Describe how the Law of Cosines can be used to solve the ambiguous case of the oblique triangle ABC, where a=12 feet, b=30 feet, and A = 20° Is the result the same as when the Law of Sines is used to solve the triangle? Describe the advantages and the disadvantages of each method.

A 350-kg sailboat has an acceleration of

$$0.62 \mathrm { m } / \mathrm { s } ^ { 2 }$$

at an angle of

$$64 ^ { \circ }$$

north of east. Find the magnitude and direction of the net force that acts on the sailboat.

Write the given number in the form $a+i b$. $i(1-i)(2-i)(2+6 i)$

Sketch the regions defined by the polar coordinate inequalities.

$$0 \leq r \leq 6 \cos \theta$$

You and your friend are in the studio audience on a television game show. From an audience of 300 people, 2 people are randomly selected as contestants. What is the probability that you and your friend are chosen?

A number whose proper factors (factors other than the number itself) add up to the number is called a perfect number. For example, 6 is a perfect number because its prop er factors are 1, 2, and 3, and 1+2+3=6. Determine which, if any, of the following numbers are perfect numbers. 72

Determine the domains of (a) f, (b) g, and (c) $f \circ g$. Use a graphing utility to verify your results. $f(x)=\sqrt{x+3}, \quad g(x)=\frac{x}{2}$

Consider the following chemical equation:

$$Zn(s) + H_2SO_4(aq)→ H_2(g) + ZnSO_4(aq) + energy$$

(a) Name the products of this reaction. (b) What liquid is also present in the reaction vessel, along with the reactants and products? (c) What evidence would indicate that this reaction is occurring? (d) Will the test tube in which this reaction is occurring become warmer or cooler during the reaction? Why? (e) What evidence would indicate that the reaction has stopped? (f) How does the quantity of zinc metal change as the reaction proceeds?

Use Cramer’s rule to solve the system of equation.

$$\left\{ \begin{array} { l } { 2 x + 2 y = - 1 } \\ { 3 x + 4 y = 0 } \end{array} \right.$$

Two point charges, $q _ { 1 } = + 20.0 \mathrm { nC }$ and $q _ { 2 } = + 10.0 \mathrm { nC }$, are located on the x-axis at x=0 and x=1.00 m, respectively. Where on the x-axis is the electric field equal to zero.

Determine the range and domain of the following functions.

Solve. a - 3/28 = 3

Wheat is poured through a chute at the rate of 10 ft³/min and falls in a conical pile whose bottom radius is always half the altitude. How fast will the circumference of the base be increasing when the pile is 8 ft high?

Solve the equation. -3 = x² + 4x.