When a guitar string is vibrating in its fundamental mode, is the wavelength of the sound it produces in air typically the same as the wavelength of the standing wave on the string? Explain.

In this exercise, use the Fundamental Theorem of Calculus to evaluate the definite integral.

$$\int_{-2}^2\left(x^4+2 x^2-5\right) d x$$

Use Part I of the Fundamental Theorem to compute each integral exactly. $\int_{\pi / 4}^{\pi / 2} 3 \csc x \cot x d x$

Use Part I of the Fundamental Theorem to compute each integral exactly. $\int_{0}^{\pi / 4} \sec ^{2} t d t$

Describe what evidence the electron double-slit interference experiment provides that suggests that (a) electrons have particle properties (b) electrons have wave properties

Compute the magnitude of the fundamental cross product for the surface defined parametrically.

$$\mathbf{R}(u, v)=u \mathbf{i}+v^{2} \mathbf{j}+u^{3} \mathbf{k}$$

use the fundamental trigonometric identities to simplify the expression. There is more than one correct form of each answer.

$$\newline\cot\theta\sec\theta$$

The "pitiless wave" in line 22 most likely symbolizes the

A passage of time $\mathrm{B}$ changing shoreline C force of a storm D speaker's thoughts

Express the units of angular momentum

(a) using only the fundamental units kilogram, meter, and second;

(b) in a form involving newtons;

(c) in a form involving joule

What is electromagnetic radiation? Give some examples of such radiation. Explain what the wavelength $(\lambda)$ and frequency $(\nu)$ of electromagnetic radiation represent. Sketch a representation of a wave and indicate on your drawing one wavelength of the wave. At what speed does electromagnetic radiation move through space? How is this speed related to $\lambda$ and $\nu$ ?

Classify each item as an asset, liability, common stock, revenue, or expense.

(c) Amounts owed to suppliers.

Stock splits Nathan Detroit owns 400 shares of the food company General Mills, Inc., which he purchased during the recession in January 2009 for $35 per share. General Mills is regarded as a relatively safe company because it provides a basic product that consumers need in good and bad economic times. Nathan read in the Wall Street Journal that the company’s board of directors had voted to split the stock 2-for-1. In June 2010, just before the stock split, General Mills shares were trading for$75.14.

Answer the following questions about the impact of the stock split on his holdings and taxes. Nathan is in the 28% federal income tax bracket.

e. What is Nathan’s tax liability from the event?

Give an example of a transaction that creates the described effects for the case below:
 Decreases an asset and decreases a liability.

Use fundamental definitions and statements from Chapters 1 and 2 to establish the fact that $6.022 \times 10^{23} \mathrm{u}=1.000 \mathrm{~g}$