Use the Half-angle Formulas to find the exact value of each expression. $\tan \frac{7 \pi}{8}$

Describe and solve a real-life problem that involves finding the circumference of a circle.

Choose the letter of the sentence in which the indicated word is used incorrectly.

a. We discussed the 'prose' and cons of turbo engines.

b. Edgar Allan Poe wrote both poetry and 'prose'.

c. Trying to smarten himself up to become a gentleman, a character in a French play is amazed when his tutor tells him he has been speaking 'prose' all his life.

d. In Charlie and the Chocolate Factory, a scolding voice speaking in rhyme sometimes interrupts the 'prose'.

Compare and Contrast How are plateaus and mountains alike? How are they different?

Solve the puzzle by figuring out the missing month.

SUDOKU des mois fran$\c{c}$ais

Respond to each of the items using the following time series data.

$$\begin{array}{|cc|cc|} \hline \text { Period } & \text { Demand } & \text { Period } & \text { Demand } \\ \hline 1 & 138 & 8 & 103 \\ 2 & 131 & 9 & 142 \\ 3 & 149 & 10 & 122 \\ 4 & 110 & 11 & 121 \\ 5 & 175 & 12 & 130 \\ 6 & 194 & 13 & 126 \\ 7 & 166 & 14 & 140 \\ \hline \end{array}$$

a. Graph the time series data. What do you observe? b. Compute all possible forecasts using exponential smoothing with a smoothing coefficient $(\alpha)$ of $0.4$ c. Compute all possible forecasts using exponential smoothing with a smoothing coefficient $(\alpha)$ of $0.9$. d. Compute the MADs for each forecast model. e. Which forecast model would you choose? Why?

a. The volume, V, of a cylinder is given by the formula V = $\pi r^2L$ where r is the cylinder’s radius and L is its length. Using this formula, write a C++ function named cylvol() that accepts a cylinder’s radius and length and returns its volume. b. Include the function written in previous Exercise in a working program. Make sure your function is called from main() and returns a value to main() correctly. Have main() use a cout statement to display the returned value. Test the function by passing various data to it.

Use Green’s theorem to evaluate line integral $\int _ { C } \mathbf { h } \cdot d \mathbf { r }$ if $\mathbf { h } ( x , y ) = e ^ { y } \mathbf { i } - \sin \pi x \mathbf { j }$, where C is a triangle with vertices (1, 0), (0, 1), and (−1, 0) (−1, 0) traversed counterclockwise.

Why do you think the author uses the old style of coplas to express her modern poetry?

Evaluate the expression for $a=2, b=3$, and $c=-2$.

$$(a-c)(c+5)$$

How does the bird's life help you understand the lives of the oppressed?

The speed of a car in miles per hour and its stopping distance in feet are recorded in the table.

Use a graphing utility to plot the data and graph the model.

Solve for c, where c represents the length of the hypotenuse of a right triangle. Simplify the result, if possible. a.

$$c ^ { 2 } = 64$$

b.

$$c ^ { 2 } = 15$$

c.

$$c ^ { 2 } = 24$$

$$\begin{array}{|c|c|c|c|c|c} x & 2 & 4 & 6 & 8 & \quad y=2 x+1 \\ y & 3 & 6 & 4 & 5 & \quad y=2 x+1.4 \\ \end{array}$$