Draw a family tree of your immediate family. Next to each person, write a word to describe him or her. Then, write three sentences about your favorite relatives.

Answer the following questions: If you were an immigrant arriving in the U.S. at the turn of the century, how would you have felt upon reading the inscription on the base of the statue? Explain by citing a specific example from the text.

Use the methods of this section to solve the following differential equations. Compare computer solutions and reconcile differences. $(x-y) d y+(y+x+1) d x=0$

Determine whether each statement is true or false. If false, explain why. The distance between the points (0, 0) and (4, 4) is 4.

$$\begin{array} { l l l } \text { White } & \text { Black } & \text { Total } \\ & + & = & n ^ { 2 } \end{array}$$

First simplify each of the following numbers to the $x + iy$ form or to the $r e^{i \theta}$ form. Then plot the number in the complex plane. $5\left(\cos \frac{2 \pi}{5}+i \sin \frac{2 \pi}{5}\right)$

Find the distance from the origin to the plane $3x − 2y − 6z = 7.$

Find the equation(s) of the tangent line(s) at the point(s) on the graph of the equation $y^{3}-x y-x^{3}=2$ where x = 1. Round all approximate values to two decimal places.

Use a graphing calculator to graph the normal probability density function $f(x)=\frac{1}{\sigma \sqrt{2 \pi}} e^{-(x-\mu)^{2} / 2 \sigma^{2}}$ that has the given mean $\mu$ and standard deviation $\sigma$. $\mu=300, \sigma=25$

Find $f^{\prime}(x)$ and find the value(s) of x where the tangent line is horizontal. $f(x)=\frac{x-1}{(x-3)^{3}}$

Use a graphing calculator to graph each equation in the standard viewing window. 3x+4y=6

Consider two objects with $m_{1}>m_{2}$ connected by a light string that passes over a pulley having a moment of inertia of I about its axis of rotation. The string does not slip on the pulley or stretch. The pulley turns without friction. The two objects are released from rest separated by a vertical distance 2h (a) Use the principle of conservation of energy to find the translational speeds of the objects as they pass each other. (b) Find the angular speed of the pulley at this time.

Solve each equation for x. $\frac{x-1}{2 a}=2 x-a$

Assume you are a business consultant. The owner of a company sends you an e-mail expressing concern that the company is not taking advantage of its discounts offered by vendors. The company currently uses the gross method of recording purchases. The owner is considering a review of all invoices and payments from the previous period. Due to the volume of purchases, however, the owner recognizes that this is time-consuming and costly. The owner seeks your advice about monitoring purchase discounts in the future. Provide a response in memorandum form.