Write a variable expression for each word phrase. 3 divided by n

For which positive integers k can the number $5 + 2 ^ { - k }$ be represented exactly (with no rounding error) in double precision floating point arithmetic?

Differentiate the given function. $L(x)=\ln \left[\frac{x^{2}+2 x-3}{x^{2}+2 x+1}\right]$

Solve each equation. a. $x^2 - 9 = 0$ b. $(x - 3)^2 - 16 = 0$ c. $\bigg(x- \dfrac{3}{2}\bigg)^2 - \dfrac{1}{4} =0$ d. Express $x$ in terms of $a$ and $b$ if $(x - a)^2 - b^2 = 0.$

Simplify each root. $\sqrt[3]{m^{9}}$

Change the percent to a decimal number. 21.7%

Define joint, or articulation. Name and describe the differences among the three major classes of joints.

The Latin root-vis-means "see." The root appears in the word improvised, which literally means "not seen before." It also appears in these words and phrases:

$$\begin{array}{ll}{\text { visitor }} & {\text { revise }} \\ {\text { supervisor }} & {\text { visual aid }} \\ {\text { invisible }} & {\text { envision }}\end{array}$$

Identify the word or phrase above that matches each clue. Not able to be seen

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I solved a formula for one of its variables, so now I have a numerical value for that variable.

Copy and complete the graphic organizer. In each row, draw an example of each strategy that might be used when positioning a figure for a coordinate proof.

$$\begin{matrix} \text{Positioning Strategy} & \text{Example}\\ \text{Use origin as a vertex.}\\ \text{Center figure at origin.}\\ \text{Center side of figure at origin.}\\ \text{Use aes as sides of figure.}\\ \end{matrix}$$

The degree of dissociation, $\alpha,$ of $\mathrm{CO}_{3}(\mathrm{g})$ into CO(g) and $\mathrm{O}_{2}(\mathrm{g})$ at high temperatures and 1 bar total pressure was found to vary with temperature as follows:

$$\begin{matrix} \text{$T / K$} & \text{1395} & \text{1443} & \text{1498}\\ \text{$\alpha / 10^{-4}$} & \text{1.44} & \text{2.5} & \text{4.71}\\ \end{matrix}$$

Assume $\Delta_{r} H^{0}$ to be constant over this temperature range, and calculate K, $\Delta_{r} G^{0}, \Delta_{r} H^{0},$ and $\Delta_{r} S^{0}$ at 1443 K. Make any justifiable approximations.

Imagine you have a close family member who bicycles to work on major streets during rush hour. During this time, air pollution is at its worst, and a cyclist inhales a lot of it. Write a dialogue in which you encourage the family member to consider the negative effects of this practice. Explain the problems that can result.

Evaluate each expression for the given values of the variable.

$$\frac { y ( y - 3 ) } { y - 2 }$$

y=4

Explain whether the given equation defines an exponential function. Give reasons for your answers. Write the base for each exponential function. $y = x ^ { x }$