"Ordered Pair: (Devising a System of Equality)" By Raven Burnett ORDERED PAIR: (Devising a System of Equality) Solve the following problems: 1. Create A Rational Expressio: Her childhood dog dies. Her mother
calls you on the phone and asks you to relay the information because she herself
is not tactful in these situations. She gets home at 5:45. It is 3:45 when you
receive the news. In these 2 hours devise a means of conveying this information
that allows Her to therapeutically mourn the loss of Her dog without becoming
so caught up in the reaction of grief that the incident itself gets blown out
of proportion. 2. The transitive property of equality: In October of 2001 your friends invite you to a Rock and Roll concert. You accept and purchase tickets. Later that day She informs you that her uncle is getting married for the 4th time and that your presence at the ceremony would be greatly appreciated. Unfortunately, the wedding ceremony conflicts with the concert. When you mention this information to Her, She becomes agitated that you would even consider going to a rock concert instead of Her uncle's wedding. Something about this situation leads you to believe that its resolution will affect the power dynamic of your relationship for years to come. Choose either to go to the wedding or to the concert and then consult Table 1.1 or 1.2 respectfully. Next, using the information from either Table, graph projections for both of your places in the relationship starting from one year before you made your decision concerning the concert in 2001. Follow it for the next five years. Keep an eye on your "Authority Rating" (Ar) throughout the relationship.
TABLE 1.1: You chose to go to the wedding: You Year: 2000 2001 2002 2003 2004 2005 Ar: 10 5 4 3 2 1 ------------------------------------------------------------ Her: Year: 2000 2001 2002 2003 2004 2005 Ar: 10 15 16 17 18 19 TABLE 1.2 You chose to go to the concert: You: Yea: 2000 2001 2002 2003 2004 2005 Ar: 10 15 16 17 18 19 ---------------------------------------------------------- Her: Year: 2000 2001 2002 2003 2004 2005 Ar: 10 5 4 3 2 1 3. Forming coefficient matrices and augmented matrices: You work Monday, Wednesday, Friday and Saturday as a dishwasher at the local deli. Your shift is 2:30 to 9:30 pm. On Tuesdays and Thursdays you go to school at the same time. She works 5 days a week as a floral designer. Her shift is 7:00-5:30 pm. You both have Sundays off. This is the only time you get to see each other. However, the laundry must be done on Sundays and Sunday is also your day to do homework. Your homework averages five hours or so and the laundry averages three or four hours. First, find out the most time-efficient way to do your laundry and your homework and then subtract that time from the total time in the day (usually 24 hours). Secondly, write a theorem illustrating how best to structure the remaining time in order to keep your relationship going for another week.
4. A system with no solution: You receive three bills in the mail. Two are overdue and one you still have a good credit record with. You only have enough money to pay one bill. Do you pay the bill that is not overdue and keep your good credit or do you pay off one of the overdue bills and sacrifice your good credit with the other bill? TIP: Try drawing a graph of the projected interest for each bill, it might make your decision easier.
5. Analyzing complimentary functions: She thinks that you are lazy, selfish and irresponsible, you think that she is anal-retentive, manipulative and demanding. Analyze the data in Table 1.3 and draw two separate graphs, one of them illustrating her behavior over the past month and one of them illustrating yours. When this is done. Analyze the two graphs and write a function which best describes your relationship with one another.
TABLE 1.3 Data for the month of October 2001 Him: Left the dishes un-done despite constant reminders on the following dates: the 1st, 2nd, 4th, 6th, 7th, 8th, 9th, 14th. 15th, 21st, 25th, 26th and 30th. Ate her microwaveable pizza even though you knew it was hers. Refused to discuss the future on the following dates: 1st-31st. Made dinner on the following nights: Refused to vacuum on the following dates: 1st, ,2nd, 14th, 20th and the 25th. Paid the one bill that was not late and left the others until next month. Will still not get a dog. ------------------------------------------------------------------------------------------------------------- Her: Nagged you to do the dishes on the following dates: the 1st, 2nd, 4th, 6th, 7th, 8th, 9th, 14th. 15th, 21st, 25th, 26th and 30th. Demanded the money, in cash, for her microwaveable pizza after you ate it. Demanded you map out your plans for the future on the following dates: lst-31st Made Dinner the following nights: lst-31st Refused to vacuum on the following dates: 2nd, 3rd, 4th, 5th, 6th etc.... Paid all the bills last month Demands a dog, to be purchased together, as a sort of "training kid." 6. Raising both sides to the nth degree: She decides that she wants to make-out with other people because she does not consider kissing to be an innately sexual activity and therefore, does not officially constitute cheating. You disagree. Tempers rise and the evening ends with the two of you standing at opposing ends of the house and throwing things at each other. Despite the fact that the impact from these missiles is painful, as long as they are flying, there is an open channel of communication between the two of you. However, as soon as the missiles cease flying, she will become despondent and cold and lock herself in her room all night. Logistically, you will have to sleep on the couch. Emotionally, you will be a wreck without some kind of closure. On the other hand, she has a finite tolerance for being hit with knick-knacks and will lock herself in her room anyway if you throw too hard or too fast. Find a rate of fire that keeps the two of you talking long enough for you to arrive at some sort of a compromise.
7. Division of a polynomial by a monomial: Your friends do not like Her and the feeling is mutual. However, you have had these friends for more than half your life and are not about to stop seeing them. Nor are you about to stop seeing Her. It is a Friday night and you go to a bar with Her for some drinks. You run into your friends. She slinks off into a corner at the other end of the bar. Since you have a rusty social mechanism and you have not seen your friends in several weeks, it will take you approximately 2 hours (cumulatively) of awkward, halting conversation before you are caught up enough to enjoy "quality time" with them. However, She will get fed up and leave if you do not return to Her table every 15 minutes and stay with Her for at least that long. You plan on staying at the bar for approximately 4 hours altogether. Find a way to satisfy both Her and Them in the allotted span of time.
8. Temperature-reduction formula: She comes home early from work with a fever. Her mouth is also running hot. She says some inflammatory things to you. You are not feeling so well yourself and your immediate response is to yell back. However, when you look in Her eyes, you can tell that it is the fever talking and that She does not mean what She says. Write a list of things that comfort Her and then plan the quickest route (by bike) to the stores that carry these things. Return home and arrange pillows on the couch in such a way that their weight reminds Her of the old family dog and the way it used to lie on Her when She was sick as a little girl. Read to Her the way Her mother never did.
9. Determining the absolute value of a real number: You show her an essay that you have written. She reads it and then tells you that she doesn't like it, that it is unrealistic. You get angry and storm off into your room. Later she knocks on the door and apologizes, saying that she was only telling you the truth. She asks if you would prefer it if, in the future, she lied instead. You think about this. Calculate the value of honesty.
10. Reversing straight line depreciation: Things have been going well for weeks now. You have not had a single fight. No dishes have been broken in almost a month. Life has become predictable. She gets home from work and vacuums. You get home from work and do the dishes. You eat dinner together, discuss your day and then watch television or listen to music. Life goes on like this with only the change in day to remind you of passing time. Graph your existence. It should be a straight line, but somehow, it is sinking. Experiment with radical numbers.
11. Negating Actions with Quantifiers: After watching a certain talk show on television, She decides that your relationship needs more romance in order for it to function properly. She demands rose petals and spontaneous candle-lit dinners in unlikely locations. She demands that you serenade her with love songs in public. You tell her that voluntary embarrassment and expensive gestures are merely clumsy attempts at articulating affection by those who are unable to do so verbally or intellectually. You tell Her that you are a writer and, as such, have no problem articulating your emotions. You place an arm around Her shoulder and She shrugs it off. You decide to do something "romantic" just to make Her happy, just to show Her that you can. However, you find that you have absolutely no idea how to go about it. Examine the following table. Notice each gesture and its corresponding romantic value (rv). Notice also the time-required (tr) for each gesture as well as the monetary-investment (mi). Keeping to a budget of $100 and a time limit of six hours (the time She gets home from work to the time She goes to bed) plan an evening that costs no more than $100, takes no longer than six hours and has a romantic value of 100 or over.
TABLE 1.4: Activity: Mi: Tr: Rv: Dinner for Two at Quaint Italian Bistro: $50 1.5 hrs. 5 Dinner for Two at "Ye Olde Coutry Buffet": $20 30 min. .5 A bottle of wine, a loaf of bread and Thou: $15 20 min. 6 Tickets for Two to a Movie: $13.50 1.5 hrs. 3 Trip to the City for a Little Night-Life: $50 4 hrs. 5 Cocktails at the Local Liquor Locker: $20 2 hrs. 3 Vandalism in her honor: NA* 10 min.** 10 Serenading her in public: NA 3 min.** 10 Dancing at the Local Meat Market: $10 2 hrs. 1 Pizza and Sex: $12 15 min. 1 Just The Sex: NA 5 min. 0 A dozen roses (red, for love): $35 NA 2 Going out with your other "couple" friends: $30 4 hrs. 1
*Plus possible fines **Plus possible jail-time NOTE: If you are having trouble reaching an Rv of 100, examine the Rv's of each gesture or activity and took for a pattern. Does the Mi correspond to the Rv? To the Tr? If so. in what way? Could you suggest a 4th value category? If so, what would it be and how would if affect the other values?
EXTRA CREDIT: Try compiling your own list of activities! Determine the Mi, the Tr and the Rv for each. 12. Force required to move a block: You are almost finished with school. You know this and She knows this. She asks you again and again, in the nicest way She knows how, if you have any idea what you're going to do after you graduate, where you're going to live. Even though She doesn't out-right say it, you know that She is really asking you whether or not you plan on taking Her along when you go Devise a series of distractions that keeps you from answering Her yet again.
13. Simplifying the equation and contending with unexpected variables: The new Fall fashion line-up does not, apparently, include long-sleeves. She comes down with Pneumonia. Her doctor misdiagnoses Her. He prescribes aspirin. Her condition worsens. You receive a phone-call from Her work telling you that She has collapsed. Your heart drops out of your chest. You visit Her at the hospital and refuse to leave Her side. She mutters things in Her sleep. You hold Her hand. She stops muttering. You do not sleep. You do not eat. Your body streamlines its operations in order to run more efficiently on fewer resources. Your mind clears. As the fluid in Her lungs slowly drains away, so does the fog that has been clouding your vision. You see clearly for the first time in years: your fears have been misplaced. Locate the nearest pet-store. Return before she wakes up. From now on, live for three. | 
2004 McGraw-Hill Higher Education