Solvolysis of 2-bromo-2-methylbutane in acetic acid containing potassium acetate gave three products. Identify them.

Write an equivalent expression using exponential notation.

$$\frac{3 a}{\sqrt[5]{c^2}}$$

Write an equivalent inequality using absolute value.

$x$ is less than $1$ unit from $5$.

For this exercise, you will write an equivalent exponential equation.

$\log _8 2=\frac{1}{3}$

Functions of the form

$$y=c+a \cdot f[b(x-d)]$$

have been graphed with the assumption that b>0. To see what happens when b<0,

Find the intervals of concavity and the inflection points.

$$f(x)=2+2x^2-x^4$$

In Exercise given below, determine whether the improper integral diverges or converges. Evaluate the integral if it converges.

$$\int_{1 / 2}^{\infty} \frac{1}{\sqrt{2 x-1}} d x$$

Solve the given quadratic equation below by factoring. Check your answer.

$$x^2-4 x-32=0$$

Solve each quadratic equation by factoring. Check your answer.

$$2 x ^ { 2 } + 5 x - 3 = 0$$

Use the unit circle to verify each relationship. $\cos (-t)=\cos t$

You are a scientist called to testify before Congress about acid rain. The government is proposing putting limits on emissions that lead to acid rain.

Communicate Some of the members of Congress do not think acid rain causes real damage. What do you tell them?

How can you tell that the relationship between the corresponding terms involves multiplication?

Let $U=\{ a,b,c,d,e,f,g,h\},\quad K=\{c,d,e,f,h\}$ and $R=\{ a,c,d,g \}$. Find the following: The number of subsets of R.

The Chebyshev (Tchebichef) polynomials $T_n(x)$ are orthogonal on the interval $[-1,1]$ with respect to the weight function $w(x)=\left(1-x^2\right)^{-1 / 2}$. Verify this fact for the first three Chebyshev polynomials:

$$T_0(x) \equiv 1, \quad T_1(x)=x, \quad T_2(x)=2 x^2-1 .$$