Evaluate the integral.

$$\int \cot ^ { 3 } x d x$$

Find the midpoint of the segment with the given endpoints. Then find the distance between the points. Write your answer in simplest form. (8, 15), (-6, -9)

For the following exercise,

Write the equation of the hyperbola in standard form, and give the center, vertices, foci, and asymptotes.

$$16 y^2-9 x^2+128 y+112=0$$

(a) find the standard form of the equation of the hyperbola, (b) find the center, vertices, foci, and asymptotes of the hyperbola, and (c) sketch the hyperbola. $x^{2}-y^{2}=\frac{9}{4}$

Complete the square and write the equation in standard form. Then give the center and radius of each circle and graph the equation.

$$x ^ { 2 } + y ^ { 2 } + 12 x - 6 y - 4 = 0$$

Describe each circle by finding the center and radius. You need to "complete the square" to rewrite the equation in part (b) in graphing form. (a) $(x-2)^2+(y+3)^2=25$ (b) $x^2+2x+y^2+6y-6=0$

Write the standard form of the equation of the circle that passes through the points with the given coordinates. Then identify the center and radius. $(7,-1),(11,-5),(3,-5)$

Write the equation of the hyperbola in standard form. Then give the center, vertices, and foci.

$$\frac{(y+1)^2}{16}-\frac{(x-4)^2}{36}=1$$

Greg and Jane left a 15% tip after dinner. The amount of the tip was $9. Greg's dinner cost$24. Which equation can you use to find x, the cost of Jane's dinner? (A) 0.15x+24=9, (B) 0.15(x+24)=9, (C) 15(x+24)=9, (D) 0.15x=24+9

Complete parts a-c for the quadratic equation.

a. Find the value of the discriminant.

b. Describe the number and type of roots.

c. Find the exact solutions by using the Quadratic Formula.

$$5 x^2-x-1=0$$

Write each expression as an algebraic expression of a single trigonometric function (e.g. 2 sin x +3)
tan² α-1/ 1+ tan α

Find the exact value of:

$$\sin \frac{17 \pi}{24} \sin \frac{\pi}{24}$$

The reaction taking place in the cell in which ${Al}_2 {O}_3$ and aluminum salts are electrolyzed is ${Al}^{3+}({aq})+$ $3 e^{-} \rightarrow {Al}({s})$. If the electrolysis cell operates at $5.0 {~V}$ and $1.0 \times 10^5 {~A}$, what mass of aluminum metal can be produced in a 24-hour day?

$$\dfrac{x}{24}=\dfrac{30}{36}$$