3. In the figure below, point Z is the image of point X resulting from successive reflections through parelle! lines, /, and /,. a - 11 Ne ee $\mathscr { A }$ a) Label the distance from X to /, 2 and the distance from ¥ to i, &. Also label the distances from Y to |, and Z to i, in terms of aand b.

p) What is the distance between !, and f, in terms of @ and bb?

The freezing point of a $0.010 \mathrm{~m}$ aqueous solution of a nonvolatile solute is $-0.072{ }^{\circ} \mathrm{C}$. What would you expect the normal boiling point of this same solution to be?

Perform the indicated operation and, if possible, simplify.

$$\frac{a}{6 a-9 b}-\frac{b}{4 a-6 b}$$

Name five major characteristics of amphibians.

Perform the indicated operation

$$\left(w^6-w^3\right)-\left(-w^2+w\right)$$

a. Write four terms of a sequence of numbers that you can describe both recursively and explicitly. b. Write a recursive formula and an explicit formula for your sequence. c. Find the 20th term of the sequence by evaluating one of your formulas. Use the other formula to check your work.

The largest interval $I$ over which the explicit solutions $\phi_1(x) = \sqrt{25-x^2}$ and $\phi_2(x)=-\sqrt{25-x^2}$ of

$$\dfrac{dy}{dx} = \dfrac{x}{y}$$

are defined is the open interval $(-5, 5)$. Why can't the interval $I$ of definition be the closed interval $[- 5, 5]$?

At what temperature would 250 mL of water boil? 1000 mL? Is the boiling point an intensive or extensive property? Explain.

Perform the indicated operation. Then simplify :

$$8 \div 2 \frac{2}{3}$$

Refrigerant 134a enters a compressor operating at a steady state as saturated vapor at $-4^{\circ} \mathrm{C}$ and exits at a pressure of 14 bar. The isentropic compressor efficiency is $75 \%$. Heat transfer between the compressor and its surroundings can be ignored. Kinetic and potential energy effects are also negligible. Find

(a) the exit temperature, in ${ }^{\circ} \mathrm{C}$.

(b) the work input, in $\mathrm{kJ}$ per $\mathrm{kg}$ of refrigerant flowing.

Shabby Fitch is the president and principal stockholder of Shabby’s Bar & Grill, Inc. To expand, the business is applying for a $350,000 bank loan. To get the loan, Fitch is considering two options for beefing up the stockholders’ equity of the business:

Option 1. - Issue$200,000 of common stock for cash. A friend has wanted to invest in the company. This may be the right time to extend the offer.

Option 2. - Transfer $200,000 of Fitch’s personal land to the business, and issue common stock to Fitch. Then, after obtaining the loan, Fitch can transfer the land back to himself, and the balance in the common stock account will then equal$0.

Requirements

Use the ethical decision model in Chapter 1 to answer the following questions:

1. What is the ethical issue?

2. Who are the stakeholders? What are the possible consequences to each?

3. Analyze the alternatives from the following standpoints: (a) economic, (b) legal, and (c) ethical.

4. What would you do? How would you justify your decision? How would your decision make you feel afterward?

On December 1, 20X1, Rone Imports, a U.S. company, purchased clocks from Switzerland for 15,000 francs (SFr) to be paid on January 15, 20X2. Rone's fiscal year ends on December 31, and its reporting currency is the U.S. dollar. The exchange rates are

$$\begin{array}{lr} \text{December 1, 20X1} & \text{1 SFr = \$0.70}\\ \text{December 31, 20X1} & \text{1 SFr = 0.66}\\ \text{January 15, 20X2} & \text{1 SFr = 0.68}\\ \end{array}$$

Required

In which currency is the transaction denominated?

For the following problem, write an equation for the inverse relation by interchanging the variables and solving for y in terms of x. Then plot the function and its inverse on the same screen, using function mode. Sketch the result, showing that the function and its inverse are reflections across the line y = x. Tell whether or not the inverse relation is a function.

$$y=-0.5 x^2-2$$

Distance to an airplane A straight road makes an angle of $22^{\circ}$ with the horizontal. From a certain point $P$ on the road, the angle of elevation of an airplane at point $A$ is $57^{\circ}$. At the same instant, from another point $Q, 100$ meters farther up the road, the angle of elevation is $63^{\circ}$. As indicated in the figure, the points $P, Q$, and $A$ lie in the same vertical plane. Approximate the distance from $P$ to the airplane.