(a) sketch the graph of the function, highlighting the part indicated by the given interval, (b) find a definite integral that represents the arc length of the curve over the indicated interval and observe that the integral cannot be evaluated with the techniques studied so far, and (c) use the integration capabilities of a graphing utility to approximate the arc length. x = e^(-y), 0 ≤ y ≤ 2

Graph two full periods of the given cosecant or secant function.

$$y = 3 \sec ( x + \pi )$$

Determine whether the given set of matrices under the specified operation, matrix addition or multiplication, is a group. Recall that a diagonal matrix is a square matrix whose only nonzero entries lie on the main diagonal, from the upper left to the lower right corner. An upper-triangular matrix is a square matrix with only zero entries below the main diagonal. Associated with each n x n matrix A is a number called the determinant of A, denoted by det(A). If A and B are both n x n matrices, then det(AB) = det(A) det(B). Also,

$$det(I_n) = 1$$

and A is invertible if and only if det(A) ≠ 0. All n x n upper-triangular matrices under matrix addition.

What did Whit show Slim during the card game in "Of Mice and Men"?

Find a value of c that satisfies the conclusion of the Integral Mean Value Theorem. $\int_{-1}^{1}\left(x^{2}-2 x\right) d x\left(=\frac{2}{3}\right)$

How might a limited resource, such as food, affect the survival of an individual organism? How might a sever limitation affect the long-term survival of a species?

Use the quadratic formula to solve each equation. If necessary, round answers to the nearest hundredth.

$$x ^ { 2 } + 4 x - 8 = 0$$

Use the runs test with a significance level of a = 0.05. (All data are listed in order by row.) Test the claim that the sequence of World Series wins by American League and National League teams is random. Given on the next page are recent results, with A = American League and N = National League. A N A N N N A A A A N A A A A N A N N A A N N A A A A N A N N A A A A A N A N A N A N A A A A A A A N N A N A N N A A N N N A N A N A N A A A N N A A N N N N A A A N A N A N A A A N A N A A A N A N A A N A N A N N N A N

$$\left. \begin{array} { l } { \text { For any group element a and any integer } k , \text { show that } C ( a ) \subseteq C \left( a ^ { k } \right) } \\ { \text { Use this fact to complete the following statement: 'In a group, if } x } \\ { \text { commutes with } a , \text { then } \ldots . ' \text { Is the converse true? } } \end{array} \right.$$

Harrison is saving money to buy new speakers that cost at least $120.25. He earns$6.50 per hour working at a grocery store. Write and solve an inequality to find the number of hours he must work to earn enough money for the speakers.

use the graph of the function to determine whether the function is even, odd, or neither. Verify your answer algebraically.

$$g(x) = csc x$$

Simplify.

$$1 \frac { 1 } { 4 } + 2 \frac { 1 } { 4 }$$

$$\begin{array} { r } { \frac { 1 } { 3 } } \\ { + \quad \frac { 1 } { 6 } } \\ \hline \end{array}$$

Graph each ellipse and locate the foci.

$$4 x ^ { 2 } + 9 y ^ { 2 } = 36$$