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

Change the percent to a decimal number. 21.7%

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

(a) Find the Taylor polynomial of degree 4 for $f ( x ) = x ^ { - 2 }$ about the point x=1. (b) Use the result of (a) to approximate f(0.9) and f(1.1), (c) Use the Taylor remainder to find an error formula for the Taylor polynomial. Give error bounds for each of the two approximations made in part (b). Which of the two approximations in part (b) do you expect to be closer to the correct value? (d) Use a calculator to compare the actual error in each case with your error bound from part (c).

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.

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

Convert the following base 10 numbers to binary and express each as a floating point number fl(x) by using the Rounding to Nearest Rule: (a) 1/4, (b) 1/3, (c) 2/3, (d) 0.9

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.

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

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

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.

Find the first 15 bits in the binary representation of $\pi$.

Do the following sums by hand in IEEE double precision computer arithmetic, using the Rounding to Nearest Rule. (Check your answers, using MATLAB.) (a) $\left( 1 + \left( 2 ^ { - 51 } + 2 ^ { - 53 } \right) \right) - 1$, (b) $\left( 1 + \left( 2 ^ { - 51 } + 2 ^ { - 52 } + 2 ^ { - 53 } \right) \right) - 1$