Sketch the graph of the function g(x) = x + |x|.

For the following exercises, write the linear system from the augmented matrix.

$$\begin{array}{r} -1.06 x-2.25 y=5.51 \\ -5.03 x-1.08 y=5.40 \end{array}$$

Determine the radius and interval convergence of the following power series. $\sum_{k=0}^{\infty}\left(-\frac{x}{10}\right)^{2 k}$

Find the planar density and packing fraction for FCC nickel in the $(100)$, $(110)$, and $(111)$ planes. Which, if any, of these planes are close packed?

Find the limit of the following sequences or determine that the sequence diverges. $\left\{n \sin \frac{6}{n}\right\}$

(a) Derive planar density expressions for FCC (100) and (111) planes in terms of the atomic radius R. (b) Compute and compare planar density values for these same two planes for aluminum (Al).

(a) Calculate %IC of the interatomic bonds for the intermetallic compound $\mathrm{Al}_{6} \mathrm{Mn}$. (b) On the basis of this result, what type of interatomic bonding would you expect to be found in $\mathrm{Al}_{6} \mathrm{Mn}$?

For the following exercises, use the matrices below to perform the indicated operation if possible. If not possible, explain why the operation cannot be performed. Use a calculator to verify your solution.

$$A=\left[\begin{array}{rrr} -2 & 0 & 9 \\ 1 & 8 & -3 \\ 0.5 & 4 & 5 \end{array}\right], B=\left[\begin{array}{rrr} 0.5 & 3 & 0 \\ -4 & 1 & 6 \\ 8 & 7 & 2 \end{array}\right], C=\left[\begin{array}{lll} 1 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 1 \end{array}\right]$$

AB

In the following exercises, show that matrix A is the inverse of matrix B.

$$A=\left[\begin{array}{rrr} 3 & 8 & 2 \\ 1 & 1 & 1 \\ 5 & 6 & 12 \end{array}\right], B=\frac{1}{36}\left[\begin{array}{rrr} -6 & 84 & -6 \\ 7 & -26 & 1 \\ -1 & -22 & 5 \end{array}\right]$$

For the following exercises, graph the given ellipses, noting center, vertices, and foci. $4 x^{2}+16 x+4 y^{2}+16 y+16=0$

For the following exercises, solve using a system of linear equations. A small fair charges $1.50 for students,$1 for children, and $2 for adults. In one day, three times as many children as adults attended. A total of 800 tickets were sold for a total revenue of$1,050. How many of each type of ticket was sold?

Compute %IC of the interatomic bond for each of the following compounds: MgO, GaP, CsF, CdS, and FeO.

For the following exercises, solve each system by addition.

$$\begin{array}{c} 7 x+6 y=2 \\ -28 x-24 y=-8 \end{array}$$

Find the inverse function $f^{-1}$ for the exponential function $f(x)=2 \cdot e^{x+1}-5.$