Phoenix Industries has pulled off a miraculous recovery. Four years ago it was near bankruptcy. Today, it announced a $1 per share dividend to be paid a year from now, the first dividend since the crisis. Analysts expect dividends to increase by$1 a year for another 2 years. After the third year (in which dividends to increase by $1 a year for another 2 years. After the third year (in which dividends are$3 per share) dividend growth is expected to settle down to a more moderate long-term growth rate of 6%. If the firm's investors expect to earn a return of 14% on this stock, what must be its price?

Riley and Rhoda plan to buy several bags of dog food and a dog collar. Each bags of dog food costs $7, and the dog collar costs$5. a. Use the information above to write an expression for the amount of money they will spend if they buy b bags of food. b. Riley and Rhoda have $30. Use this information and the expression you wrote for Part (a) to write an inequality for finding the number of bags of food they could buy. c. Solve the inequality and graph the solutions. Check your answer in the original situation.

Suppose G is an infinite cyclic group with generator $\sigma$. (a) Prove that multiplication by

$$\sigma-1 \in \mathbb{Z} G$$

defines a free G-module resolution of

$$\mathbb{Z}: 0 \rightarrow \mathbb{Z} G \stackrel{\sigma-1}{\rightarrow} \mathbb{Z} G \rightarrow \mathbb{Z} \rightarrow 0.$$

(b) Show that

$$H^{0}(G, A) \cong A^{G},$$

that

$$H^{1}(G, A) \cong A /(\sigma-1) A.$$

and that $H^{n}(G, A)=0$ for all n $\geq$ 2. Deduce that

$$H^{1}(G, \mathbb{Z} G) \cong \mathbb{Z}$$

(so free modules neednot be cohomologically trivial).

An RC series circuit consists of an AC source, a $33.0 - \mu \text F$ capacitor, and a 30.0-$\Omega$ resistor. If the source emf is given by $\varepsilon = \varepsilon_ { max } \sin ( \omega t )$, where $E _ { \max } = 180.0 \mathrm { V }$ and $\omega = 20.0 \mathrm { s } ^ { - 1 }$, what is the current amplitude?

Refer to the table. Which lap has the slowest time?

Lap	Time (minutes)
1	1.59
2	185
3	1.64

A squirrel has $x$- and $y$-coordinates $(1.1 \mathrm{~m}, 3.4 \mathrm{~m})$ at time $t_1=0$ and coordinates $(5.3 \mathrm{~m},-0.5 \mathrm{~m})$ at time $t_2=3.0 \mathrm{~s}$. For this time interval, find
(b) the magnitude and direction of the average velocity.

Is the elastic limit a limiting force or a limiting distance?

Find the distance between the two points. If necessary, you may draw graphs but you shouldn't need to use the distance formula.

$(0,0)$ and $(3,4)$

Set U: integers from 1 to 20, Set P: prime numbers, Set T: multiples of 3, Set F: multiples of 5. Create a Venn diagram of these sets.

The distance from the surface of a lens to the focal point is the

Make sense of problems. A sale on dog food that costs $10 a bag says buy 1, get one$$$\frac { 1 } { 2 }$ off. What is the true percent discount on the dog food?

Abel and Family Perfumes wants to add one or more of four new products to its current line of colognes. Historically, Abel has used a 5-year project recovery period and a MARR of 20% per year. (a) Determine which of the four options the company should undertake on the basis of a present worth analysis, provided the total amount of investment capital available is $800,000. Use a hand solution, unless assigned otherwise. (b) What products are selected if the investment limit is increased to$900,000? Use a spreadsheet, unless assigned otherwise. (All cash flows are in $1000 units.)$ $$ \begin{matrix} \text{Product Line} & \text{R1} & \text{S2} & \text{T3} & \text{U4}\\ \hline \text{Investment, \$} & \text{$-200$} & \text{$-400$} & \text{$-500$} & \text{$-700$}\\ \text{M&O cost, \$/year} & \text{$-50$} & \text{$-200$} & \text{$-300$} & \text{$-400$}\\ \text{Revenue, \$/year} & \text{150} & \text{450} & \text{520} & \text{770}\\ \hline \end{matrix} $$ $

Integrative: Determining relevant cash flows Lombard Company is contemplating the purchase of a new high-speed widget grinder to replace the existing grinder. The existing grinder was purchased 2 years ago at an installed cost of $60,000; it was being depreciated under MACRS using a 5 -year recovery period. The existing grinder is expected to have a usable life of 5 more years. The new grinder costs$ 105,000 and requires $5,000 in installation costs; it has a 5-year usable life and would be depreciated under MACRS using a 5 -year recovery period. Lombard can currently sell the existing grinder for$ 70,000 without incurring any removal or cleanup costs. To support the increased business resulting from purchase of the new grinder, accounts receivable would increase by $40,000, inventories by$ 30,000, and accounts payable by $58,000. At the end of 5 years, the existing grinder would have a market value of zero; the new grinder would be sold to net$ 29,000 after removal and cleanup costs and before taxes. The firm is subject to a 40% tax rate. The estimated earnings before depreciation, interest, and taxes over the 5 years for both the new and the existing grinder are shown in the following table.

Year	New grinder	Existing grinder
1	$43,000	$26,000
2	43,000	24,000
3	43,000	22,000
4	43,000	20,000
5	43,000	18,000

b. Determine the incremental operating cash flows associated with the proposed grinder replacement. (Note: Be sure to consider the depreciation in year 6.)

In previous question, let the height h equal $6.00$ m and the speed v$_{boy}$ equal $2.00$ m/s. Assume that the food pack starts from rest.

(a) Tabulate and graph the speed–time graph.

(b) Tabulate and graph the acceleration–time graph. Let the range of time be from $0$ s to $5.00$ s and the time intervals be $0.500$ s.