Above the underlined word in each of the following sentences, rewrite the word correctly if it is misspelled. If the word is already spelled correctly, write C above it. Use a dictionary if necessary.

Would you $\underline{\text{beleive}}$ that it was about famous magicians?

In this problem, write the given expression as a product of two trigonometric functions of different frequencies.

$$\cos (\pi t)+\cos (4 \pi t)$$

Write the expression

$$\begin{gather*} \cos 11t - \cos 3t, \end{gather*}$$

as a product of two trigonometric functions of different frequencies.

In this problem, write the given expression as a product of two trigonometric functions of different frequencies.

$$\sin (4 t)+\sin (5 t)$$

VHF covers frequencies from
a. $300 \mathrm{kHz}$ to $3 \mathrm{MHz}$
b. 3 to $30 \mathrm{MHz}$
c. 30 to $300 \mathrm{MHz}$
d. $300 \mathrm{MHz}$ to $3 \mathrm{GHz}$

Write the expression

$$\begin{gather*} \cos 7\pi t + \cos 2\pi t, \end{gather*}$$

as a product of two trigonometric functions of different frequencies.

Write the expression

$$\begin{gather*} \sin 9t + \sin 4t \end{gather*}$$

as a product of two trigonometric functions of different frequencies.

In this problem, write the given expression as a product of two trigonometric functions of different frequencies.

$$\sin (9 t)-\sin (6 t)$$

Write the expression

$$\begin{gather*} \sin 7t - \sin 4t, \end{gather*}$$

as a product of two trigonometric functions of different frequencies.

Make the given changes to the indicated examples of this section and then solve the indicated problem.
In Previous Example, change the class limits to $1.0,2.0,3.0,4.0$, and $5.0$ and then make a table showing the frequencies and relative frequencies.

Compare the average frequencies of total and annular eclipses over a 25-year interval, say, 2001-2025.

Find the centroid of the region bounded below by the x-axis and above by the curve $y=1-x^n, n$ an even positive integer. What is the limiting position of the centroid as $n \rightarrow \infty$ ?

The reaction of magnesium with nitrogen produces magnesium nitride, as follows. 3Mg(s) + N$_2$(g) $\to$ Mg$_3$N$_2$(s). If the reaction is started with 2.24 mol Mg and 0.848 mol N$_2$, find the following:
a. the limiting reactant
b. the excess reactant
c. The number of moles of magnesium nitride produced

Phosgenite (Pb$_2$Cl$_2$CO$_3$) was prepared by the reaction of the following equation:

$$2\text{PbO}+2\text{NaCl}+\text{H}_2\text{O}+\text{CO}_2\rightarrow \text{Pb}_2\text{Cl}_2\text{CO}_3+2\text{NaOH}$$

How many grams of phosgenite can be obtained from 10.0 g PbO and 10.0g NaCl in the presence of excess water and CO$_2$? What is the limiting reactant?