Find an equation of the tangent line to the graph at the given point.

Rotated ellipse: $7x^2-6\sqrt{3}xy+13y^2-16=0$ Point: $\left(\sqrt{3},1\right)$

There are 42 Major League baseball players (as of 2011) that have hit 50 or more home runs in one season. Construct a stem and leaf plot and analyze the data.

$$\begin{array}{llllll}50 & 51 & 52 & 54 & 59 & 51 \\ 54 & 50 & 58 & 51 & 54 & 54 \\ 56 & 58 & 56 & 70 & 54 & 52 \\ 58 & 54 & 64 & 52 & 73 & 57 \\ 50 & 60 & 56 & 50 & 66 & 54 \\ 52 & 51 & 58 & 63 & 57 & 52 \\ 51 & 50 & 61 & 52 & 65 & 50\end{array}$$

Plot each point given in polar coordinates. $\left(-3,-\frac{\pi}{2}\right)$

Find an equation of the tangent line to the graph of the function at the given point.

$$\begin{matrix} \text{Function} & \text{Point}\\ \text{y=tan x} & \text{}{\left(-\frac{\pi}{4},-1\right)}\\ \end{matrix}$$

To protect a circular area of a park, cameras are placed on a lamppost in the center of the area. If each camera can observe an arc measure of $75^{\circ}$, how many cameras are needed to observe the entire area around the lamppost?

Give the word derived from Greek and/or Latin elements that matches given of the following. Verify your answer in a medical dictionary. Note that the wording of the dictionary definition may vary from the wording below.
Formation of calculi ________________

Simplify the following given expression. Assume all variables are positive.

$$\sqrt[6]{2 x^6}$$

Determine a rotation $\mathbf{x}=P \mathbf{x}^{\prime}$ that removes the cross-product terms, and give its equation in the $x^{\prime} y^{\prime} z^{\prime}$-system. Name the quadric.

$$2 x^2+3 y^2+23 z^2+72 x z+150=0$$

Find (a) the fourth partial sum and (b) the sum of the infinite series. $\sum_{k=1}^{\infty} \frac{4}{10^{k}}$

In this exercise, find the first through the fourth derivatives. Be sure to simplify each derivative before proceeding.

$$f(x)=\frac{x+3}{x-2}$$

Find an equation of the tangent line to the given curve $2\left(x^2+y^2\right)^2=25\left(x^2-y^2\right)$ at the point $(3,1)$.

Perform the given translation on (3, 1). Give the coordinates of the translated point. 2 units right.

How long (in seconds) will it take you to swim 100 meters if you swim at $1.25 \mathrm{~m} / \mathrm{sec}$ ?

The element cesium (Cs) freezes at $28.4^{\circ} \mathrm{C}$, and its molar enthalpy of fusion is $\Delta H_{\text {fus }}=2.09 \mathrm{~kJ} / \mathrm{mol}$

When molten cesium solidifies to $\mathrm{Cs}(\mathrm{s})$ at its normal melting point, is $\Delta S$ positive or negative?