Two walkers start walking on different paths in the town park. Walker A starts at the 0.5m mark on his path and walks at a speed of lm/sec. Walker B starts at the 2m mark on her path and walks at a speed of 0.5m/sec. a) Make a table the keeps track of where each walker is over ten seconds of time. Walker A( , ) Walker B( , ) b) Where does it appear that the two walkers meet? c) Use the starting point and speed to write an equation for each walker: Walker A:_______________________ Walker B: ___________________________ d) Graph the two equations on the same set of axes.

Rewrite the (numerical) matrix equation below in symbolic form as a vector equation, using symbols $\mathbf{v}_{1}, \mathbf{v}_{2}, \dots$ for the vectors and $c_{1}, c_{2}, \dots$ for scalars. Define what each symbol represents, using the data given in the matrix equation.

$$\left[\begin{array}{rrrrr} -3 & 5 & -4 & 9 & 7 \\ 5 & 8 & 1 & -2 & -4 \end{array}\right]\left[\begin{array}{r} -3 \\ 1 \\ 2 \\ -1 \\ 2 \end{array}\right]=\left[\begin{array}{r} 11 \\ -11 \end{array}\right]$$

If the graph of an equation is symmetric with respect to the y-axis and 6 is an x-intercept of this graph, name another x-intercept.

The amounts $x_{1}(t) \text { and } x_{2}(t)$ of salt in the two brine tanks satisfy the differential equations $\frac{d x_{1}}{d t}=-k_{1} x_{1}, \quad \frac{d x_{2}}{d t}=k_{1} x_{1}-k_{2} x_{2}$, where $k_{i}=r / V_{i}$ for i = 1, 2. The following problem the volumes $V_{1}$ and $V_{2}$ are given. First solve for $x_{1}$(t) and $x_{2}$(t), assuming that r = 10 (gal/min), $x_{1}$(0) = 15 (lb), and $x_{2}(0)$ = 0. Then find the maximum amount of salt ever in tank 2. Finally, construct a figure showing the graphs of $x_{1}$(t) and $x_{2}$(t). $V_{1}=50(\text { gal }), V_{2}=25(\text { gal })$

Fill in the blanks.

The tangent line at $P(a, f(a))$ to the graph of f is the line passing through $P$ and having slope ____.

Consider the system

$$\begin{array}{l} a_{1} x+b_{1} y+c_{1}z=d_{1} \\ a_{2} x+b_{2} y+c_{2} z=d_{2} \end{array}$$

of two equations in three unknowns. Explain why the system must have infinitely many solutions if $d_{1}=0=d_{2}$.

Determine whether the number describes a population parameter or a sample statistic. Explain your reasoning. A survey of 2008 U.S. adults found that 80% think that the militant group known as ISIS is a major threat to the well-being of the United States.

What volume of $\mathrm{O}_{2}$ at STP is required to oxidize 8.0 L of NO at STP to $\mathrm{NO}_{2}$? What volume of $v$ is produced at STP?

Sally wants to make cookies for her little sister's tea party. Sally is cutting a roll of cookie dough into pieces that are $\frac{1}{2}$ inch thick. If the roll is $11 \frac{1}{2}$ inches long, how many cookies can she make?

Give an example of a bipartite graph different from those in the examples of this section. Specify the disjoint vertex sets.

Let F be a field and let $n \in \mathbb{Z}^{+}$. Write out all the elements of $G L_{2}\left(\mathbb{F}_{2}\right)$ and compute the order of each element.

Let Y be the group whose presentation is displayed in (1.3). (a) Show that $v^{2}=v^{-1}$. [Use the relation: $v^{3}=1$.] (b) Show that v commutes with $u^{3}$. [Show that $v^{2} u^{3} v=u^{3}$ by writing the left hand side as $\left(v^{2} u^{2}\right)(u v)$ and using the relations to reduce this to the right hand side. Then use part (a).] (c) Show that v commutes with u. [Show that $u^{9}=u$ and then use part (b).] (d) Show that uv = 1. [Use part (c) and the last relation. (e) Show that u = 1, deduce that v = 1, and conclude that Y = 1. [Use part (d) and the equation $u^{4} v^{3}=1.]$

The area of a high school basketball court is (50x - 300) square feet. Factor 50x - 300 to find possible dimensions of the basketball court.

Define a function $f: \mathbb{R} \rightarrow \mathbb{R}$ by $f(x)=x^{5}+2 x$. Show that the inverse function of f exists.