Graphical Reasoning Consider an n-sided regular polygon inscribed in a circle of radius r. Join the vertices of the polygon to the center of the circle, forming $n$ congruent triangles.
Let $A_n$ be the sum of the areas of the $n$ triangles. Find $\lim _{n \rightarrow \infty} A_{n^{-}}$

We have seen that x = 0 is a regular singular point of any Cauchy-Euler equation $a x^{2} y^{\prime \prime}+b x y^{\prime}+c y=0$. Are the indicial equation (14) for a Cauchy-Euler equation and its auxiliary equation related ? Discuss.

Write the preview word that answers the riddle. Preview Words: base, congruent, heptagon, lateral face, nonagon, polygon, polyhedron, prism, pyramid, regular polygon, unit cube, volume. I am a polygon that connects with the bases of a polyhedron. _________.

The window frame is a regular octagon. It is made from eight pieces of wood shaped like congruent isosceles trapezoids. What are $\mathrm{m} \angle A, \mathrm{~m} \angle B, \mathrm{~m} \angle C$, and $\mathrm{m} \angle D$ in trapezoid $A B C D$ ?

$\text{\blue{WHAT IF?}}$ Most prairies experience regular fires, typically every few years. If these disturbances were relatively modest, how would the species diversity of a prairie likely be affected if no burning occurred for 100 years? Explain.

Determine the independent and dependent variables for the study.

A study was conducted to determine if workers who had a flexible work schedule had greater job satisfaction than those workers who worked a regular nine-to-five work schedule.

The height of a regular square pyramid is equal to the side length of the base. The expression 3x - 17.5 represents the height and 6y - 3 represents the side length of the base. If y = 7, what is x? What is the volume of the pyramid? What is its surface area?

A 7-sided shape is called a heptagon.

a) Does a regular heptagon tessellate? Explain your answer.

b) If your answer to Part A is yes, sketch the tessellation.

c) If your answer to Part A is no, sketch a heptagon that tessellates.

C1CCCCCC1

The regular price of a sleeping bag is $39.95. It is on sale for 20% off. There is a 13% sales tax. The discount is typically applied before the tax is added. Assume the tax is calculated first. Would the total cost be more or less in this case? Why?

Complete the sentences about what students did last summer with the correct preterite endings of each -ar verb. Pay attention to the regular endings in the chart above and to the accent marks.

\lparenusar\rparen Esteban us____ la computadora.

$P$ is a transition matrix for a Markov chain. Identify any absorbing states and classify the chain as regular, absorbing, or neither.

$$P=\begin{matrix} A \\ B \end{matrix} \overset{\text{$A$ \quad $B$ }}{\begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix}}$$

Which statement about these poems is not true?
$F$ Both poems use rhyme.
$G$ Both poems follow a regular meter.
$H$ Each speaker asks a woman to read his verses.
$J$ Both poems are bitter in tone.

On the line provided in each of the following sentences, spell the word in parentheses, adding the prefix that is given.

Example: Red tape marks the $\underline{\textit{irregular}}$ spots on these sale items. (ir + regular)

The ______________ in the steel made it weak- (im + purities)

How many pounds of regular coffee (selling for $4 per pound) and how many pounds of Kona coffee (selling for$11.50 per pound) must be combined to get 20 pounds of a mixture worth $6 per pound?