State the number of significant digits and the implied precision of the following number.

$$0.003$$

Give two ways that a rational number is different from an irrational number.

Sketch a $180^{\circ}$ angle in standard position. Pick a point on the terminal side, and write the horizontal coordinate, vertical coordinate, and radius. Use these numbers to find the exact values of the six trigonometric functions of $180^{\circ}$.

Find the sum.

$$\sum_{k=1}^{\infty}(0.1)^k$$

Identify the given as A. a real number or B. not a real number.

$$\sqrt[3]{-9}$$

State the number of significant digits and the implied precision of the following number.

$$0.004502 \mathrm{~m}$$

Use the formula for the sum of the first n terms of a geometric series to find $S_{9}$ for the series $12,6,3, \frac{3}{2}, \ldots$

How do de Broglie’s matter waves account for the “allowed” electron orbits?

Use the Taylor series for

$$1 / \left( 1 - x ^ { 2 } \right)$$

to obtain a series for

$$2 x / \left( 1 - x ^ { 2 } \right) ^ { 2 }.$$

The sum of a positive number and its reciprocal is to be as small as possible. What is the number?

Find the interval of convergence of the (non-power) series and the corresponding series of derivatives. $\sum_{k=0}^{\infty} e^{-2 k x}$

Carefully reread the scene in which Winterbourne comes across Daisy and Giovanelli in the Colosseum (para. $496$). How does James create a sense of foreboding? What is significant about Daisy’s observation that Winterbourne looks at her and Giovanelli “as one of the old lions or tigers may have looked at the Christian martyrs” (para. $497$)?

Make a table of values, and sketch a graph of the equation.

$$x-4 y=8$$

Estimate the number of protons and the number of neutrons in $1 \mathrm{~m}^3$ of air.