Consider the following curves on the given intervals. a. Write the integral that gives the area of the surface generated when the curve is revolved about the given axis. b. Use a calculator or software to approximate the surface area. $y=(2 x+3)^{2}$, for $0 \leq x \leq 1$; about the y-axis

Rewrite each expression as a sum. $2 a b-5 a b^{2}-9 a^{2} b$

Let R be the region bounded by the following curves. Find the volume of the solid generated when R is revolved about the given axis. y=sin x on $[0, \pi]$ and y=0; about the x axis (Hint. Recall that $\sin ^{2} x=\frac{1-\cos 2 x}{2}$.)

Without solving, what method would you choose to solve the system: graphing, substitution, or elimination? Explain your reasoning.

$$\begin{array}{l}{2 x-y=4} \\ {x+3 y=16}\end{array}$$

Read what the people want to do and write sentences explaining where they go.

1. Quiero preparar arroz con pollo.
2. Nosotras queremos cocinar con verduras.
3. Marisa y Susana quieren pan para desayunar.
4. Tú quieres comprar frutas.

The protein-coding strand of the average human gene consists of 1,350 nucleotides. Assuming that each nucleotide can take any of four values (A, T, C, or G), how many different genes with exactly 1,350 nucleotides are possible?

Solve the inequality and graph the solutions.

$$-13<3 c+2 \leq 17$$

Solve the system using any method. Tell why you chose the method you used.

$$\begin{array}{l}{y=x+2} \\ {y=-2 x+3}\end{array}$$

Let R be the region bounded by the following curves. Find the volume of the solid generated when R is revolved about the given line. y=sin x and y=1-sin x on the interval $\frac{\pi}{6} \leq x \leq \frac{5 \pi}{6}$, about y=-1

Solve by elimination.

$$\begin{array}{l}{9 x+5 y=34} \\ {8 x-2 y=-2}\end{array}$$

Write one equation of the line through the given points in point-slope form and one in standard form using integers. (5, 3), (4, 5)

Evaluate the following integrals.

$$\int_{0}^{4} f(x) d x \text { for } f(x)=\left\{\begin{array}{ll}{2 x+1} & {\text { if } x \leq 3} \\ {3 x^{2}+2 x-8} & {\text { if } x>3}\end{array}\right.$$

The interior angles of a regular polygon each measure $165^{\circ}$. How many sides does the polygon have?

Solve by graphing. Check your solution.

$$\begin{array}{l}{y=\frac{1}{2} x+1} \\ {y=-3 x+8}\end{array}$$