

$$3^8=6,561$$

Acetylene $\left(\mathrm{C}_2 \mathrm{H}_2\right)$ enters a torch and burns completely with $110 \%$ of theoretical air entering at $74{ }^{\circ} \mathrm{F}, 1 \mathrm{~atm}, 50 \%$ relative humidity. Obtain the balanced reaction equation, and determine the dew point temperature of the product. in ${ }^{\circ} \mathrm{F}$, at $1 \mathrm{~atm}$.

Is it possible to transform the graph of

$$f(x) = e^x$$

to obtain the graph of g(x) = ln x? Explain your reasoning.

Methyl alcohol $(CH_3OH)$ burns in dry air according to the reaction

$$\begin{aligned} \mathrm{CH}_{3} \mathrm{OH} &+3.3\left(\mathrm{O}_{2}+3.76 \mathrm{N}_{2}\right) \rightarrow \mathrm{CO}_{2}+2 \mathrm{H}_{2} \mathrm{O} \\ &+1.8 \mathrm{O}_{2}+12.408 \mathrm{N}_{2} \end{aligned}$$

Determine the a. air-fuel ratio on a mass basis. b. equivalence ratio. c. percent excess air.

Find the equation of the line tangent to the function at the given point. $f(x) = 5x^2$ at x = 10