Determine whether the following series converge. Justify your answers. $\sum_{k=3}^{\infty} \frac{(-1)^{k} \ln k}{k^{1 / 3}}$

Find the equation of the axis of symmetry and the coordinates of the vertex of the graph of the function.

$$y=x^{2}-8 x-9$$

Make a scatter plot of the data. Identify any outliers, gaps, or clusters.

$$\begin{matrix} \text{Study Time (min), x} & \text{30} & \text{20} & \text{80} & \text{90} & \text{45} & \text{10} & \text{30} & \text{75} & \text{120} & \text{80}\\ \text{Test Score, y} & \text{80} & \text{74} & \text{95} & \text{97} & \text{85} & \text{62} & \text{83} & \text{90} & \text{70} & \text{91}\\ \end{matrix}$$

Solve the following initial value problems. $y^{\prime}(t)=t e^{t}, y(0)=-1$

Two farmers use combines to harvest corn from their fields. One farmer has 600 acres of corn, and the other has 1000 acres of corn. Each farmer's combine can harvest 100 acres per day. Write two equations for the number of acres y of corn not harvested after x days. Are the graphs of the equations parallel, perpendicular, or neither? How do you know?

Find the x- and y-intercepts of the line that passes through the given points. $(-2, 8), (4, 2)$

Solve the following initial value problems. y'(x)=-y+2, y(0)=-2

Between what two consecutive integers is the square root?

$$\sqrt{170}$$

Graph each function by translating $y = |x|$. $y=|x|-3$

Graph the function. Label the axis of symmetry and the vertex.

$$y=2 x^{2}-8 x-5$$

A generator contains 60 gallons of fuel and uses 2.5 gallons per hour. A more efficient power generator contains 40 gallons of fuel and uses 1.5 gallons per hour. After how many hours do the generators have the same amount of fuel? Which generator runs longer? Justify your answers.

Use a calculator or computer program to carry out the following steps. a. Approximate the value of y(T) using Euler's method with the given time step on the interval [0, T]. b. Using the exact solution ( also given), find the error in the approximation to y(T) (only at the right endpoint of the time interval). c. Repeating parts (a) and (b) using half the time step used in those calculations, again find an approximation to y(T). d. Compare the errors in the approximations to y(T). $y^{\prime}(t)=-2 y, y(0)=1 ; \Delta t=0.2, T=2 ; y(t)=e^{-2 t}$

In ___, water molecules diffuse through a selectively permeable membrane.

What is the graph of the equation $y+7=-\frac{4}{5}(x-4) ?$