Determine whether the Law of Sines or the Law of Cosines can be used to find another measure of the triangle. Then solve the triangle. $a=8, \quad c=5, \quad B=40^{\circ}$

The resistance of a parallel circuit with 3 bulbs is $\frac{1}{\frac{1}{R_{1}}+\frac{1}{R_{2}}+\frac{1}{R_{3}}}.$ The resistance of a parallel circuit with 3 bulbs is 1.5 ohms. Find the resistances of the bulbs, if two of them have equal resistances, while the resistance of the 3rd is 3 ohms less.

Some SF2 (at a partial pressure of 2.3×10^-4 atm) is placed in a closed container at 298 K with some F3SSF (at a partial pressure of 0.0484 atm) . Enough argon is added to raise the total pressure to 1.000 atm. (a) Calculate the initial reaction quotient for the decomposition of F3SSF to SF2. (b) As the gas mixture reaches equilibrium, will there be net formation or dissociation of F3SSF?

Compare the mass of the reactants and the mass of the products in a chemical reaction, and explain how these masses are related.

find the inclination θ (in radians and degrees) of the line with slope m. m = -1

Suppose a scientists wants to measure the lengths of twenty queen bees from twenty different hives. How would the scientists find the mean of the data set? Why might the scientists choose to compare the queens lengths in a bar graph?

A building contractor obtained bids for some asphalt paving, based on a specification. Three paving subcontractors quoted the following prices and terms of payment: $$ \begin{matrix} \text{Paving Co.} & \text{Price} & \text{Payment Schedule}\\ \text{Quick} & \text{\$85,000} & \text{50% payable immediately 25% payable in 6 months 25% payable at year end}\\ \text{Tartan} & \text{82,000} & \text{Payable immediately}\\ \text{Faultless} & \text{84,000} & \text{25% payable immediately 75% payable in 6 months}\\ \end{matrix} $$ The building contractor uses a 12% nominal interest rate, compounded monthly. Which paving subcontractor should be awarded the paving job?

An engraver charges a $10 fee plus$6 for each line of engraving. Write a function to describe the situation. Find a reasonable domain and range for the function for up to 8 lines.

Find an equation of the tangent line at the point indicated. y = ln(sin x),

$$x = \frac { \pi } { 4 }$$

Use matrices A, B, C, and D. Find each product, sum, or difference.

$$A=\left[\begin{array}{rr}{3} & {4} \\ {6} & {-2} \\ {1} & {0}\end{array}\right] \quad B=\left[\begin{array}{rr}{-3} & {1} \\ {2} & {-4} \\ {-1} & {5}\end{array}\right] \quad C=\left[\begin{array}{rr}{1} & {2} \\ {-3} & {1}\end{array}\right] \quad D=\left[\begin{array}{ll}{5} & {1} \\ {0} & {2}\end{array}\right]$$

-3C

Analyze the behavior of f(x) = x² - 2x + 5. Which of the following are true? Select all that apply. A. As x approaches infinity, y approaches infinity. B. As x approaches negative infinity, y approaches negative infinity. C. f has an axis of symmetry at x = 1. D. The domain of f is the set of all real numbers. E. The maximum value of f is 4, for x = 1.

A region R in the z-plane and a complex mapping $w=f(z)$ are given. In each case, find the image region $R^{\prime}$ in the w-plane. Strip $\pi / 4 \leq y \leq \pi / 2$ under $w=e^{z}$

Find the angle $\alpha$ between the two nonvertical lines $L_1$ and $L_2$ (assume $L_1$ and $L_2$ are not perpendicular). The angle $\alpha$ satisfies the equation $\tan \alpha=\left|\frac{m_{2}-m_{1}}{1+m_{2} m_{1}}\right|$ where $m_1$ and $m_2$ are the slopes of $L_1$ and $L_2$ , respectively.

$$\begin{array}{l}{L_{1}: 2 x+y=8} \\ {L_{2}: x-5 y=-4}\end{array}$$

Suppose you hit a baseball and its flight takes a parabolic path. The height of the ball at certain times appears in the table below.

$$\begin{matrix} \text{Time (s)} & \text{0.5} & \text{0.75} & \text{1} & \text{1.25}\\ \text{Height (ft)} & \text{10} & \text{10.5} & \text{9} & \text{5.5}\\ \end{matrix}$$

Find a quadratic model for the ball's height as a function of time.