In a triangle with sides a, b, c and angles A, B, C, the Law of Cosines states that __________.

How are cases selected to be heard by the Court?

Find

$$\sin \frac { \theta } { 2 } , \cos \frac { \theta } { 2 } , \text { and } \tan \frac { \theta } { 2 }$$

for the set of conditions.

$$\sin \theta = - \frac { 24 } { 25 } \text { and } 180 ^ { \circ } < \theta < 270 ^ { \circ }$$

Use logarithmic differentiation to evaluate f'(x). $f ( x ) = x ^ { 2 } \cos x$

Simplify each expression. $2 x+3 y-5 x+2 y$

Determine whether the sequence is an arithmetic sequence. If it is, state the common difference. 7, 6, 5, 4, ...

Estimate the sum or difference.

$$2 \frac { 3 } { 5 } - 1 \frac { 3 } { 8 }$$

Estimate: __________

In the search to reduce thermal pollution and take advantage of renewable energy sources, some people have proposed that we take advantage of such sources as discharges from electric power plants. geothermal energy, and ocean thermal energy. Although many of these sources contain an enormous amount of energy, the amount of work they are capable of producing is limited. How might you use the work potential to assign an "energy quality" to these proposed sources? Test your proposed "energy quality" measure by applying it to the ocean thermal source. Where the temperature 30 m below the surface is perhaps $5^{\circ} \mathrm{C}$ lower than at the surface. Apply it also to the geothermal water source, where the temperature 2 to 3 km below the surface is perhaps $150^{\circ} \mathrm{C}$ hotter than at the surface.

Find the areas of the parallelograms whose vertices are given. A(1, 0, -1), B(1, 7, 2), C(2, 4, -1), D(0, 3, 2)

The four cases in which we can solve a triangle are ASA SSA SAS SSS. Which of the cases listed can lead to more than one solution (the ambiguous case)?

$$180 ^ { \circ } < \alpha < 360 ^ { \circ }$$

and

$$\cos \alpha = \frac { 8 } { 17 }$$

. Find the following.

$$\sin \frac { \alpha } { 2 }$$

Write each equation in standard form. $x+\frac{1}{3} y=\frac{2}{9}$

Work cooperatively. Solve each equation or inequality. $\frac{4}{x}=\frac{6}{x^{2}}$

A migrating salmon heads in the direction N

$$45 ^ { \circ }$$

E. swimming at 5 mi/h relative to the water. The prevailing ocean currents flow due east at 3 mi/h. Find the true velocity of the fish as a vector.