ࡱ> s#` 0bjbjmm @SJ J J J  99989:, kr;?4*@*@*@*@*@*@[[[[\d[D fD q$Wthvtr oF*@*@oFoFrJ J *@*@%r_S_S_SoFNJ *@v *@[_SoF[_S_S:W,h  W *@; 4}B9M2W *X;r0krW 3wR3wX3w X(*@DB_SC4Dw*@*@*@rrRp*@*@*@kroFoFoFoF /9 9 J J J J J J  CHAPTER 2 THE BASICS OF SUPPLY AND DEMAND QUESTIONS FOR REVIEW 1. Suppose that unusually hot weather causes the demand curve for ice cream to shift to the right. Why will the price of ice cream rise to a new market-clearing level? Assume the supply curve is fixed. The unusually hot weather will cause a rightward shift in the demand curve, creating short-run excess demand at the current price. Consumers will begin to bid against each other for the ice cream, putting upward pressure on the price. The price of ice cream will rise until the quantity demanded and the quantity supplied are equal.  EMBED PowerPoint.Show.4  Figure 2. SEQ Figure \* ARABIC 1 2. Use supply and demand curves to illustrate how each of the following events would affect the price of butter and the quantity of butter bought and sold: a. An increase in the price of margarine. Most people consider butter and margarine to be substitute goods. An increase in the price of margarine will cause people to increase their consumption of butter, thereby shifting the demand curve for butter out from D1 to D2 in Figure 2.2.a. This shift in demand will cause the equilibrium price to rise from P1 to P2 and the equilibrium quantity to increase from Q1 to Q2.  EMBED PowerPoint.Show.4  Figure 2.2.a b. An increase in the price of milk. Milk is the main ingredient in butter. An increase in the price of milk will increase the cost of producing butter. The supply curve for butter will shift from S1 to S2 in Figure 2.2.b, resulting in a higher equilibrium price, P2, covering the higher production costs, and a lower equilibrium quantity, Q2.  EMBED PowerPoint.Show.4  Figure 2.2.b Note: Given that butter is in fact made from the fat that is skimmed off of the milk, butter and milk are joint products. If you are aware of this relationship, then your answer will change. In this case, as the price of milk increases, so does the quantity supplied. As the quantity supplied of milk increases, there is a larger supply of fat available to make butter. This will shift the supply of butter curve to the right and the price of butter will fall. c. A decrease in average income levels. Assume that butter is a normal good. A decrease in the average income level will cause the demand curve for butter to shift from D1 to D2. This will result in a decline in the equilibrium price from P1 to P2, and a decline in the equilibrium quantity from Q1 to Q2. See Figure 2.2.c.  EMBED PowerPoint.Show.4  Figure 2.2.c 3. If a 3-percent increase in the price of corn flakes causes a 6-percent decline in the quantity demanded, what is the elasticity of demand? The elasticity of demand is the percentage change in the quantity demanded divided by the percentage change in the price. The elasticity of demand for corn flakes is EMBED Equation. This is equivalent to saying that a 1% increase in price leads to a 2% decrease in quantity demanded. This is in the elastic region of the demand curve, where the elasticity of demand exceeds -1.0. 4. Explain the difference between a shift in the supply curve and a movement along the supply curve. A movement along the supply curve is caused by a change in the price or the quantity of the good, since these are the variables on the axes. A shift of the supply curve is caused by any other relevant variable that causes a change in the quantity supplied at any given price. Some examples are changes in production costs and an increase in the number of firms supplying the product. 5. Explain why for many goods, the long-run price elasticity of supply is larger than the short-run elasticity. The elasticity of supply is the percentage change in the quantity supplied divided by the percentage change in price. An increase in price induces an increase in the quantity supplied by firms. Some firms in some markets may respond quickly and cheaply to price changes. However, other firms may be constrained by their production capacity in the short run. The firms with short-run capacity constraints will have a short-run supply elasticity that is less elastic. However, in the long run all firms can increase their scale of production and thus have a larger long-run price elasticity. 6. Why do long-run elasticities of demand differ from short-run elasticities? Consider two goods: paper towels and televisions. Which is a durable good? Would you expect the price elasticity of demand for paper towels to be larger in the short-run or in the long-run? Why? What about the price elasticity of demand for televisions? Long-run and short-run elasticities differ based on how rapidly consumers respond to price changes and how many substitutes are available. If the price of paper towels, a non-durable good, were to increase, consumers might react only minimally in the short run. In the long run, however, demand for paper towels would be more elastic as new substitutes entered the market (such as sponges or kitchen towels). In contrast, the quantity demanded of durable goods, such as televisions, might change dramatically in the short run following a price change. For example, the initial result of a price increase for televisions would cause consumers to delay purchases because durable goods are built to last longer. Eventually consumers must replace their televisions as they wear out or become obsolete, and therefore, we expect the demand for durables to be more inelastic in the long run. 7. Are the following statements true or false? Explain your answer. a. The elasticity of demand is the same as the slope of the demand curve. False. Elasticity of demand is the percentage change in quantity demanded for a given percentage change in the price of the product. The slope of the demand curve is the change in price for a given change in quantity demanded, measured in units of output. Though similar in definition, the units for each measure are different. b. The cross price elasticity will always be positive. False. The cross price elasticity measures the percentage change in the quantity demanded of one product for a given percentage change in the price of another product. This elasticity will be positive for substitutes (an increase in the price of hot dogs is likely to cause an increase in the quantity demanded of hamburgers) and negative for complements (an increase in the price of hot dogs is likely to cause a decrease in the quantity demanded of hot dog buns). c. The supply of apartments is more inelastic in the short run than the long run. True. In the short run it is difficult to change the supply of apartments in response to a change in price. Increasing the supply requires constructing new apartment buildings, which can take a year or more. Since apartments are a durable good, in the long run a change in price will induce suppliers to create more apartments (if price increases) or delay construction (if price decreases). 8. Suppose the government regulates the prices of beef and chicken and sets them below their market-clearing levels. Explain why shortages of these goods will develop and what factors will determine the sizes of the shortages. What will happen to the price of pork? Explain briefly. If the price of a commodity is set below its market-clearing level, the quantity that firms are willing to supply is less than the quantity that consumers wish to purchase. The extent of the excess demand implied by this response will depend on the relative elasticities of demand and supply. For instance, if both supply and demand are elastic, the shortage is larger than if both are inelastic. Factors such as the willingness of consumers to eat less meat and the ability of farmers to change the size of their herds and hence produce less will determine these elasticities and influence the size of excess demand. Customers whose demands are not met will attempt to purchase substitutes, thus increasing the demand for substitutes and raising their prices. If the prices of beef and chicken are set below market-clearing levels, the price of pork will rise, assuming that pork is a substitute for beef and chicken. 9. The city council of a small college town decides to regulate rents in order to reduce student living expenses. Suppose the average annual market-clearing rent for a two-bedroom apartment had been $700 per month, and rents are expected to increase to $900 within a year. The city council limits rents to their current $700 per month level. a. Draw a supply and demand graph to illustrate what will happen to the rental price of an apartment after the imposition of rent controls. The rental price will stay at the old equilibrium level of $700 per month. The expected increase to $900 per month may have been caused by an increase in demand. Given this is true, the price of $700 will be below the new equilibrium and there will be a shortage of apartments. b. Do you think this policy will benefit all students? Why or why not. It will benefit those students who get an apartment, though these students may also find that the costs of searching for an apartment are higher given the shortage of apartments. Those students who do not get an apartment may face higher costs as a result of having to live outside of the college town. Their rent may be higher and the transportation costs will be higher. 10. In a discussion of tuition rates, a university official argues that the demand for admission is completely price inelastic. As evidence she notes that while the university has doubled its tuition (in real terms) over the past 15 years, neither the number nor quality of students applying has decreased. Would you accept this argument? Explain briefly. (Hint: The official makes an assertion about the demand for admission, but does she actually observe a demand curve? What else could be going on?) If demand is fixed, the individual firm (a university) may determine the shape of the demand curve it faces by raising the price and observing the change in quantity sold. The university official is not observing the entire demand curve, but rather only the equilibrium price and quantity over the last 15 years. If demand is shifting upward, as supply shifts upward, demand could have any elasticity. (See Figure 2.7, for example.) Demand could be shifting upward because the value of a college education has increased and students are willing to pay a high price for each opening. More market research would be required to support the conclusion that demand is completely price inelastic.  EMBED PowerPoint.Show.4  Figure 2.10 11. Suppose the demand curve for a product is given by Q=10-2P+Ps, where P is the price of the product and Ps is the price of a substitute good. The price of the substitute good is $2.00. a. Suppose P=$1.00. What is the price elasticity of demand? What is the cross-price elasticity of demand? First you need to find the quantity demanded at the price of $1.00. Q=10-2(1)+2=10. Price elasticity of demand =  EMBED Equation  Cross-price elasticity of demand =  EMBED Equation  b. Suppose the price of the good, P, goes to $2.00. Now what is the price elasticity of demand? What is the cross-price elasticity of demand? First you need to find the quantity demanded at the price of $2.00. Q=10-2(2)+2=8. Price elasticity of demand =  EMBED Equation  Cross-price elasticity of demand =  EMBED Equation  12. Suppose that rather than the declining demand assumed in Example 2.8, a decrease in the cost of copper production causes the supply curve to shift to the right by 40 percent. How will the price of copper change? If the supply curve shifts to the right by 40% then the new quantity supplied will be 140 percent of the old quantity supplied at every price. The new supply curve is therefore Q = 1.4*(-4.5+16P) = -6.3+22.4P. To find the new equilibrium price of copper, set the new supply equal to demand so that 6.3+22.4P=13.5-8P. Solving for price results in P=65 cents per pound for the new equilibrium price. The price decreased by 10 cents per pound, or 13.3%. 13. Suppose the demand for natural gas is perfectly inelastic. What would be the effect, if any, of natural gas price controls? If the demand for natural gas is perfectly inelastic, then the demand curve is vertical. Consumers will demand a certain quantity and will pay any price for this quantity. In this case, a price control will have no effect on the quantity demanded. EXERCISES 1. Suppose the demand curve for a product is given by Q=300-2P+4I, where I is average income measured in thousands of dollars. The supply curve is Q=3P-50. a. If I=25, find the market clearing price and quantity for the product. Given I=25, the demand curve becomes Q=300-2P+4*25, or Q=400-2P. Setting demand equal to supply we can solve for P and then Q: 400-2P=3P-50 P=90 Q=220. b. If I=50, find the market clearing price and quantity for the product. Given I=50, the demand curve becomes Q=300-2P+4*50, or Q=500-2P. Setting demand equal to supply we can solve for P and then Q: 500-2P=3P-50 P=110 Q=280. c. Draw a graph to illustrate your answers. Equilibrium price and quantity are found at the intersection of the demand and supply curves. When the income level increases in part b, the demand curve will shift up and to the right. The intersection of the new demand curve and the supply curve is the new equilibrium point. 2. Consider a competitive market for which the quantities demanded and supplied (per year) at various prices are given as follows: Price ($)Demand (millions)Supply (millions) 602214 80201610018181201620a. Calculate the price elasticity of demand when the price is $80 and when the price is $100. We know that the price elasticity of demand may be calculated using equation 2.1 from the text: EMBED Equation With each price increase of $20, the quantity demanded decreases by 2. Therefore, EMBED Equation At P = 80, quantity demanded equals 20 and EMBED Equation Similarly, at P = 100, quantity demanded equals 18 and EMBED Equation b. Calculate the price elasticity of supply when the price is $80 and when the price is $100. The elasticity of supply is given by: EMBED Equation With each price increase of $20, quantity supplied increases by 2. Therefore, EMBED Equation At P = 80, quantity supplied equals 16 and EMBED Equation Similarly, at P = 100, quantity supplied equals 18 and EMBED Equation c. What are the equilibrium price and quantity? The equilibrium price and quantity are found where the quantity supplied equals the quantity demanded at the same price. As we see from the table, the equilibrium price is $100 and the equilibrium quantity is 18 million. d. Suppose the government sets a price ceiling of $80. Will there be a shortage, and if so, how large will it be? With a price ceiling of $80, consumers would like to buy 20 million, but producers will supply only 16 million. This will result in a shortage of 4 million. 3. Refer to Example 2.5 on the market for wheat. At the end of 1998, both Brazil and Indonesia opened their wheat markets to U.S. farmers. Suppose that these new markets add 200 million bushels to U.S. wheat demand. What will be the free market price of wheat and what quantity will be produced and sold by U.S. farmers in this case? The following equations describe the market for wheat in 1998: QS = 1944 + 207P and QD = 3244 - 283P. If Brazil and Indonesia add an additional 200 million bushels of wheat to U.S. wheat demand, the new demand curve would be equal to QD + 200, or QD = (3244 - 283P) + 200 = 3444 - 283P. Equating supply and the new demand, we may determine the new equilibrium price, 1944 + 207P = 3444 - 283P, or 490P = 1500, or P* = $3.06122 per bushel. To find the equilibrium quantity, substitute the price into either the supply or demand equation, e.g., QS = 1944 + (207)(3.06122) = 2,577.67 and QD = 3444 - (283)(3.06122) = 2,577.67 4. A vegetable fiber is traded in a competitive world market, and the world price is $9 per pound. Unlimited quantities are available for import into the United States at this price. The U.S. domestic supply and demand for various price levels are shown below. PriceU.S. SupplyU.S. Demand(million lbs.)(million lbs.)3234642896221281615101018124 a. What is the equation for demand? What is the equation for supply? The equation for demand is of the form Q=a-bP. First find the slope, which is  EMBED Equation  You can figure this out by noticing that every time price increases by 3, quantity demanded falls by 6 million pounds. Demand is now Q=a-2P. To find a, plug in any of the price quantity demanded points from the table: Q=34=a-2*3 so that a=40 and demand is Q=40-2P. The equation for supply is of the form Q = c + dP. First find the slope, which is  EMBED Equation  You can figure this out by noticing that every time price increases by 3, quantity supplied increases by 2 million pounds. Supply is now  EMBED Equation  To find c plug in any of the price quantity supplied points from the table:  EMBED Equation  so that c=0 and supply is  EMBED Equation  b. At a price of $9, what is the price elasticity of demand? What is it at price of $12? Elasticity of demand at P=9 is  EMBED Equation  Elasticity of demand at P=12 is  EMBED Equation  c. What is the price elasticity of supply at $9? At $12? Elasticity of supply at P=9 is  EMBED Equation  Elasticity of supply at P=12 is  EMBED Equation  d. In a free market, what will be the U.S. price and level of fiber imports? With no restrictions on trade, world price will be the price in the United States, so that P=$9. At this price, the domestic supply is 6 million lbs., while the domestic demand is 22 million lbs. Imports make up the difference and are 16 million lbs. 5. Much of the demand for U.S. agricultural output has come from other countries. In 1998, the total demand for wheat was Q = 3244 - 283P. Of this, domestic demand was QD = 1700 - 107P. Domestic supply was QS = 1944 + 207P. Suppose the export demand for wheat falls by 40 percent. a. U.S. farmers are concerned about this drop in export demand. What happens to the free market price of wheat in the United States? Do the farmers have much reason to worry? Given total demand, Q = 3244 - 283P, and domestic demand, Qd = 1700 - 107P, we may subtract and determine export demand, Qe = 1544 - 176P. The initial market equilibrium price is found by setting total demand equal to supply: 3244 - 283P = 1944 + 207P, or P = $2.65. The best way to handle the 40 percent drop in export demand is to assume that the export demand curve pivots down and to the left around the vertical intercept so that at all prices demand decreases by 40 percent, and the reservation price (the maximum price that the foreign country is willing to pay) does not change. If you instead shifted the demand curve down to the left in a parallel fashion the effect on price and quantity will be qualitatively the same, but will differ quantitatively. The new export demand is 0.6Qe=0.6(1544-176P)=926.4-105.6P. Graphically, export demand has pivoted inwards as illustrated in figure 2.5a below. Total demand becomes QD = Qd + 0.6Qe = 1700 - 107P + 926.4-105.6P = 2626.4 - 212.6P.  EMBED Word.Picture.6  Figure 2.5a Equating total supply and total demand, 1944 + 207P = 2626.4 - 212.6P, or P = $1.63, which is a significant drop from the market-clearing price of $2.65 per bushel. At this price, the market-clearing quantity is 2280.65 million bushels. Total revenue has decreased from $6614.6 million to $3709.0 million. Most farmers would worry. b. Now suppose the U.S. government wants to buy enough wheat each year to raise the price to $3.50 per bushel. With this drop in export demand, how much wheat would the government have to buy? How much would this cost the government? With a price of $3.50, the market is not in equilibrium. Quantity demanded and supplied are QD = 2626.4-212.6(3.5)=1882.3, and QS = 1944 + 207(3.5) = 2668.5. Excess supply is therefore 2668.5-1882.3=786.2 million bushels. The government must purchase this amount to support a price of $3.5, and will spend $3.5(786.2 million) = $2751.7 million per year. 6. The rent control agency of New York City has found that aggregate demand is QD = 160 - 8P. Quantity is measured in tens of thousands of apartments. Price, the average monthly rental rate, is measured in hundreds of dollars. The agency also noted that the increase in Q at lower P results from more three-person families coming into the city from Long Island and demanding apartments. The citys board of realtors acknowledges that this is a good demand estimate and has shown that supply is QS = 70 + 7P. a. If both the agency and the board are right about demand and supply, what is the free market price? What is the change in city population if the agency sets a maximum average monthly rental of $300, and all those who cannot find an apartment leave the city? To find the free market price for apartments, set supply equal to demand: 160 - 8P = 70 + 7P, or P = $600, since price is measured in hundreds of dollars. Substituting the equilibrium price into either the demand or supply equation to determine the equilibrium quantity: QD = 160 - (8)(6) = 112 and QS = 70 + (7)(6) = 112. We find that at the rental rate of $600, the quantity of apartments rented is 1,120,000. If the rent control agency sets the rental rate at $300, the quantity supplied would then be 910,000 (QS = 70 + (7)(3) = 91), a decrease of 210,000 apartments from the free market equilibrium. (Assuming three people per family per apartment, this would imply a loss of 630,000 people.) At the $300 rental rate, the demand for apartments is 1,360,000 units, and the resulting shortage is 450,000 units (1,360,000-910,000). However, excess demand (supply shortages) and lower quantity demanded are not the same concepts. The supply shortage means that the market cannot accommodate the new people who would have been willing to move into the city at the new lower price. Therefore, the city population will only fall by 630,000, which is represented by the drop in the number of actual apartments from 1,120,000 (the old equilibrium value) to 910,000, or 210,000 apartments with 3 people each. b. Suppose the agency bows to the wishes of the board and sets a rental of $900 per month on all apartments to allow landlords a fair rate of return. If 50 percent of any long-run increases in apartment offerings come from new construction, how many apartments are constructed? At a rental rate of $900, the supply of apartments would be 70 + 7(9) = 133, or 1,330,000 units, which is an increase of 210,000 units over the free market equilibrium. Therefore, (0.5)(210,000) = 105,000 units would be constructed. Note, however, that since demand is only 880,000 units, 450,000 units would go unrented. 7. In 1998, Americans smoked 470 billion cigarettes, or 23.5 billion packs of cigarettes. The average retail price was $2 per pack. Statistical studies have shown that the price elasticity of demand is -0.4, and the price elasticity of supply is 0.5. Using this information, derive linear demand and supply curves for the cigarette market. Let the demand curve be of the general form Q=a-bP and the supply curve be of the general form Q=c + dP, where a, b, c, and d are the constants that you have to find from the information given above. To begin, recall the formula for the price elasticity of demand  EMBED Equation  You are given information about the value of the elasticity, P, and Q, which means that you can solve for the slope, which is b in the above formula for the demand curve.  EMBED Equation  To find the constant a, substitute for Q, P, and b into the above formula so that 23.5=a-4.7*2 and a=32.9. The equation for demand is therefore Q=32.9-4.7P. To find the supply curve, recall the formula for the elasticity of supply and follow the same method as above:  EMBED Equation  To find the constant c, substitute for Q, P, and d into the above formula so that 23.5=c+5.875*2 and c=11.75. The equation for supply is therefore Q=11.75+5.875P. 8. In Example 2.8 we examined the effect of a 20 percent decline in copper demand on the price of copper, using the linear supply and demand curves developed in Section 2.4. Suppose the long-run price elasticity of copper demand were -0.4 instead of -0.8. a. Assuming, as before, that the equilibrium price and quantity are P* = 75 cents per pound and Q* = 7.5 million metric tons per year, derive the linear demand curve consistent with the smaller elasticity. Following the method outlined in Section 2.6, we solve for a and b in the demand equation QD = a - bP. First, we know that for a linear demand function EMBED Equation. Here ED = -0.4 (the long-run price elasticity), P* = 0.75 (the equilibrium price), and Q* = 7.5 (the equilibrium quantity). Solving for b, EMBED Equation, or b = 4. To find the intercept, we substitute for b, QD (= Q*), and P (= P*) in the demand equation: 7.5 = a - (4)(0.75), or a = 10.5. The linear demand equation consistent with a long-run price elasticity of -0.4 is therefore QD = 10.5 - 4P. b. Using this demand curve, recalculate the effect of a 20 percent decline in copper demand on the price of copper. The new demand is 20 percent below the original (using our convention that quantity demanded is reduced by 20% at every price): ADVANCE \L 5.5EMBED EquationEMBED Equation. Equating this to supply, 8.4 - 3.2P = -4.5 + 16P, or P = 0.672. With the 20 percent decline in the demand, the price of copper falls to 67.2 cents per pound. 9. Example 2.9 analyzes the world oil market. Using the data given in that example: a. Show that the short-run demand and competitive supply curves are indeed given by D = 24.08 - 0.06P SC = 11.74 + 0.07P. First, considering non-OPEC supply: Sc = Q* = 13. With ES = 0.10 and P* = $18, ES = d(P*/Q*) implies d = 0.07. Substituting for d, Sc, and P in the supply equation, c = 11.74 and Sc = 11.74 + 0.07P. Similarly, since QD = 23, ED = -b(P*/Q*) = -0.05, and b = 0.06. Substituting for b, QD = 23, and P = 18 in the demand equation gives 23 = a - 0.06(18), so that a = 24.08. Hence QD = 24.08 - 0.06P. b. Show that the long-run demand and competitive supply curves are indeed given by D = 32.18 - 0.51P SC = 7.78 + 0.29P. As above, ES = 0.4 and ED = -0.4: ES = d(P*/Q*) and ED = -b(P*/Q*), implying 0.4 = d(18/13) and -0.4 = -b(18/23). So d = 0.29 and b = 0.51. Next solve for c and a: Sc = c + dP and QD = a - bP, implying 13 = c + (0.29)(18) and 23 = a - (0.51)(18). So c = 7.78 and a = 32.18. c. In 2002, Saudi Arabia accounted for 3 billion barrels per year of OPECs production. Suppose that war or revolution caused Saudi Arabia to stop producing oil. Use the model above to calculate what would happen to the price of oil in the short run and the long run if OPECs production were to drop by 3 billion barrels per year. With OPECs supply reduced from 10 bb/yr to 7 bb/yr, add this lower supply of 7 bb/yr to the short-run and long-run supply equations: Sc( = 7 + Sc = 11.74 + 7 + 0.07P = 18.74 + 0.07P and S( = 7 + Sc = 14.78 + 0.29P. These are equated with short-run and long-run demand, so that: 18.74 + 0.07P = 24.08 - 0.06P, implying that P = $41.08 in the short run; and 14.78 + 0.29P = 32.18 - 0.51P, implying that P = $21.75 in the long run. 10. Refer to Example 2.10, which analyzes the effects of price controls on natural gas. a. Using the data in the example, show that the following supply and demand curves did indeed describe the market in 1975: Supply: Q = 14 + 2PG + 0.25PO Demand: Q = -5PG + 3.75PO where PG and PO are the prices of natural gas and oil, respectively. Also, verify that if the price of oil is $8.00, these curves imply a free market price of $2.00 for natural gas. To solve this problem, we apply the analysis of Section 2.6 to the definition of cross-price elasticity of demand given in Section 2.4. For example, the cross-price-elasticity of demand for natural gas with respect to the price of oil is: EMBED Equation EMBED Equation is the change in the quantity of natural gas demanded, because of a small change in the price of oil. For linear demand equations, EMBED Equation is constant. If we represent demand as: QG = a - bPG + ePO (notice that income is held constant), then EMBED Equation = e. Substituting this into the cross-price elasticity, EMBED Equation, where EMBED Equation and EMBED Equation are the equilibrium price and quantity. We know that EMBED Equation = $8 and EMBED Equation = 20 trillion cubic feet (Tcf). Solving for e, EMBED Equation, or e = 3.75. Similarly, if the general form of the supply equation is represented as: QG = c + dPG + gPO, the cross-price elasticity of supply is EMBED Equation, which we know to be 0.1. Solving for g, EMBED Equation, or g = 0.25. The values for d and b may be found with equations 2.5a and 2.5b in Section 2.6. We know that ES = 0.2, P* = 2, and Q* = 20. Therefore, EMBED Equation, or d = 2. Also, ED = -0.5, so EMBED Equation, or b = -5. By substituting these values for d, g, b, and e into our linear supply and demand equations, we may solve for c and a: 20 = c + (2)(2) + (0.25)(8), or c = 14, and 20 = a - (5)(2) + (3.75)(8), or a = 0. If the price of oil is $8.00, these curves imply a free market price of $2.00 for natural gas. Substitute the price of oil in the supply and demand curves to verify these equations. Then set the curves equal to each other and solve for the price of gas. 14 + 2PG + (0.25)(8) = -5PG + (3.75)(8) 7PG = 14 PG = $2.00. b. Suppose the regulated price of gas in 1975 had been $1.50 per thousand cubic feet, instead of $1.00. How much excess demand would there have been? With a regulated price of $1.50 for natural gas and a price of oil equal to $8.00 per barrel, Demand: QD = (-5)(1.50) + (3.75)(8) = 22.5, and Supply: QS = 14 + (2)(1.5) + (0.25)(8) = 19. With a supply of 19 Tcf and a demand of 22.5 Tcf, there would be an excess demand of 3.5 Tcf. c. Suppose that the market for natural gas had not been regulated. If the price of oil had increased from $8 to $16, what would have happened to the free market price of natural gas? If the price of natural gas had not been regulated and the price of oil had increased from $8 to $16, then Demand: QD = -5PG + (3.75)(16) = 60 - 5PG, and Supply: QS = 14 + 2PG + (0.25)(16) = 18 + 2PG. Equating supply and demand and solving for the equilibrium price, 18 + 2PG = 60 - 5PG, or PG = $6. The price of natural gas would have tripled from $2 to $6. 11. The table below shows the retail price and sales for instant coffee and roasted coffee for 1997 and 1998. Retail Price ofSales of Retail Price ofSales of Instant CoffeeInstant CoffeeRoasted CoffeeRoasted CoffeeYear($/lb)(million lbs)($/lb)(million lbs)199710.35754.11820199810.48703.76850 a. Using this data alone, estimate the short-run price elasticity of demand for roasted coffee. Derive a linear demand curve for roasted coffee. To find elasticity, you must first estimate the slope of the demand curve:  EMBED Equation  Given the slope, we can now estimate elasticity using the price and quantity data from the above table. Since the demand curve is assumed to be linear, the elasticity will differ in 1997 and 1998 because price and quantity are different. You can calculate the elasticity at both points and at the average point between the two years:  EMBED Equation  To derive the demand curve for roasted coffee Q=a-bP, note that the slope of the demand curve is -85.7=-b. To find the coefficient a, use either of the data points from the table above so that a=830+85.7*4.11=1172.3 or a=850+85.7*3.76=1172.3. The equation for the demand curve is therefore Q=1172.3-85.7P. b. Now estimate the short-run price elasticity of demand for instant coffee. Derive a linear demand curve for instant coffee. To find elasticity, you must first estimate the slope of the demand curve:  EMBED Equation  Given the slope, we can now estimate elasticity using the price and quantity data from the above table. Since the demand curve Q=a-bP is assumed to be linear, the elasticity will differ in 1997 and 1998 because price and quantity are different. You can calculate the elasticity at both points and at the average point between the two years:  EMBED Equation   EMBED Equation   EMBED Equation  To derive the demand curve for instant coffee, note that the slope of the demand curve is -38.5=-b. To find the coefficient a, use either of the data points from the table above so that a=75+38.5*10.35=473.5 or a=70+38.5*10.48=473.5. The equation for the demand curve is therefore Q=473.5-38.5P. c. Which coffee has the higher short-run price elasticity of demand? Why do you think this is the case? Instant coffee is significantly more elastic than roasted coffee. In fact, the demand for roasted coffee is inelastic and the demand for instant coffee is elastic. Roasted coffee may have an inelastic demand in the short-run as many people think of coffee as a necessary good. Changes in the price of roasted coffee will not drastically affect demand because people must have this good. Many people, on the other hand, may view instant coffee, as a convenient, though imperfect, substitute for roasted coffee. For example, if the price rises a little, the quantity demanded will fall by a large percentage because people would rather drink roasted coffee instead of paying more for a low quality substitute.   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R!dd dd dd dd dd   Ap0 W1A}E 2 s ddRClick to edit Master text styles Second level Third level Fourth level Fifth level RR R!dd dd dd dd dd/> WM?M />  />!ʅ2M# 9E/>  @@``@v@& '2WM% &')ddddd7GcXYhhhYDGa[3(ddddd7G&aXYhhhYDGa[3(2_M+,l/>/>\/>r#####dddddddddd2dddddddddd2     dddddddddd2dddddddddd3dddddddddd00 2@OMTimes New Roman`=A:A "Arial_=AL_==_E0:`:Century SchoolbookMb03'Century Schoolbook0l7G^d6*XXj|VDHP LaserJet 4/4MHPPCL5ELPT1: uy50<)4AlBD XP\I%oc5i F-[.QHP LaserJet 4/4M D.Xt @ p@ "$Bd!$(-*/.0 1@p!ޭ d X    .  & Timesw@0 [wdw0-!P !Q-  PSymbolw@y [wdw0-PIC 35dMETA PICT 48CompObj/K      !"#$%&'()*+,-.0379:;<=>?@ABCDEFGHIJKLMOPQRSTUVWXYZ[\]^_`abcdefhkoqrstuvwxyz{|}~!D Timesw@0 [wdw0-!Q PSymbolw@y [wdw0-!DTimesw@0 [wdw0-!P  PSymbolw@y [wdw0-!="Timesw@0 [wdw0-!1 /!10, , 7!(:PSymbolw@y [wdw0-!->Timesw@0 [wdw0-!2E!)KPSymbolw@y [wdw0-!=R!-\Timesw@0 [wdw0-!2 g!10d d oPSymbolw@y [wdw0-!=t!-~Timesw@0 [wdw0-!0!.!2!. & 'dxpr MTHU Grphbj " currentpoint " + P(Q" ( D)Q(D)P" ("=( /1(,10" , (:()-)2)))=) -( g2(d10" d (t=) -)0).)2)./MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 4832 div 960 3 -1 roll exch div scale currentpoint translate 64 39 translate /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 406 moveto 310 0 rlineto stroke 374 406 moveto 558 0 rlineto stroke 1358 406 moveto 396 0 rlineto stroke 3153 406 moveto 396 0 rlineto stroke /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 384 /Times-Italic f1 (P) 47 264 sh (Q) 17 798 sh (Q) 639 264 sh (P) 658 798 sh 384 /Symbol f1 (D) 404 264 sh (D) 423 798 sh 384 /Symbol f1 (=) 1040 505 sh (-) 1942 505 sh (=) 2570 505 sh (-) 2884 505 sh (=) 3657 505 sh (-) 3971 505 sh 384 /Times-Roman f1 (1) 1460 264 sh (10) 1348 798 sh (2) 2152 505 sh (2) 3255 264 sh (10) 3143 798 sh (0) 4181 505 sh (2) 4469 505 sh 384 /Times-Roman f1 (\() 1800 505 sh (\)) 2353 505 sh (.) 4373 505 sh (.) 4661 505 sh end MTsave restore dMATHxM PQDQDP=110(-2)=-210=-0.2.m FMathType Equation1ELO Equationx PQDQDP=110(-2)=-210=-0.2. Equationd 4 lObjInfo791Ole10Native:2|Ole10FmtProgID 4 _1010475038? F+-}B+-}BOle 5PIC <>6dMETA 8RPICT =AN@ 4   h .  & Timesw@@ [wdw0-!P Timesw@ [wdw0-!s Timesw@@ [wdw0-!Q-  PSymbolw@ [wdw0-!D Timesw@@ [wdw0-!Q PSymbolw@ [wdw0-!DTimesw@@ [wdw0-!PTimesw@ [wdw0-!s  PSymbolw@@ [wdw0-!=$Timesw@ [wdw0-!2 1!10. . 9!(<!1?!)DPSymbolw@@ [wdw0-!=KTimesw@ [wdw0-!0U!.[!2^!.d & '@hdxpr MTHUhGrphbj h"h currentpoint " + P +s (Q"  ( D)Q(D)P +s"  ($=( 12(.10" . (<()1)))=) 0).)2)./MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 3328 div 992 3 -1 roll exch div scale currentpoint translate 64 39 translate /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 406 moveto 355 0 rlineto stroke 419 406 moveto 582 0 rlineto stroke 1427 406 moveto 396 0 rlineto stroke /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 384 /Times-Italic f1 (P) 38 264 sh (Q) 39 798 sh (Q) 696 264 sh (P) 684 798 sh 224 ns (s) 209 360 sh (s) 855 894 sh 384 /Symbol f1 (D) 461 264 sh (D) 449 798 sh 384 /Symbol f1 (=) 1109 505 sh (=) 2360 505 sh 384 /Times-Roman f1 (2) 1529 264 sh (10) 1417 798 sh (1) 1973 505 sh (0) 2669 505 sh (2) 2957 505 sh 384 /Times-Roman f1 (\() 1869 505 sh (\)) 2143 505 sh (.) 2861 505 sh (.) 3149 505 sh end MTsave restore dMATHt P s QDQDP s =210(1)=0.2.۠ FMathType Equation1ELO EqCompObjgKObjInfo@BiOle10NativeCjxOle10FmtProgID l uationt P s QDQDP s =210(1)=0.2. Equationd X_1010475182H F+-}B+-}BOle mPIC EGndMETA p    .  & Timesw@ [wdw0-!P !Q-  PSymbolw@' [wdw0-!D Timesw@ [wdw0-!Q PSymbolw@' [wdw0-!DTimesw@ [wdw0-!P  PSymbolw@' [wdw0-!="Timesw@ [wdw0-!2 -!8- , 2!(5PSymbolw@' [wdw0-!-9Timesw@ [wdw0-!2@!)FPSymbolw@' [wdw0-!=M!-WTimesw@ [wdw0-!4 `!8` _ fPSymbolw@' [wdw0-!=j!-tTimesw@ [wdw0-!0z!.!5!. & 'PICT FJCompObjKObjInfoIKOle10NativeLvdxpr MTHU Grphbj " currentpoint " + P(Q" ( D)Q(D)P" ("=( -2*8" ,(5()-)2)))=) -( `4*8" _(j=) -)0).)5)./MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 4512 div 960 3 -1 roll exch div scale currentpoint translate 64 39 translate /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 406 moveto 310 0 rlineto stroke 374 406 moveto 558 0 rlineto stroke 1358 406 moveto 235 0 rlineto stroke 2992 406 moveto 241 0 rlineto stroke /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 384 /Times-Italic f1 (P) 47 264 sh (Q) 17 798 sh (Q) 639 264 sh (P) 658 798 sh 384 /Symbol f1 (D) 404 264 sh (D) 423 798 sh 384 /Symbol f1 (=) 1040 505 sh (-) 1781 505 sh (=) 2409 505 sh (-) 2723 505 sh (=) 3341 505 sh (-) 3655 505 sh 384 /Times-Roman f1 (2) 1379 264 sh (8) 1381 798 sh (2) 1991 505 sh (4) 3020 264 sh (8) 3018 798 sh (0) 3865 505 sh (5) 4153 505 sh 384 /Times-Roman f1 (\() 1639 505 sh (\)) 2192 505 sh (.) 4057 505 sh (.) 4345 505 sh end MTsave restore d~MATHr PQDQDP=28(-2)=-48=-0.5.m FMathType Equation1ELO Equationr PQDQDP=28(-2)=-48=-0.5.Ole10FmtProgID  _10104751812Q F+-}B+-}BOle PIC NPd Equationd 44l 4   i .  & Timesw@0 [wdw0-!P Timesw@ [wdw0META RPICT OS=CompObjKObjInfoRT-!s Timesw@0 [wdw0-!Q-  PSymbolw@ [wdw0-!D Timesw@0 [wdw0-!Q PSymbolw@ [wdw0-!DTimesw@0 [wdw0-!PTimesw@ [wdw0-!s  PSymbolw@0 [wdw0-!=$Timesw@ [wdw0-!2 /!8/ . 4!(7!1:!)?PSymbolw@0 [wdw0-!=FTimesw@ [wdw0-!0P!.V!25Y!.e & '=idxpr MTHUiGrphbj i"i currentpoint " + P +s (Q"  ( D)Q(D)P +s"  ($=( /2*8" .(7()1)))=) 0).)25) ./MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 3360 div 992 3 -1 roll exch div scale currentpoint translate 64 39 translate /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 406 moveto 355 0 rlineto stroke 419 406 moveto 582 0 rlineto stroke 1427 406 moveto 235 0 rlineto stroke /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 384 /Times-Italic f1 (P) 38 264 sh (Q) 39 798 sh (Q) 696 264 sh (P) 684 798 sh 224 ns (s) 209 360 sh (s) 855 894 sh 384 /Symbol f1 (D) 461 264 sh (D) 449 798 sh 384 /Symbol f1 (=) 1109 505 sh (=) 2199 505 sh 384 /Times-Roman f1 (2) 1448 264 sh (8) 1450 798 sh (1) 1812 505 sh (0) 2508 505 sh (25) 2796 505 sh 384 /Times-Roman f1 (\() 1708 505 sh (\)) 1982 505 sh (.) 2700 505 sh (.) 3180 505 sh end MTsave restore dMATHt P s QDQDP s =28(1)=0.25.۠ FMathType Equation1ELO Equationt P s QDQDP s =28(1)=0.25.Ole10NativeUxOle10FmtProgID  _927563850$\X F+-}B+-}BOle  Equation FMathType Equation Equation Equation9q   .1   &  & MathTypeCompObjWZ\ObjInfoOlePres000Y[Ole10Native-_3_-(:  t  Century Schoolbook- 2 @E 2 IQ 2 ! Q 2 P 2 P 2 1P 2 *Q 2 !d Q 2  P Century Schoolbookx- 2 PGD 2 D 2 q1D 2 I; D 2 qu DSymbol- 2 = 2 = 2 ID 2 RD 2 ! D 2 & DCentury Schoolbooky- 2  .Y & "System-  E D =DQ D Q D DPP=PQ D DQ D DP..d X  /  f .  & PSymbolw@ /[wdw0-!D Timesw@c p[wdw0_927563851` F+-}B+-}BOle PIC ]_dMETA f      !"#$%&(+,-./0123456789:;<=>?@ABDHJKLMNOPQRSTUVWXYZ\]^_`abcdefghijklmnopqrstuwz{|}~-!Q Timesw@ 0[wdw0-!D PSymbolw@c q[wdw0-!D Timesw@ 1[wdw0-!P-PSymbolw@c r[wdw0-! ! ! ! !=(!- 2Timesw@ 2[wdw0-!2 9!2031?PSymbolw@c s[wdw0-!=C!-MTimesw@ 3[wdw0-!0S!.Y!1\!.b & 'fdxpr MTHU fGrphbj f"f currentpoint " +PICT ^bCompObj'\ObjInfoad)OlePres000*. D)Q + D ( D)P"(  *  (  *  ((=( 2-)2(320"1(C=) -)0).)1).k/MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 3264 div 960 3 -1 roll exch div scale currentpoint translate 64 39 translate /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 182 438 moveto 744 0 rlineto stroke 1534 438 moveto 452 0 rlineto stroke /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 384 /Symbol f1 (D) 212 296 sh (D) 324 830 sh 384 /Times-Italic f1 (Q) 447 296 sh (P) 559 830 sh 224 ns (D) 712 392 sh 384 /Symbol f1 (\346) -15 355 sh (\350) -15 764 sh (\366) 936 355 sh (\370) 936 764 sh (=) 1216 537 sh (-) 1562 296 sh (=) 2094 537 sh (-) 2408 537 sh 384 /Times-Roman f1 (2) 1772 296 sh (20) 1568 830 sh (0) 2618 537 sh (1) 2906 537 sh 384 /Times-Roman f1 (.) 2810 537 sh (.) 3098 537 sh end MTsave restore dnMATHb6 DQ D DP()=-220=-0.1.m FMathType Equation1ELO Equation9qTCIP#fdxpr MTHU fGrphbj f"f currentpoint " + D)Q + D ( D)P"(  *  (  *  ((=( 2-)2(320"1(C=) -)0).)1).k/MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 3264 div 960 3 -1 roll exch div scale currentpoint translate 64 39 translate /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 182 438 moveto 744 0 rlineto stroke 1534 438 moveto 452 0 rlineto stroke /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 384 /Symbol f1 (D) 212 296 sh (D) 324 830 sh 384 /Times-Italic f1 (Q) 447 296 sh (P) 559 830 sh 224 ns (D) 712 392 sh 384 /Symbol f1 (\346) -15 355 sh (\350) -15 764 sh (\366) 936 355 sh (\370) 936 764 sh (=) 1216 537 sh (-) 1562 296 sh (=) 2094 537 sh (-) 2408 537 sh 384 /Times-Roman f1 (2) 1772 296 sh (20) 1568 830 sh (0) 2618 537 sh (1) 2906 537 sh 384 /Times-Roman f1 (.) 2810 537 sh (.) 3098 537 sh end MTsave restore dnMATHb6 DQ D DP()=-220=-0.1.mb DQ D DP()=-220=-0.1. Equationd  XOle10NativeceCfOle10FmtProgID E _927563852Vzj F+-}B+-}BOle FPIC giGdMETA InPICT hl[CompObjv\  3   .  & Timesw@A [wdw0-!ETimesw@ [wdw0-!D PSymbolw@A [wdw0-!=Timesw@ [wdw0-!80 "!20"-".PSymbolw@A [wdw0-! ! ! /! /!-:Timesw@ [wdw0-!0@!.F!1IPSymbolw@A [wdw0-!(5!)NPSymbolw@ [wdw0-!=U!-_Timesw@A [wdw0-!0f!.l!40o!.{ & 'dxpr MTHU Grphbj " currentpoint " +E +D (=( "80*20"" (  *  ( / *  (:-)0).)1 (5()))=) -)0).)40) ./MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 4064 div 960 3 -1 roll exch div scale currentpoint translate 64 42 translate /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 1034 435 moveto 427 0 rlineto stroke /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 384 /Times-Italic f1 (E) 6 534 sh 224 ns (D) 244 630 sh 384 /Symbol f1 (=) 534 534 sh (\346) 837 355 sh (\350) 837 758 sh (\366) 1471 355 sh (\370) 1471 758 sh (-) 1794 534 sh /f3 {ff 3 -1 roll .001 mul 3 -1 roll .001 mul matrix scale makefont dup /cf exch def sf} def 384 1000 1171 /Symbol f3 (\() 1653 544 sh (\)) 2462 544 sh 384 /Symbol f1 (=) 2676 534 sh (-) 2990 534 sh 384 /Times-Roman f1 (80) 1050 293 sh (20) 1055 827 sh (0) 2004 534 sh (1) 2292 534 sh (0) 3200 534 sh (40) 3488 534 sh 384 /Times-Roman f1 (.) 2196 534 sh (.) 3392 534 sh (.) 3872 534 sh end MTsave restore dxMATHl E D =8020()-0.1()=-0.40.m FMathType Equation1ELO Equation9qObjInfoknxOlePres000yOle10NativemopOle10FmtProgID  TCIP#dxpr MTHU Grphbj " currentpoint " +E +D (=( "80*20"" (  *  ( / *  (:-)0).)1 (5()))=) -)0).)40) ./MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 4064 div 960 3 -1 roll exch div scale currentpoint translate 64 42 translate /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 1034 435 moveto 427 0 rlineto stroke /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 384 /Times-Italic f1 (E) 6 534 sh 224 ns (D) 244 630 sh 384 /Symbol f1 (=) 534 534 sh (\346) 837 355 sh (\350) 837 758 sh (\366) 1471 355 sh (\370) 1471 758 sh (-) 1794 534 sh /f3 {ff 3 -1 roll .001 mul 3 -1 roll .001 mul matrix scale makefont dup /cf exch def sf} def 384 1000 1171 /Symbol f3 (\() 1653 544 sh (\)) 2462 544 sh 384 /Symbol f1 (=) 2676 534 sh (-) 2990 534 sh 384 /Times-Roman f1 (80) 1050 293 sh (20) 1055 827 sh (0) 2004 534 sh (1) 2292 534 sh (0) 3200 534 sh (40) 3488 534 sh 384 /Times-Roman f1 (.) 2196 534 sh (.) 3392 534 sh (.) 3872 534 sh end MTsave restore dxMATHl E D =8020()-0.1()=-0.40.ml E D =8020()-0.1()=-0.40. Equation_927563853t F+-}B+-}BOle PIC qsdMETA pd P X  4   .  & Timesw@ L[wdw0-!ETimesw@ J[wdw0-!D PSymbolw@ M[wdw0-!=Timesw@ K[wdw0-!100 "!18%-"3PSymbolw@ N[wdw0-! ! ! 5! 5!-?Timesw@ L[wdw0-!0E!.K!1NPSymbolw@ O[wdw0-!(:!)SPSymbolw@ M[wdw0-!=Z!-dTimesw@ P[wdw0-!0k!.q!56t!. & 'dxpr MTHU Grphbj " currentpoint " +E +D (=( "100+18""(  *  ( 5 *  (?-)0).)1 (:(PICT rvCompObj\ObjInfouxOlePres000)))=) -)0).)56) ./MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 4224 div 960 3 -1 roll exch div scale currentpoint translate 64 42 translate /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 1034 435 moveto 588 0 rlineto stroke /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 384 /Times-Italic f1 (E) 6 534 sh 224 ns (D) 244 630 sh 384 /Symbol f1 (=) 534 534 sh (\346) 837 355 sh (\350) 837 758 sh (\366) 1632 355 sh (\370) 1632 758 sh (-) 1955 534 sh /f3 {ff 3 -1 roll .001 mul 3 -1 roll .001 mul matrix scale makefont dup /cf exch def sf} def 384 1000 1171 /Symbol f3 (\() 1814 544 sh (\)) 2623 544 sh 384 /Symbol f1 (=) 2837 534 sh (-) 3151 534 sh 384 /Times-Roman f1 (100) 1024 293 sh (18) 1127 827 sh (0) 2165 534 sh (1) 2453 534 sh (0) 3361 534 sh (56) 3649 534 sh 384 /Times-Roman f1 (.) 2357 534 sh (.) 3553 534 sh (.) 4033 534 sh end MTsave restore d{MATHo E D =10018()-0.1()=-0.56. FMathType Equation1ELO Equation9qTCIP1#dxpr MTHU Grphbj " currentpoint " +E +D (=( "100+18""(  *  ( 5 *  (?-)0).)1 (:()))=) -)0).)56) ./MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 4224 div 960 3 -1 roll exch div scale currentpoint translate 64 42 translate /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 1034 435 moveto 588 0 rlineto stroke /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 384 /Times-Italic f1 (E) 6 534 sh 224 ns (D) 244 630 sh 384 /Symbol f1 (=) 534 534 sh (\346) 837 355 sh (\350) 837 758 sh (\366) 1632 355 sh (\370) 1632 758 sh (-) 1955 534 sh /f3 {ff 3 -1 roll .001 mul 3 -1 roll .001 mul matrix scale makefont dup /cf exch def sf} def 384 1000 1171 /Symbol f3 (\() 1814 544 sh (\)) 2623 544 sh 384 /Symbol f1 (=) 2837 534 sh (-) 3151 534 sh 384 /Times-Roman f1 (100) 1024 293 sh (18) 1127 827 sh (0) 2165 534 sh (1) 2453 534 sh (0) 3361 534 sh (56) 3649 534 sh 384 /Times-Roman f1 (.) 2357 534 sh (.) 3553 534 sh (.) 4033 534 sh end MTsave restore d{MATHo E D =10018()-0.1()=-0.56.o E D =10018()-0.1()=-0.56.Ole10NativewysOle10FmtProgID  _927563854p| F+-}B+-}BOle  Equation FMathType Equation Equation Equation9q   .1   &@  & MathTypeCompObj{~\ObjInfoOlePres000}Ole10Native-L__-dl    Century Schoolbook- 2 @E 2 IfQ 2 !Q 2 P 2 uP 2 1UP 2 Q 2 ! Q 2 V P Century Schoolbookx- 2 P9S 2 iS 2 qS 2 IS 2 q SSymbol- 2 Y= 2 = 2 ID 2 D 2 !# D 2  DCentury Schoolbooky- 2  .Y & "System- E S =DQ S Q S DPP=PQ S DQ S DP. q2 2 9      !"#$%&'()*+,-/23456789:;<=>?@ABCDEFGHJNPQRSTUVWXYZ[\]^_`bcdefghijklmnopqrstuvwxyz|d DX  !  ] .  & PSymbolw@ [[wdw0-!D Timesw@ [wdw0_927563855 F+-}B+-}BOle PIC dMETA J-!Q Timesw@ \[wdw0-!S PSymbolw@ [wdw0-!D Timesw@ ][wdw0-!P-PSymbolw@ [wdw0-! ! ! ! !=&Timesw@ ^[wdw0-!2 4!2010<PSymbolw@ [wdw0-!=ATimesw@ _[wdw0-!0J!.P!1S!.Y & ']dxpr MTHU ]Grphbj ]"] currentpoint " +PICT CompObj.\ObjInfo0OlePres0001 D)Q + S ( D)P"(  *  (  *  (&=( 42(120"0 (A=) 0).)1).K/MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 2976 div 960 3 -1 roll exch div scale currentpoint translate 64 39 translate /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 182 438 moveto 694 0 rlineto stroke 1484 438 moveto 427 0 rlineto stroke /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 384 /Symbol f1 (D) 212 296 sh (D) 299 830 sh 384 /Times-Italic f1 (Q) 447 296 sh (P) 534 830 sh 224 ns (S) 704 392 sh 384 /Symbol f1 (\346) -15 355 sh (\350) -15 764 sh (\366) 886 355 sh (\370) 886 764 sh (=) 1166 537 sh (=) 2019 537 sh 384 /Times-Roman f1 (2) 1601 296 sh (20) 1505 830 sh (0) 2328 537 sh (1) 2616 537 sh 384 /Times-Roman f1 (.) 2520 537 sh (.) 2808 537 sh end MTsave restore dhMATH\  DQ S DP()=220=0.1. FMathType Equation1ELO Equation9qTCIP #]dxpr MTHU ]Grphbj ]"] currentpoint " + D)Q + S ( D)P"(  *  (  *  (&=( 42(120"0 (A=) 0).)1).K/MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 2976 div 960 3 -1 roll exch div scale currentpoint translate 64 39 translate /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 182 438 moveto 694 0 rlineto stroke 1484 438 moveto 427 0 rlineto stroke /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 384 /Symbol f1 (D) 212 296 sh (D) 299 830 sh 384 /Times-Italic f1 (Q) 447 296 sh (P) 534 830 sh 224 ns (S) 704 392 sh 384 /Symbol f1 (\346) -15 355 sh (\350) -15 764 sh (\366) 886 355 sh (\370) 886 764 sh (=) 1166 537 sh (=) 2019 537 sh 384 /Times-Roman f1 (2) 1601 296 sh (20) 1505 830 sh (0) 2328 537 sh (1) 2616 537 sh 384 /Times-Roman f1 (.) 2520 537 sh (.) 2808 537 sh end MTsave restore dhMATH\  DQ S DP()=220=0.1.\ DQ S DP()=220=0.1. Equationd 4X  %  i .Ole10NativeI`Ole10FmtProgID K _927563857f' F+-}B+-}BOle LPIC MdMETA ORPICT a`CompObj{\  & Timesw@A [wdw0-!ETimesw@ [wdw0-!S PSymbolw@A [wdw0-!=Timesw@ [wdw0-!80 !!16 - ,PSymbolw@A [wdw0-! ! ! .! .Timesw@ [wdw0-!08!.>!1APSymbolw@A [wdw0-!(3!)FPSymbolw@ [wdw0-!=MTimesw@A [wdw0-!0V!.\!5_!.e & '`idxpr MTHU iGrphbj i"i currentpoint " +E +S (=( !80( 16" (  *  ( . *  (80).)1 (3()))=) 0).)5)./MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 3360 div 960 3 -1 roll exch div scale currentpoint translate 64 42 translate /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 984 435 moveto 418 0 rlineto stroke /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 384 /Times-Italic f1 (E) 6 534 sh 224 ns (S) 236 630 sh 384 /Symbol f1 (=) 484 534 sh (\346) 787 355 sh (\350) 787 758 sh (\366) 1412 355 sh (\370) 1412 758 sh /f3 {ff 3 -1 roll .001 mul 3 -1 roll .001 mul matrix scale makefont dup /cf exch def sf} def 384 1000 1171 /Symbol f3 (\() 1594 544 sh (\)) 2188 544 sh 384 /Symbol f1 (=) 2402 534 sh 384 /Times-Roman f1 (80) 996 293 sh (16) 987 827 sh (0) 1730 534 sh (1) 2018 534 sh (0) 2711 534 sh (5) 2999 534 sh 384 /Times-Roman f1 (.) 1922 534 sh (.) 2903 534 sh (.) 3191 534 sh end MTsave restore doMATHc E S =8016()0.1()=0.5.Di FMathType Equation1ELO Equation9qTCIPy#``idxpr MTHU iGrphbj i"iObjInfo}OlePres000~Ole10NativegOle10FmtProgID   currentpoint " +E +S (=( !80( 16" (  *  ( . *  (80).)1 (3()))=) 0).)5)./MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 3360 div 960 3 -1 roll exch div scale currentpoint translate 64 42 translate /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 984 435 moveto 418 0 rlineto stroke /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 384 /Times-Italic f1 (E) 6 534 sh 224 ns (S) 236 630 sh 384 /Symbol f1 (=) 484 534 sh (\346) 787 355 sh (\350) 787 758 sh (\366) 1412 355 sh (\370) 1412 758 sh /f3 {ff 3 -1 roll .001 mul 3 -1 roll .001 mul matrix scale makefont dup /cf exch def sf} def 384 1000 1171 /Symbol f3 (\() 1594 544 sh (\)) 2188 544 sh 384 /Symbol f1 (=) 2402 534 sh 384 /Times-Roman f1 (80) 996 293 sh (16) 987 827 sh (0) 1730 534 sh (1) 2018 534 sh (0) 2711 534 sh (5) 2999 534 sh 384 /Times-Roman f1 (.) 1922 534 sh (.) 2903 534 sh (.) 3191 534 sh end MTsave restore doMATHc E S =8016()0.1()=0.5.Dic E S =8016()0.1()=0.5. Equationd $ X  &  u ._927563858 F+-}B.}BOle PIC dMETA T  & Timesw@ [wdw0-!ETimesw@ [wdw0-!S PSymbolw@ [wdw0-!=Timesw@ [wdw0-!100 !18#- 2PSymbolw@ [wdw0-! ! ! 3! 3Timesw@ [wdw0-!0=!.C!1FPSymbolw@ [wdw0-!(9!)KPSymbolw@ [wdw0-!=RTimesw@ [wdw0-!0\!.b!56e!.q & 'iudxpr MTHU uGrphbj u"u currentpoint " +E +S (=( 100+18" (  *  ( 3 *  (=0).)1 (9()))=) 0).)56) ./MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 3744 div 960 3 -1 roll exch div scale currentpoint translate 64 42 translate /tPICT iCompObj\ObjInfoOlePres000hick 0 def /th { dup setlinewidth /thick exch def } def 16 th 984 435 moveto 588 0 rlineto stroke /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 384 /Times-Italic f1 (E) 6 534 sh 224 ns (S) 236 630 sh 384 /Symbol f1 (=) 484 534 sh (\346) 787 355 sh (\350) 787 758 sh (\366) 1582 355 sh (\370) 1582 758 sh /f3 {ff 3 -1 roll .001 mul 3 -1 roll .001 mul matrix scale makefont dup /cf exch def sf} def 384 1000 1171 /Symbol f3 (\() 1764 544 sh (\)) 2358 544 sh 384 /Symbol f1 (=) 2572 534 sh 384 /Times-Roman f1 (100) 974 293 sh (18) 1077 827 sh (0) 1900 534 sh (1) 2188 534 sh (0) 2881 534 sh (56) 3169 534 sh 384 /Times-Roman f1 (.) 2092 534 sh (.) 3073 534 sh (.) 3553 534 sh end MTsave restore duMATHi, E S =10018()0.1()=0.56. FMathType Equation1ELO Equation9qTCIP #iiudxpr MTHU uGrphbj u"u currentpoint " +E +S (=( 100+18" (  *  ( 3 *  (=0).)1 (9()))=) 0).)56) ./MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 3744 div 960 3 -1 roll exch div scale currentpoint translate 64 42 translate /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 984 435 moveto 588 0 rlineto stroke /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 384 /Times-Italic f1 (E) 6 534 sh 224 ns (S) 236 630 sh 384 /Symbol f1 (=) 484 534 sh (\346) 787 355 sh (\350) 787 758 sh (\366) 1582 355 sh (\370) 1582 758 sh /f3 {ff 3 -1 roll .001 mul 3 -1 roll .001 mul matrix scale makefont dup /cf exch def sf} def 384 1000 1171 /Symbol f3 (\() 1764 544 sh (\)) 2358 544 sh 384 /Symbol f1 (=) 2572 534 sh 384 /Times-Roman f1 (100) 974 293 sh (18) 1077 827 sh (0) 1900 534 sh (1) 2188 534 sh (0) 2881 534 sh (56) 3169 534 sh 384 /Times-Roman f1 (.) 2092 534 sh (.) 3073 534 sh (.) 3553 534 sh end MTsave restore duMATHi, E S =10018()0.1()=0.56.i E S =10018()0.1()=0.56. Equationd 0  [  f .Ole10NativemOle10FmtProgID  _1010490113D F.}B.}BOle PIC dMETA PICT CompObjK      "#$%&'()*+,-./012346;>@ABCDEFGHIJKMNOPQRSTUVWXYZ[\]^`fhijklmnopqrstvwxyz{|}~  & PSymbolw@[ [wdw0-!D Timesw@3 [wdw0-!Q PSymbolw@[ [wdw0-!DTimesw@3 [wdw0-!P -  PSymbolw@[ [wdw0-!=!- !Timesw@3 [wdw0-!6 (!3$  -PSymbolw@[ [wdw0-!=2!-;Timesw@3 [wdw0-!2BPSymbolw@[ [wdw0-!=K!-UTimesw@3 [wdw0-!b\Timesw@[ [wdw0-!.b & 'fdxpr MTHU fGrphbj f"f currentpoint " + D)Q(D)P" (=( !-)6($3" (2=) -)2) =) -)b)./MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 3264 div 896 3 -1 roll exch div scale currentpoint translate 64 39 translate /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 406 moveto 558 0 rlineto stroke 984 406 moveto 449 0 rlineto stroke /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 384 /Symbol f1 (D) 30 264 sh (D) 49 798 sh 384 /Times-Italic f1 (Q) 265 264 sh (P) 284 798 sh (b) 2895 505 sh 384 /Symbol f1 (=) 666 505 sh (-) 1012 264 sh (=) 1541 505 sh (-) 1855 505 sh (=) 2355 505 sh (-) 2669 505 sh 384 /Times-Roman f1 (6) 1222 264 sh (3) 1118 798 sh (2) 2065 505 sh 384 /Times-Roman f1 (.) 3081 505 sh end MTsave restore dTMATHH  DQDP=-63=-2=-b.۠ FMathType Equation1ELO EquationH DQDP=-63=-2=-b. EquationL40ObjInfoOle10NativeLOle10FmtProgID  _1004702167*F.}B.}BOle PIC LPICT !CompObj5W-dxpr MTHU -Grphbj -"- currentpoint " + D)Q(D)P" (=( !2*3" ()./MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 1440 div 896 3 -1 roll exch div scale currentpoint translate 64 39 translate /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 406 moveto 558 0 rlineto stroke 984 406 moveto 235 0 rlineto stroke /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 384 /Symbol f1 (D) 30 264 sh (D) 49 798 sh 384 /Times-Italic f1 (Q) 265 264 sh (P) 284 798 sh 384 /Symbol f1 (=) 666 505 sh 384 /Times-Roman f1 (2) 1005 264 sh (3) 1011 798 sh 384 /Times-Roman f1 (.) 1257 505 sh end MTsave restore d?MATH3 DQDP=23.mFMathType Equation 3.6+DNQEEquation.DSMT36ObjInfo7Ole10Native87Ole10FmtProgID 9 Equation Native :U3 DQDP=23. Equation9 DQDP=23=d.d404   < ._1010571573 F.}B.}BOle <PIC =dMETA ?(  & Timesw@ [wdw0-!QPSymbolw@ [wdw0-!= Timesw@ [wdw0-!cPSymbolw@ ![wdw0-!+Timesw@ [wdw0-!2 (!3(- ( .Timesw@ "[wdw0-!P1Timesw@ [wdw0-!.8 & '<dxpr MTHU E?@ABCDGIXHJNKLMPOUQRSTVWY^sZ[\]_`afbcdegkhijmlrnopqtwuvxzy{|}~  & Timesw@ ;[wdw0-!QPSymbolw@ :[wdw0-!= Timesw@ <[wdw0-!2PSymbolw@ ;[wdw0-!=Timesw@ =[wdw0-!c)PSymbolw@ <[wdw0-!+1Timesw@ >[wdw0-!2 ;!3;- : A!(C!3G!)M & 'Rdxpr MTHU RGrphbj R"R currentpoint " +Q) =) 2) =) c)+( ;2*3" :(C()3))/MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 2624 div 896 3 -1 roll exch div scale currentpoint translate 64 42 translate /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 1813 403 moveto 235 0 rlineto stroke /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 384 /Times-Italic f1 (Q) -15 502 sh (c) 1257 502 sh 384 /Symbol f1 (=) 354 502 sh (=) 951 502 sh (+) 1511 502 sh 384 /Times-Roman f1 (2) 661 502 sh (2) 1834 261 sh (3) 1840 795 sh (3) 2224 502 sh 384 /Times-Roman f1 (\() 2094 502 sh (\)) 2408 502 sh end MTsave restore d?MATH3 Q=2=c+23(3)ħ FMathType Equation1ELO Equation3 Q=2=c+23(3) Equationdr\0Ole10Native7Ole10FmtProgID  _1010571672 F.}B.}BOle PIC dMETA |PICT OCompObjKr :  + .  & Timesw@[ [wdw0-!QPSymbolw@ I[wdw0-!= Timesw@[ ![wdw0-!2 !3-  Timesw@ J[wdw0-!P Timesw@[ "[wdw0-!.' & 'O+dxpr MTHU +Grphbj +"+ currentpoint " +Q) =( 2*3" ( P).W/MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 1376 div 896 3 -1 roll exch div scale currentpoint translate 64 42 translate /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 672 403 moveto 235 0 rlineto stroke /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 384 /Times-Italic f1 (Q) -15 502 sh (P) 977 502 sh 384 /Symbol f1 (=) 354 502 sh 384 /Times-Roman f1 (2) 693 261 sh (3) 699 795 sh 384 /Times-Roman f1 (.) 1204 502 sh end MTsave restore d0MATH$ Q=23P.-- FMathType Equation1ELO EquationObjInfoOle10Native(Ole10FmtProgID  _1010571721 F.}B.}B$ Q=23P. Equationd:D X:    .  & Timesw@ v[wdw0-!Ole PIC dMETA PICT P !Q-  PSymbolw@3 [wdw0-!D Timesw@ w[wdw0-!Q PSymbolw@3 [wdw0-!DTimesw@ x[wdw0-!P  PSymbolw@3 [wdw0-!="Timesw@ y[wdw0-!9 0!22- , 8!(;PSymbolw@3 [wdw0-!-?Timesw@ z[wdw0-!2F!)LPSymbolw@3 [wdw0-!=S!- ^Timesw@ {[wdw0-!18 d!22a ] oPSymbolw@3 [wdw0-!=t!-~Timesw@ |[wdw0-!0!.!82!. & 'dxpr MTHU Grphbj " currentpoint " + P(Q" ( D)Q(D)P" ("=( 09(-22" , (;()-)2)))=( ^-)18(a22" ](t=) -)0).)82) ./MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 5024 div 960 3 -1 roll exch div scale currentpoint translate 64 39 translate /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 406 moveto 310 0 rlineto stroke 374 406 moveto 558 0 rlineto stroke 1358 406 moveto 427 0 rlineto stroke 2919 406 moveto 631 0 rlineto stroke /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 384 /Times-Italic f1 (P) 47 264 sh (Q) 17 798 sh (Q) 639 264 sh (P) 658 798 sh 384 /Symbol f1 (D) 404 264 sh (D) 423 798 sh 384 /Symbol f1 (=) 1040 505 sh (-) 1973 505 sh (=) 2601 505 sh (-) 2947 264 sh (=) 3658 505 sh (-) 3972 505 sh 384 /Times-Roman f1 (9) 1478 264 sh (22) 1379 798 sh (2) 2183 505 sh (18) 3157 264 sh (22) 3042 798 sh (0) 4182 505 sh (82) 4470 505 sh 384 /Times-Roman f1 (\() 1831 505 sh (\)) 2384 505 sh (.) 4374 505 sh (.) 4854 505 sh end MTsave restore dMATH~ PQDQDP=922(-2)=-1822=-0.82.۠ FMathType Equation1ELO Equation~ PQDQDP=922(-2)=-1822=-0.82. EquationCompObjKObjInfoOle10NativeOle10FmtProgID  _1010571812 F.}B.}BOle PIC dMETA d X    .  & Timesw@] )[wdw0-!P !Q-  PSymbolw@m [wdw0-     !"#$%&(+,023456789:;<=>?@ABCDEFHIJKLMNOPQRSTUVWXYZ[\]^_`abcehimopqrstuvwxyz{|}~!D Timesw@] *[wdw0-!Q PSymbolw@m [wdw0-!DTimesw@] +[wdw0-!P  PSymbolw@m [wdw0-!="Timesw@] ,[wdw0-!12 ,!16, , 7!(:PSymbolw@m [wdw0-!->Timesw@] -[wdw0-!2E!)KPSymbolw@m [wdw0-!=R!- ]Timesw@] .[wdw0-!24 c!16_ \ oPSymbolw@m [wdw0-!=s!-}Timesw@] /[wdw0-!1!.!5!. & 'dxpr MTHU Grphbj " currentpoint " + P(Q" ( D)Q(D)P" ("=( ,12*16" , (:()-)2)))=( ]-)24(_16" \(s=) -)1)PICT  CompObj'KObjInfo)Ole10Native*.)5)./MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 4832 div 960 3 -1 roll exch div scale currentpoint translate 64 39 translate /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 406 moveto 310 0 rlineto stroke 374 406 moveto 558 0 rlineto stroke 1358 406 moveto 396 0 rlineto stroke 2888 406 moveto 643 0 rlineto stroke /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 384 /Times-Italic f1 (P) 47 264 sh (Q) 17 798 sh (Q) 639 264 sh (P) 658 798 sh 384 /Symbol f1 (D) 404 264 sh (D) 423 798 sh 384 /Symbol f1 (=) 1040 505 sh (-) 1942 505 sh (=) 2570 505 sh (-) 2916 264 sh (=) 3639 505 sh (-) 3953 505 sh 384 /Times-Roman f1 (12) 1348 264 sh (16) 1350 798 sh (2) 2152 505 sh (24) 3126 264 sh (16) 3003 798 sh (1) 4163 505 sh (5) 4451 505 sh 384 /Times-Roman f1 (\() 1800 505 sh (\)) 2353 505 sh (.) 4355 505 sh (.) 4643 505 sh end MTsave restore dMATH~ PQDQDP=1216(-2)=-2416=-1.5.m FMathType Equation1ELO Equation~ PQDQDP=1216(-2)=-2416=-1.5. Equationd; 4 lOle10FmtProgID - _1010571907 F.}B.}BOle .PIC /d; 4    .  & Timesw@> [wdw0-!P !Q- PSymbolw@k ^[wdw0-!D Timesw@> [wdw0-!Q META 1jPICT GCompObjdKObjInfofPSymbolw@k _[wdw0-!DTimesw@> [wdw0-!P PSymbolw@k `[wdw0-!="Timesw@> [wdw0-!9 -!6-,2!2 ;!3<;APSymbolw@k a[wdw0-! 5! 5! B! B!=KTimesw@> [wdw0-!18 U!18UU`PSymbolw@k b[wdw0-!=eTimesw@> [wdw0-!1m!.s!0v!.| & 'dxpr MTHU Grphbj " currentpoint " + P(Q"( D)Q(D)P" ("=( -9*6",( ;2+3";( 5 *  ( B *  (K=( U18*18"U (e=)1).)0)./MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 4096 div 992 3 -1 roll exch div scale currentpoint translate 64 42 translate /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 435 moveto 310 0 rlineto stroke 374 435 moveto 558 0 rlineto stroke 1358 435 moveto 230 0 rlineto stroke 1834 435 moveto 235 0 rlineto stroke 2677 435 moveto 383 0 rlineto stroke /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 384 /Times-Italic f1 (P) 47 293 sh (Q) 17 827 sh (Q) 639 293 sh (P) 658 827 sh 384 /Symbol f1 (D) 404 293 sh (D) 423 827 sh 384 /Symbol f1 (=) 1040 534 sh (\346) 1637 355 sh (\350) 1637 758 sh (\366) 2079 355 sh (\370) 2079 758 sh (=) 2359 534 sh (=) 3168 534 sh 384 /Times-Roman f1 (9) 1380 293 sh (6) 1377 827 sh (2) 1855 293 sh (3) 1861 827 sh (18) 2667 293 sh (18) 2667 827 sh (1) 3444 534 sh (0) 3732 534 sh 384 /Times-Roman f1 (.) 3636 534 sh (.) 3924 534 sh end MTsave restore dMATHF PQDQDP=9623()=1818=1.0.۠ FMathType Equation1ELO Equation PQDQDP=96Ole10NativegOle10FmtProgID j _1010571906 F.}B.}BOle k23()=1818=1.0. Equationd 4 l 4    .  & PIC ldMETA njPICT  CompObjKTimesw@ `[wdw0-!P !Q- PSymbolw@C [wdw0-!D Timesw@ a[wdw0-!Q PSymbolw@C [wdw0-!DTimesw@ b[wdw0-!P PSymbolw@C [wdw0-!="Timesw@ c[wdw0-!12 ,!8/,7!2 A!3A@FPSymbolw@C [wdw0-! :! :! H! H!=PTimesw@ d[wdw0-!24 [!24[ZgPSymbolw@C [wdw0-!=kTimesw@ e[wdw0-!1t!.z!0}!. & ' dxpr MTHU Grphbj " currentpoint " + P(Q"( D)Q(D)P" ("=( ,12+8", ( A2*3"@( : *  ( H *  (P=( [24*24"Z (k=) 1).)0)./MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 4320 div 992 3 -1 roll exch div scale currentpoint translate 64 42 translate /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 435 moveto 310 0 rlineto stroke 374 435 moveto 558 0 rlineto stroke 1358 435 moveto 396 0 rlineto stroke 2000 435 moveto 235 0 rlineto stroke 2843 435 moveto 426 0 rlineto stroke /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 384 /Times-Italic f1 (P) 47 293 sh (Q) 17 827 sh (Q) 639 293 sh (P) 658 827 sh 384 /Symbol f1 (D) 404 293 sh (D) 423 827 sh 384 /Symbol f1 (=) 1040 534 sh (\346) 1803 355 sh (\350) 1803 758 sh (\366) 2245 355 sh (\370) 2245 758 sh (=) 2525 534 sh (=) 3377 534 sh 384 /Times-Roman f1 (12) 1348 293 sh (8) 1462 827 sh (2) 2021 293 sh (3) 2027 827 sh (24) 2864 293 sh (24) 2864 827 sh (1) 3653 534 sh (0) 3941 534 sh 384 /Times-Roman f1 (.) 3845 534 sh (.) 4133 534 sh end MTsave restore dMATH PQDQDP=12823()=2424=1.0.۶ FMathType Equation1ELO Equation PQDQDP=12823()=2424=1.0. EquationObjInfoOle10NativeOle10FmtProgID  _1010837652 F.}B.}BPIC dMETA PICT CompObj\d7T7    . -###*#-- $-+#Timesw@ F[wdw0-!QTimesw@ [wdw0-!e'Timesw@ G[wdw0-!1!5!4!4'-!9!2!6!.!4'7(-!81!.1!71 !71'3-!P ' MSWD  ##! *#"q"## +# ,Times .+Q + e (1)5)4)4 (9)2)6).)4 (7(18).)7)7 3( P FMicrosoft Word 6.0 PictureNB6WWord.Picture.6ܥhS e(  l ll l  ObjInfoObjectPool.}B.}BWordDocument SummaryInformation( V = . . . . 0 0 0 0 0 0 & X 0V .  h. . . V . l l . . . . l  .  l l l l . . . .  Qe P 8.77 926.4 1544 NN 72 0(p0.YU 20( - 20(#mA 2 0(x(/ 2 0(<-/i 0 0&X @$9  8  ((00&,),-, *(00&X ,$% $ ((00&X D/ ((00&X !I H ((ࡱ;    '(&uhuDac $%&'(@X@K@Normala c"A@"Default Paragraph Font (( (&( (<n6f@ @=MTimes New Roman Symbol MArial MTimes"0hU BF!0Michael CaputoMichael Caputo Oh+'0  ! -9A IUr zࡱASystem 8.6:Applications:Microsoft Office:Microsoft Word 6:NormalMichael CaputoMichael Caputo'@v@v@9.l@Microsoft Word 6.0.12dX_1010916963 F.}B.}BOle PIC dMETA       !"#$&)-/0123456789:;<=>?@ABCDEFGHIJKLMORSVWX[]^_`abcdefghijklmnopqrstuvwxyz{|}~   @ .  & Timesw@] <[wdw0-!ETimesw@ E[wdw0-!P !D PSymbolw@] =[wdw0-!=Timesw@ F[wdw0-!P !Q-  &PSymbolw@] >[wdw0-!D *Timesw@ G[wdw0-!Q 1PSymbolw@] ?[wdw0-!D*Timesw@ H[wdw0-!P2 ) 9Timesw@] @[wdw0-!.; & 'PICT )CompObj%KObjInfo'Ole10Native(K)@dxpr MTHU @Grphbj @"@ currentpoint " +E +P( D + =( P(Q"  ( *D)Q(*D)P" )(;./MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 2048 div 960 3 -1 roll exch div scale currentpoint translate 64 39 translate /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 885 406 moveto 310 0 rlineto stroke 1259 406 moveto 558 0 rlineto stroke /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 384 /Times-Italic f1 (E) 6 505 sh (P) 932 264 sh (Q) 902 798 sh (Q) 1524 264 sh (P) 1543 798 sh 224 ns (P) 241 601 sh (D) 277 333 sh 384 /Symbol f1 (=) 567 505 sh 384 /Symbol f1 (D) 1289 264 sh (D) 1308 798 sh 384 /Times-Roman f1 (.) 1855 505 sh end MTsave restore dSMATHG  E PD =PQDQDP.m FMathType Equation1ELO EquationG E PD =PQDQDP. EquationLK >dxpr MTHU>Grphbj >"> currentpoint " +Ole10FmtProgID * _1004702762F.}B 90}BOle +PIC ,LPICT .CompObjNWObjInfoPOle10NativeQ-)0).)4) =( +2(%470" $( :D)Q(;D)P" 9(*D)Q(;D)P".(2=) -)0).)4(*=470+2".<(,6 *  (,P *  (2Y=) -)94)=) b)./MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 4480 div 1984 3 -1 roll exch div scale currentpoint translate 64 37 translate /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 1101 406 moveto 626 0 rlineto stroke 1791 406 moveto 558 0 rlineto stroke 0 1470 moveto 558 0 rlineto stroke 1871 1470 moveto 626 0 rlineto stroke /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 384 /Symbol f1 (-) -4 505 sh (=) 783 505 sh (=) 666 1569 sh (-) 980 1569 sh (\346) 1674 1390 sh (\350) 1674 1793 sh (\366) 2507 1390 sh (\370) 2507 1793 sh (=) 2787 1569 sh (-) 3101 1569 sh (=) 3792 1569 sh 384 /Times-Roman f1 (0) 206 505 sh (4) 494 505 sh (2) 1318 264 sh (470) 1129 798 sh (0) 1190 1569 sh (4) 1478 1569 sh (470) 1899 1328 sh (2) 2088 1862 sh (94) 3311 1569 sh 384 /Times-Roman f1 (.) 398 505 sh (.) 1382 1569 sh (.) 4287 1569 sh 384 /Symbol f1 (D) 1821 264 sh (D) 1840 798 sh (D) 30 1328 sh (D) 49 1862 sh 384 /Times-Italic f1 (Q) 2056 264 sh (P) 2075 798 sh (Q) 265 1328 sh (P) 284 1862 sh (b) 4101 1569 sh end MTsave restore dMATHM -0.4=2470DQDPDQDP=-0.44702()=-94=b.۠FMathType Equation 3.6+DNQEEquation.DSMT36 -0.4=2470DQDPDQDP=-0.44702()=-94=b. Equation -0.4=223.5DQDPDQDP=-0.423.52()=-4.7=Ole10FmtProgID  T Equation Native U_986119867F 90}B 90}BOle Y-b.LK^  radxpr- MTHU-aGrphbj a"a currentpoint " +E +P( S +=( P(Q"( (D)Q()D)P"'(40).)PIC   ZLPICT \r CompObj WObjInfo5) =(,$2(=470"0(,3D)Q(=4D)P"02(MD)Q(^D)P"Q(U=) 0).)5(M6470+2"Q5(O/ *  (OI *  (UQ=) 117).)5) =) d).w/MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 4480 div 3104 3 -1 roll exch div scale currentpoint translate 64 58 translate /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 835 406 moveto 310 0 rlineto stroke 1209 406 moveto 558 0 rlineto stroke 873 1507 moveto 626 0 rlineto stroke 1563 1507 moveto 558 0 rlineto stroke 0 2571 moveto 558 0 rlineto stroke 1643 2571 moveto 626 0 rlineto stroke /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 384 /Times-Italic f1 (E) 6 505 sh (P) 882 264 sh (Q) 852 798 sh (Q) 1474 264 sh (P) 1493 798 sh (Q) 1828 1365 sh (P) 1847 1899 sh (Q) 265 2429 sh (P) 284 2963 sh (d) 4096 2670 sh 224 ns (P) 241 601 sh (S) 269 333 sh 384 /Symbol f1 (=) 517 505 sh (=) 555 1606 sh (=) 666 2670 sh (\346) 1446 2491 sh (\350) 1446 2894 sh (\366) 2279 2491 sh (\370) 2279 2894 sh (=) 2559 2670 sh (=) 3783 2670 sh 384 /Symbol f1 (D) 1239 264 sh (D) 1258 798 sh (D) 1593 1365 sh (D) 1612 1899 sh (D) 30 2429 sh (D) 49 2963 sh 384 /Times-Roman f1 (0) -9 1606 sh (5) 279 1606 sh (2) 1090 1365 sh (470) 901 1899 sh (0) 975 2670 sh (5) 1263 2670 sh (470) 1671 2429 sh (2) 1860 2963 sh (117) 2835 2670 sh (5) 3507 2670 sh 384 /Times-Roman f1 (.) 183 1606 sh (.) 1167 2670 sh (.) 3411 2670 sh (.) 4300 2670 sh end MTsave restore dMATH$C E PS =PQDQDP0.5=2470DQDPDQDP=0.54702()=117.5=d.tiFMathType Equation 3.6+DNQEEquation.DSMT36 E PS =PQDQDP0.5=2470DQDPDQDP=0.54702Ole10NativeOle10FmtProgID  Equation Native _927563866 F 90}B 90}B()=117.5=d. Equation E PS =PQDQDP0.5=223.5DQDPDQDP=0.523.52()=5.875=d.Ole PIC dMETA PICT Ldqq   "H .  & Timesw@ [wdw0-!ETimesw@ `[wdw0-!D PSymbolw@ [wdw0-!=!-Timesw@ a[wdw0-!b#!P 1Timesw@ [wdw0-!* :Timesw@ b[wdw0-!Q0Timesw@ [wdw0-!*:-/@PSymbolw@ c[wdw0-! )! )! )! A! A! A & 'L"Hdxpr MTHU"HGrphbj "H""H currentpoint " +E +D (=) -)b( 1P) *(0Q) *"/( ) * () ( A * (A /MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 2304 div 1088 3 -1 roll exch div scale currentpoint translate 64 46 translate /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 1468 495 moveto 549 0 rlineto stroke /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 384 /Times-Italic f1 (E) 6 594 sh (b) 1074 594 sh (P) 1514 353 sh (Q) 1485 887 sh 224 ns (D) 244 690 sh 384 /Symbol f1 (=) 534 594 sh (-) 848 594 sh (\346) 1271 355 sh (\350) 1271 878 sh (\347) 1271 659 sh (\366) 2027 355 sh (\370) 2027 878 sh (\367) 2027 659 sh 384 /Times-Roman f1 (*) 1809 353 sh (*) 1818 887 sh end MTsave restore dPMATHD 5 E D =-bP*Q*()maCompObj\ObjInfoOlePres000tOle10NativeH FMathType Equation1ELO Equation9qTCIP LL"Hdxpr MTHU"HGrphbj "H""H currentpoint " +E +D (=) -)b( 1P) *(0Q) *"/( ) * () ( A * (A /MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 2304 div 1088 3 -1 roll exch div scale currentpoint translate 64 46 translate /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 1468 495 moveto 549 0 rlineto stroke /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 384 /Times-Italic f1 (E) 6 594 sh (b) 1074 594 sh (P) 1514 353 sh (Q) 1485 887 sh 224 ns (D) 244 690 sh 384 /Symbol f1 (=) 534 594 sh (-) 848 594 sh (\346) 1271 355 sh (\350) 1271 878 sh (\347) 1271 659 sh (\366) 2027 355 sh (\370) 2027 878 sh (\367) 2027 659 sh 384 /Times-Roman f1 (*) 1809 353 sh (*) 1818 887 sh end MTsave restore dPMATHD 5 E D =-bP*Q*()maD E D =-bP*Q*() Equationd0   K .Ole10FmtProgID  _927563867! F 90}B 90}BOle PIC  dMETA ^PICT #vCompObj\ObjInfo"%  & PSymbolw@T [wdw0-!-Timesw@\ [wdw0-!0!. !4PSymbolw@T [wdw0-!=!-Timesw@\ [wdw0-!b%Timesw@T [wdw0-!0 1!. 6!75 9!74!.9!5;- 1 BPSymbolw@\ [wdw0-! +! +! D! D & 'vKdxpr MTHU KGrphbj K"K currentpoint " +-)0).)4) =)-)b( 10).)75(47).)5" 1 ( + *  ( D *  /MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 2400 div 896 3 -1 roll exch div scale currentpoint translate 64 42 translate /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 1510 403 moveto 597 0 rlineto stroke /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 320 /Symbol f1 (-) -3 502 sh (=) 672 502 sh (-) 952 502 sh 384 ns (\346) 1313 355 sh (\350) 1313 694 sh (\366) 2117 355 sh (\370) 2117 694 sh 320 /Times-Roman f1 (0) 172 502 sh (4) 412 502 sh (0) 1535 261 sh (75) 1775 261 sh (7) 1615 795 sh (5) 1855 795 sh 320 /Times-Roman f1 (.) 332 502 sh (.) 1695 261 sh (.) 1775 795 sh 320 /Times-Italic f1 (b) 1146 502 sh end MTsave restore dXMATHL g  @-0.4=-b0.757.5() FMathType Equation1ELO Equation9qTCIPV vvKdxpr MTHU KGrphbj K"KOlePres000Ole10Native$&POle10FmtProgID  _9275638697) F 90}B 90}B      !"#%(*+,-./0123456789:;<=>@ABCDEFGHIJKLMNOPQRSTUVWY\]^_`abcdefghijklmnopqrstvz|}~ currentpoint " +-)0).)4) =)-)b( 10).)75(47).)5" 1 ( + *  ( D *  /MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 2400 div 896 3 -1 roll exch div scale currentpoint translate 64 42 translate /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 1510 403 moveto 597 0 rlineto stroke /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 320 /Symbol f1 (-) -3 502 sh (=) 672 502 sh (-) 952 502 sh 384 ns (\346) 1313 355 sh (\350) 1313 694 sh (\366) 2117 355 sh (\370) 2117 694 sh 320 /Times-Roman f1 (0) 172 502 sh (4) 412 502 sh (0) 1535 261 sh (75) 1775 261 sh (7) 1615 795 sh (5) 1855 795 sh 320 /Times-Roman f1 (.) 332 502 sh (.) 1695 261 sh (.) 1775 795 sh 320 /Times-Italic f1 (b) 1146 502 sh end MTsave restore dXMATHL g  @-0.4=-b0.757.5()L  @-0.4=-b0.757.5() EquationOle CompObj(+\ObjInfoOlePres000*, FMathType Equation Equation Equation9q{   .1  @`&  & MathTypeP Symbol"- 2 VcCentury Schoolbookx- 2 (Q) Century Schoolbookx- 2 YD 2  = & "Systemn-@ "Q D Cd Xd Ole10Native$D_9275638701 F 90}B 90}BOle &PIC .0'd X     .  & PSymbolw@a 6[wdw0-!= Timesw@` [wdw0-!0 !. !8 PSymbolw@a 7[wdw0-!( !) Timesw@META )~PICT /3?.CompObjX\ObjInfo25Z` [wdw0-!10 "!. ,!5 .PSymbolw@a 8[wdw0-!- 5Timesw@` [wdw0-!4 >Timesw@a 9[wdw0-!P CPSymbolw@` [wdw0-!( !) JPSymbolw@a :[wdw0-!= PTimesw@` [wdw0-!8 Y!. ^!4 `PSymbolw@a ;[wdw0-!- hTimesw@` [wdw0-!3 p!. u!2 wTimesw@a <[wdw0-!P } & '. dxpr MTHU Grphbj " currentpoint " + =) 0).)8   ( ()) +10) .)5)-) 4)P   ( (),) +=) 8).)4)-)3).)2)Pz/MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 4256 div 416 3 -1 roll exch div scale currentpoint translate 64 59 translate /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 320 /Symbol f1 (=) -3 261 sh (-) 1657 261 sh (=) 2527 261 sh (-) 3278 261 sh /f3 {ff 3 -1 roll .001 mul 3 -1 roll .001 mul matrix scale makefont dup /cf exch def sf} def 384 1000 976 /Symbol f3 (\() 260 252 sh (\)) 798 252 sh (\() 914 252 sh (\)) 2312 252 sh 320 /Times-Roman f1 (0) 398 261 sh (8) 638 261 sh (10) 1024 261 sh (5) 1424 261 sh (4) 1921 261 sh (8) 2794 261 sh (4) 3034 261 sh (3) 3531 261 sh (2) 3771 261 sh 320 /Times-Roman f1 (.) 558 261 sh (.) 1344 261 sh (.) 2954 261 sh (.) 3691 261 sh 320 /Times-Italic f1 (P) 2107 261 sh (P) 3958 261 sh end MTsave restore dnMATHbY  @=0.8()10.5-4P()=8.4-3.2P۠ FMathType Equation1ELO Equation9qTCIPT.. dxpr MTHU Grphbj " currentpoint " + =) 0).)8   ( ()) +10) .)5)-) 4)P   ( (),) +=) 8).)OlePres000[VOle10Native46ufOle10FmtProgID w _927563871-A; F 90}B 90}B4)-)3).)2)Pz/MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 4256 div 416 3 -1 roll exch div scale currentpoint translate 64 59 translate /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 320 /Symbol f1 (=) -3 261 sh (-) 1657 261 sh (=) 2527 261 sh (-) 3278 261 sh /f3 {ff 3 -1 roll .001 mul 3 -1 roll .001 mul matrix scale makefont dup /cf exch def sf} def 384 1000 976 /Symbol f3 (\() 260 252 sh (\)) 798 252 sh (\() 914 252 sh (\)) 2312 252 sh 320 /Times-Roman f1 (0) 398 261 sh (8) 638 261 sh (10) 1024 261 sh (5) 1424 261 sh (4) 1921 261 sh (8) 2794 261 sh (4) 3034 261 sh (3) 3531 261 sh (2) 3771 261 sh 320 /Times-Roman f1 (.) 558 261 sh (.) 1344 261 sh (.) 2954 261 sh (.) 3691 261 sh 320 /Times-Italic f1 (P) 2107 261 sh (P) 3958 261 sh end MTsave restore dnMATHbY  @=0.8()10.5-4P()=8.4-3.2P۠b  @=0.8()10.5-4P()=8.4-3.2P EquationOle xPIC 8:ydMETA {xPICT 9=d; ;  8  $c .  & Timesw@ zww0-!ETimesw@ zww0-!GO PSymbolw@ zww0-!=!D 'Timesw@ zww0-!Q /Timesw@ zww0-!G7PSymbolw@ zww0-!D)Timesw@ zww0-!P0Timesw@ zww0-!O!5-'=PSymbolw@ zww0-! !  !  ! >! >! >Timesw@ zww0-!P LTimesw@ zww0-!OQTimesw@ zww0-!QJTimesw@ zww0-!G!RJXPSymbolw@ zww0-! D! D! D! Z! Z! ZTimesw@ zww0-!._ & '$cdxpr MTHU$cGrphbj $c"$c currentpoint " +E +GO (=( 'D)Q +G ()D)P +O"' (  * (  ( > * (> ( LP +O (JQ +G"J ( D * (D ( Z * (Z (_./MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 3168 div 1152 3 -1 roll exch div scale currentpoint translate 64 48 translate /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 1184 525 moveto 739 0 rlineto stroke 2317 525 moveto 491 0 rlineto stroke /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 384 /Times-Italic f1 (E) 6 624 sh (Q) 1449 383 sh (P) 1496 917 sh (P) 2391 383 sh (Q) 2334 917 sh 224 ns (GO) 232 720 sh (G) 1702 479 sh (O) 1661 1013 sh (O) 2556 479 sh (G) 2587 1013 sh 384 /Symbol f1 (=) 684 624 sh (\346) 987 355 sh (\350) 987 938 sh (\347) 987 719 sh (\366) 1933 355 sh (\370) 1933 938 sh (\367) 1933 719 sh (\346) 2120 355 sh (\350) 2120 938 sh (\347) 2120 719 sh (\366) 2818 355 sh (\370) 2818 938 sh (\367) 2818 719 sh 384 /Symbol f1 (D) 1214 383 sh (D) 1261 917 sh 384 /Times-Roman f1 (.) 2994 624 sh end MTsave restore dMATH( E GO =DQ G DP O ()P O Q G ().m FMathType Equation1ELO Equation9qTCIP $cdxpr MTHU$cGrphbj $c"$c currentpoint " +E +GO (CompObj\ObjInfo<?OlePres0009Ole10Native>@=( 'D)Q +G ()D)P +O"' (  * (  ( > * (> ( LP +O (JQ +G"J ( D * (D ( Z * (Z (_./MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 3168 div 1152 3 -1 roll exch div scale currentpoint translate 64 48 translate /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 1184 525 moveto 739 0 rlineto stroke 2317 525 moveto 491 0 rlineto stroke /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 384 /Times-Italic f1 (E) 6 624 sh (Q) 1449 383 sh (P) 1496 917 sh (P) 2391 383 sh (Q) 2334 917 sh 224 ns (GO) 232 720 sh (G) 1702 479 sh (O) 1661 1013 sh (O) 2556 479 sh (G) 2587 1013 sh 384 /Symbol f1 (=) 684 624 sh (\346) 987 355 sh (\350) 987 938 sh (\347) 987 719 sh (\366) 1933 355 sh (\370) 1933 938 sh (\367) 1933 719 sh (\346) 2120 355 sh (\350) 2120 938 sh (\347) 2120 719 sh (\366) 2818 355 sh (\370) 2818 938 sh (\367) 2818 719 sh 384 /Symbol f1 (D) 1214 383 sh (D) 1261 917 sh 384 /Times-Roman f1 (.) 2994 624 sh end MTsave restore dMATH( E GO =DQ G DP O ()P O Q G ().m E GO =DQ G DP O ()P O Q G (). EquationdOle10FmtProgID  _927563872E F 90}B 90}BOle PIC BDd   "" .  & PSymbolw@ zww0-!D Timesw@ zww0-!Q Timesw@ zww0-!GPSymbolw@ zww0-META `PICT CGCompObj\ObjInfoFI!D Timesw@ zww0-!PTimesw@ zww0-!O -PSymbolw@ zww0-! ! ! ! ! !  & '""dxpr MTHU""Grphbj """"" currentpoint " + D)Q +G ( D)P +O" (  * ( (  * ( /MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 1088 div 1088 3 -1 roll exch div scale currentpoint translate 64 50 translate /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 182 491 moveto 619 0 rlineto stroke /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 320 /Symbol f1 (D) 213 349 sh (D) 255 883 sh 320 /Times-Italic f1 (Q) 408 349 sh (P) 450 883 sh 160 ns (G) 625 445 sh (O) 586 979 sh 384 /Symbol f1 (\346) -15 355 sh (\350) -15 870 sh (\347) -15 651 sh (\366) 811 355 sh (\370) 811 870 sh (\367) 811 651 sh end MTsave restore d\MATHP  @DQ @G @DP @O @() FMathType Equation1ELO Equation9qTCIP""dxprOlePres0008Ole10NativeHJTOle10FmtProgID  _927563873O F 90}B 90}B      !"#$%&')*+,-./0123456789:;<>ABCDEFGHIJKLMNOPQRSTVZ\]^_`abcdefghjklmnopqrstuvwxyz{|} MTHU""Grphbj """"" currentpoint " + D)Q +G ( D)P +O" (  * ( (  * ( /MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 1088 div 1088 3 -1 roll exch div scale currentpoint translate 64 50 translate /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 182 491 moveto 619 0 rlineto stroke /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 320 /Symbol f1 (D) 213 349 sh (D) 255 883 sh 320 /Times-Italic f1 (Q) 408 349 sh (P) 450 883 sh 160 ns (G) 625 445 sh (O) 586 979 sh 384 /Symbol f1 (\346) -15 355 sh (\350) -15 870 sh (\347) -15 651 sh (\366) 811 355 sh (\370) 811 870 sh (\367) 811 651 sh end MTsave restore d\MATHP  @DQ @G @DP @O @()P  @DQ @G @DP @O @() EquationOle PIC LNdMETA `PICT MQ(d   "" .  & PSymbolw@ [wdw0-!D Timesw@P [wdw0-!Q Timesw@ [wdw0-!GPSymbolw@P [wdw0-!D Timesw@ [wdw0-!PTimesw@P [wdw0-!O -PSymbolw@ [wdw0-! ! ! ! ! !  & '""dxpr MTHU""Grphbj """"" currentpoint " + D)Q +G ( D)P +O" (  * ( (  * ( /MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 1088 div 1088 3 -1 roll exch div scale currentpoint translate 64 50 translate /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 182 491 moveto 619 0 rlineto stroke /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 320 /Symbol f1 (D) 213 349 sh (D) 255 883 sh 320 /Times-Italic f1 (Q) 408 349 sh (P) 450 883 sh 160 ns (G) 625 445 sh (O) 586 979 sh 384 /Symbol f1 (\346) -15 355 sh (\350) -15 870 sh (\347) -15 651 sh (\366) 811 355 sh (\370) 811 870 sh (\367) 811 651 sh end MTsave restore d\MATHP  @DQ @G @DP @O @() FMathType Equation1ELO Equation9qCompObj=\ObjInfoPS?OlePres000@8Ole10NativeRTUTTCIP""dxpr MTHU""Grphbj """"" currentpoint " + D)Q +G ( D)P +O" (  * ( (  * ( /MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 1088 div 1088 3 -1 roll exch div scale currentpoint translate 64 50 translate /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 182 491 moveto 619 0 rlineto stroke /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 320 /Symbol f1 (D) 213 349 sh (D) 255 883 sh 320 /Times-Italic f1 (Q) 408 349 sh (P) 450 883 sh 160 ns (G) 625 445 sh (O) 586 979 sh 384 /Symbol f1 (\346) -15 355 sh (\350) -15 870 sh (\347) -15 651 sh (\366) 811 355 sh (\370) 811 870 sh (\367) 811 651 sh end MTsave restore d\MATHP  @DQ @G @DP @O @()P  @DQ @G @DP @O @() EquationOle10FmtProgID W _927563874Y F 90}B 90}BOle XPIC VXYdd   "" .  & PSymbolw@ 6[wdw0-!D Timesw@K P[wdw0-!Q Timesw@META [`PICT W[iCompObj~\ObjInfoZ] 7[wdw0-!GPSymbolw@K Q[wdw0-!D Timesw@ 8[wdw0-!PTimesw@K R[wdw0-!O -PSymbolw@ 9[wdw0-! ! ! ! ! !  & '""dxpr MTHU""Grphbj """"" currentpoint " + D)Q +G ( D)P +O" (  * ( (  * ( /MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 1088 div 1088 3 -1 roll exch div scale currentpoint translate 64 50 translate /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 182 491 moveto 619 0 rlineto stroke /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 320 /Symbol f1 (D) 213 349 sh (D) 255 883 sh 320 /Times-Italic f1 (Q) 408 349 sh (P) 450 883 sh 160 ns (G) 625 445 sh (O) 586 979 sh 384 /Symbol f1 (\346) -15 355 sh (\350) -15 870 sh (\347) -15 651 sh (\366) 811 355 sh (\370) 811 870 sh (\367) 811 651 sh end MTsave restore d\MATHP  @DQ @G @DP @O @() FMathType Equation1ELO Equation9qTCIP""dxpr MTHU""Grphbj """"" currentpoint " + D)Q +G ( D)P +O" (  * ( (  * ( /MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 1088 div 1088 3 -1 roll exch div scale currentpoint translate 64 50 translate /thick 0OlePres0008Ole10Native\^TOle10FmtProgID  _927563875Uic F 90}B1}B def /th { dup setlinewidth /thick exch def } def 16 th 182 491 moveto 619 0 rlineto stroke /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 320 /Symbol f1 (D) 213 349 sh (D) 255 883 sh 320 /Times-Italic f1 (Q) 408 349 sh (P) 450 883 sh 160 ns (G) 625 445 sh (O) 586 979 sh 384 /Symbol f1 (\346) -15 355 sh (\350) -15 870 sh (\347) -15 651 sh (\366) 811 355 sh (\370) 811 870 sh (\367) 811 651 sh end MTsave restore d\MATHP  @DQ @G @DP @O @()P  @DQ @G @DP @O @() Equationd< 4  &C .  & Timesw@\ [wdw0-!ETimesw@ N[wdw0Ole PIC `bdMETA pPICT ae-!PO PSymbolw@\ [wdw0-!=Timesw@ O[wdw0-!e !P-Timesw@\ [wdw0-!O2Timesw@ P[wdw0-!* 4Timesw@\ [wdw0-!Q ,Timesw@ Q[wdw0-!G#4Timesw@\ [wdw0-!*5-+:PSymbolw@ R[wdw0-! %! %! %! ;! ;! ; & '&Cdxpr MTHU&CGrphbj &C"&C currentpoint " +E +PO (=) e(-P +O ( 4* ( ,Q +G (5*"+ ( % * (% ( ; * (; /MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 2144 div 1216 3 -1 roll exch div scale currentpoint translate 64 41 translate /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 1343 564 moveto 493 0 rlineto stroke /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 384 /Times-Italic f1 (E) 6 663 sh (e) 973 663 sh (P) 1389 422 sh (Q) 1360 994 sh 224 ns (PO) 241 759 sh (O) 1554 518 sh (G) 1613 1090 sh 384 /Symbol f1 (=) 668 663 sh (\346) 1146 355 sh (\350) 1146 1016 sh (\347) 1146 797 sh (\366) 1846 355 sh (\370) 1846 1016 sh (\367) 1846 797 sh 320 /Times-Roman f1 (*) 1624 250 sh (*) 1633 822 sh end MTsave restore drMATHf ] E PO =eP O * Q G * ()-I FMathType Equation1ELO Equation9qCompObj\ObjInfodgOlePres000Ole10NativefhjTCIP< =&Cdxpr MTHU&CGrphbj &C"&C currentpoint " +E +PO (=) e(-P +O ( 4* ( ,Q +G (5*"+ ( % * (% ( ; * (; /MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 2144 div 1216 3 -1 roll exch div scale currentpoint translate 64 41 translate /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 1343 564 moveto 493 0 rlineto stroke /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 384 /Times-Italic f1 (E) 6 663 sh (e) 973 663 sh (P) 1389 422 sh (Q) 1360 994 sh 224 ns (PO) 241 759 sh (O) 1554 518 sh (G) 1613 1090 sh 384 /Symbol f1 (=) 668 663 sh (\346) 1146 355 sh (\350) 1146 1016 sh (\347) 1146 797 sh (\366) 1846 355 sh (\370) 1846 1016 sh (\367) 1846 797 sh 320 /Times-Roman f1 (*) 1624 250 sh (*) 1633 822 sh end MTsave restore drMATHf ] E PO =eP O * Q G * ()-If E PO =eP O * Q G * () Equation FMathType Equation Equation Equation9qX  Ole10FmtProgID  _927563877k F1}B1}BOle CompObjjm\ObjInfoOlePres000lnOle10NativeD_927563878_q F1}B1}B .1  ` & & MathTypeP Century Schoolbook- 2 @P Century Schoolbookv- 2 OCentury Schoolbookv- 2 06* & "System-J@ P O * FMathType Equation Equation Equation9qX   .1  ` & & MathTypeP Ole CompObjps\ObjInfoOlePres000rtCentury Schoolbook- 2 "Q Century Schoolbookv- 2 GCentury Schoolbookv- 2 0,* & "System-J@ Q G *Ole10NativeD_927563879w F1}B1}BOle CompObjvy \                 ! " # $ % & ' ( ) + , - . / 0 1 2 3 4 5 6 7 8 9 : ; < = ? B C D E F G H I J K L M N O P Q R S T U Z \ ] ^ _ ` a b c d e f g h j k l m n o p q r s t u v w x y z { | }   FMathType Equation Equation Equation9qX   .1  ` & & MathTypeP Century Schoolbook- 2 @P Century Schoolbookv-ObjInfo OlePres000xz Ole10Native D_927563880u} F1}B1}B 2 OCentury Schoolbookv- 2 06* & "System-J@ P O * FMathType Equation Equation Equation9qOle  CompObj| \ObjInfo OlePres000~ X   .1  ` & & MathTypeP Century Schoolbook- 2 "Q Century Schoolbookv- 2 GCentury Schoolbookv- 2 0,* & "System-J@ Q G *d4X4 ]  < .  & Ole10Native D_927563881 F1}B1}BOle  PIC  dMETA  PICT * CompObj> \ObjInfo@ Timesw@ [wdw0-!1!.!5 PSymbolw@ 1[wdw0-!=Timesw@ [wdw0-!eTimesw@ 2[wdw0-!8 +!20(-'3PSymbolw@ [wdw0-! !! !! 5! 5 & '<dxpr MTHU [wdw0-!2 .!20+-*6PSymbolw@W [wdw0-! $! $! 8! 8 & '?dxpr MTHU ?Grphbj ?"? currentpoint " +0).)2) =) d( .2(+20"* ( $ *  ( 8 *  /MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 2016 div 960 3 -1 roll exch div scale currentpoint translate 64 42 translate /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 1294 435 moveto 427 0 rlineto stroke /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 384 /Times-Roman f1 (0) -9 534 sh (2) 279 534 sh (2) 1411 293 sh (20) 1315 827 sh 384 /Times-Roman f1 (.) 183 534 sh 384 /Symbol f1 (=) 569 534 sh (\346) 1097 355 sh (\350) 1097 758 sh (\366) 1731 355 sh (\370) 1731 758 sh 384 /Times-Italic f1 (d) 882 534 sh end MTsave restore dCMATH7 0.2=d220()) FMathType Equation1ELO Equation9qTCIP#?dxpr MTHU ?Grphbj ?"? currentpoint " +0).)2) =)CompObj \ObjInfo OlePres000 Ole10Native ;                     ! " # % & ' ( ) * + , - . / 0 1 2 3 4 5 6 7 9 < = > ? @ A B C D E F G H I J K L M N O T V W X Y Z [ \ ] ^ _ ` a b c d e f g h i j k l m n p q r s t u v w x y z { | } ~  d( .2(+20"* ( $ *  ( 8 *  /MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 2016 div 960 3 -1 roll exch div scale currentpoint translate 64 42 translate /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 1294 435 moveto 427 0 rlineto stroke /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 384 /Times-Roman f1 (0) -9 534 sh (2) 279 534 sh (2) 1411 293 sh (20) 1315 827 sh 384 /Times-Roman f1 (.) 183 534 sh 384 /Symbol f1 (=) 569 534 sh (\346) 1097 355 sh (\350) 1097 758 sh (\366) 1731 355 sh (\370) 1731 758 sh 384 /Times-Italic f1 (d) 882 534 sh end MTsave restore dCMATH7 0.2=d220())7 0.2=d220() Equationd"dX"   E .Ole10FmtProgID  _927563885 F`F3}B`F3}BOle  PIC  dMETA  PICT $ CompObj8 \ObjInfo:      9+! -#$%&'()*,/.601234578:BO;<=>?@ADCLEFGHIJKNMUPQRSTVWqYZ[\]^_`abcdefghijklmnopruvwxyz{|}~  & PSymbolw@  [wdw0-!-Timesw@_ [wdw0-!0!.!5PSymbolw@  [wdw0-!=Timesw@_ [wdw0-!b#Timesw@  [wdw0-!2 3!200-0<PSymbolw@_ [wdw0-! )! )! =! = & 'Edxpr MTHU EGrphbj E"E currentpoint " +-)0).)5) =) b( 32(020"0 ( ) *  ( = *  /MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 2208 div 960 3 -1 roll exch div scale currentpoint translate 64 42 translate /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 1473 435 moveto 427 0 rlineto stroke /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 384 /Symbol f1 (-) -4 534 sh (=) 770 534 sh (\346) 1276 355 sh (\350) 1276 758 sh (\366) 1910 355 sh (\370) 1910 758 sh 384 /Times-Roman f1 (0) 206 534 sh (5) 494 534 sh (2) 1590 293 sh (20) 1494 827 sh 384 /Times-Roman f1 (.) 398 534 sh 384 /Times-Italic f1 (b) 1079 534 sh end MTsave restore dFMATH:~ -0.5=b220() FMathType Equation1ELO Equation9qTCIP #Edxpr MTHU EGrphbj E"E currentpoint " +-)0).)5) =) b( 32(020"0 ( ) *  ( = *  /MTsave save def 40 dict begin currentpoint 3 -1 roll sOlePres000; Ole10NativeP >Ole10FmtProgID Q _1011083523 F`F3}B`F3}Bub neg 3 1 roll sub 2208 div 960 3 -1 roll exch div scale currentpoint translate 64 42 translate /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 1473 435 moveto 427 0 rlineto stroke /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 384 /Symbol f1 (-) -4 534 sh (=) 770 534 sh (\346) 1276 355 sh (\350) 1276 758 sh (\366) 1910 355 sh (\370) 1910 758 sh 384 /Times-Roman f1 (0) 206 534 sh (5) 494 534 sh (2) 1590 293 sh (20) 1494 827 sh 384 /Times-Roman f1 (.) 398 534 sh 384 /Times-Italic f1 (b) 1079 534 sh end MTsave restore dFMATH:~ -0.5=b220(): -0.5=b220() Equationd 0 '   .  & PSymbolw@ [wdw0-!Ole R PIC S dMETA U VPICT o D Timesw@ [wdw0-!Q PSymbolw@ [wdw0-!DTimesw@ [wdw0-!P -  PSymbolw@ [wdw0-!=Timesw@ [wdw0-!820 #PSymbolw@ [wdw0-!- 8Timesw@ [wdw0-!850 A!4!!.'!11*PSymbolw@ [wdw0-!-8Timesw@ [wdw0-!3A!.G!76J  UPSymbolw@ [wdw0-!=Z!-cTimesw@ [wdw0-!30 q!0m!.s!35v l PSymbolw@ [wdw0-!=!-Timesw@ [wdw0-!85!.!7!. & 'dxpr MTHU Grphbj " currentpoint " + D)Q(D)P" (=( #820)-) 850(!4).)11)-) 3).)76" 5(Z=) -( q30(m0).)35" l(=) -)85) .)7)./MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 5600 div 896 3 -1 roll exch div scale currentpoint translate 64 39 translate /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 406 moveto 558 0 rlineto stroke 984 406 moveto 1727 0 rlineto stroke 3402 406 moveto 703 0 rlineto stroke /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 384 /Symbol f1 (D) 30 264 sh (D) 49 798 sh 384 /Times-Italic f1 (Q) 265 264 sh (P) 284 798 sh 384 /Symbol f1 (=) 666 505 sh (-) 1743 264 sh (-) 1735 798 sh (=) 2819 505 sh (-) 3133 505 sh (=) 4213 505 sh (-) 4527 505 sh 384 /Times-Roman f1 (820) 1085 264 sh (850) 2024 264 sh (4) 1012 798 sh (11) 1300 798 sh (3) 2020 798 sh (76) 2308 798 sh (30) 3558 264 sh (0) 3425 798 sh (35) 3713 798 sh (85) 4737 505 sh (7) 5217 505 sh 384 /Times-Roman f1 (.) 1204 798 sh (.) 2212 798 sh (.) 3617 798 sh (.) 5121 505 sh (.) 5409 505 sh end MTsave restore dMATH" DQDP=820-8504.11-3.76=-300.35=-85.7.#x FMathType Equation1ELO Equation DQDP=820-850CompObj KObjInfo Ole10Native Ole10FmtProgID  4.11-3.76=-300.35=-85.7. Equationd\   FMathType Equation1ELO Equation_1011083679 F`F3}B`F3}BOle  PIC  dMETA \     | .  & Timesw@_ [wdw0-!ETimesw@l [wdw0-!p Timesw@_ [wdw0-!97 PSymbolw@l [wdw0-!=Timesw@_ [wdw0-!P !Q-'PSymbolw@l [wdw0-!D +Timesw@_ [wdw0-!Q 3PSymbolw@l [wdw0-!D,Timesw@_ [wdw0-!P3*;PSymbolw@l [wdw0-!=?Timesw@_ [wdw0-!4 J!. P!11 S!820KI^!(`PSymbolw@l [wdw0-!-eTimesw@_ dw0-!85k!.w!7z!)PSymbolw@l [wdw0-!=!-Timesw@_ [wdw0-!0!.!43Timesw@l [wdw0-!E4Timesw@_ [wdw0-!p7 Timesw@l [wdw0-!98. PSymbolw@_ [wdw0-!=4Timesw@l [wdw0-!P, !Q=00'PSymbolw@_ [wdw0-!D,+Timesw@l [wdw0-!Q,3PSymbolw@_ [wdw0-!D=,Timesw@l [wdw0-!P=30*0;PSymbolw@_ ![wdw0-!=4?Timesw@l [wdw0-!3,J!.,P!76,S!850=K0I0^!(4aPSymbolw@_ "[wdw0-!-4eTimesw@l [wdw0-!854l!.4x!74{!)4PSymbolw@_ #[wdw0-!=4!-4Timesw@l [wdw0-!04!.4!384Timesw@_ $[wdw0-!EcTimesw@l [wdw0-!pf !AVE^ PSymbolw@_ %[wdw0-!=cTimesw@l [wdw0-!PN*Timesw@_ &[wdw0-!97Q/PSymbolw@l [wdw0-!+N9Timesw@_ '[wdw0-!PNCTimesw@l [wdw0-!98QHTimesw@_ ([wdw0-!2_:R(RPTimesw@l [wdw0-!Qj'Timesw@_ )[wdw0-!97m/PSymbolw@l [wdw0-!+j9Timesw@_ *[wdw0-!QjBTimesw@l [wdw0-!98mJTimesw@_ +[wdw0-!2z:n&nR`%`SPSymbolw@l [wdw0-!D\WTimesw@_ ,[wdw0-!Q\^PSymbolw@l [wdw0-!DlWTimesw@_ -[wdw0-!Pl_`V`fPSymbolw@l [wdw0-!=ckTimesw@_ .[wdw0-!3\u!.\{!935\~!835ly`u`!(cPSymbolw@l [wdw0-!-cTimesw@_ /[wdw0-!85c!.c!7c!)cPSymbolw@l [wdw0-!=c!-cTimesw@_ 0[wdw0-!0c!.c!40c!.c & 'PICT "BCompObj KObjInfo Ole10Native B|dxprH MTHUH|Grphbj |"| currentpoint " +E +p( 97 + =( P(Q"( +D)Q(,D)P"*(?=( J4).)11(K820"I(`()-)85) .)7)))=) -)0).)43(4E +p(. 98 + =(, P(=Q"0(,+D)Q(=,D)P"0*(4?=(,J3).)76(=K850"0I(4a()-)85) .)7)))=) -)0).)38(cE +p(^ AVE +=(N*P +97 (N9+) P +98 (_:2"R(((j'Q +97 (j9+) Q +98 (z:2"n&,"`%.(\WD)Q(lWD)P"`V(ck=(\u3).)935(ly835"`u(c()-)85) .)7)))=) -)0).)40) ./MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 7232 div 3968 3 -1 roll exch div scale currentpoint translate 64 58 translate /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 935 406 moveto 310 0 rlineto stroke 1309 406 moveto 558 0 rlineto stroke 2293 406 moveto 691 0 rlineto stroke 934 1507 moveto 310 0 rlineto stroke 1308 1507 moveto 558 0 rlineto stroke 2292 1507 moveto 707 0 rlineto stroke 8 th 1243 2605 moveto 1294 0 rlineto stroke 1179 3480 moveto 1422 0 rlineto stroke 16 th 1147 3037 moveto 1486 0 rlineto stroke 2697 3037 moveto 558 0 rlineto stroke 3681 3037 moveto 888 0 rlineto stroke /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 384 /Times-Italic f1 (E) 6 505 sh (P) 982 264 sh (Q) 952 798 sh (Q) 1574 264 sh (P) 1593 798 sh (E) 6 1606 sh (P) 981 1365 sh (Q) 951 1899 sh (Q) 1573 1365 sh (P) 1592 1899 sh (E) 6 3136 sh (P) 1281 2463 sh (P) 2094 2463 sh (Q) 1196 3338 sh (Q) 2073 3338 sh (Q) 2962 2895 sh (P) 2981 3429 sh 224 ns (p) 254 601 sh (p) 254 1702 sh (p) 254 3232 sh (AVE) 281 2964 sh 224 /Times-Roman f1 (97) 265 333 sh (98) 265 1434 sh (97) 1449 2559 sh (98) 2262 2559 sh (97) 1449 3434 sh (98) 2326 3434 sh 384 ns (4) 2321 264 sh (11) 2609 264 sh (820) 2345 798 sh (85) 3382 505 sh (7) 3862 505 sh (0) 4794 505 sh (43) 5082 505 sh (3) 2308 1365 sh (76) 2596 1365 sh (850) 2352 1899 sh (85) 3397 1606 sh (7) 3877 1606 sh (0) 4809 1606 sh (38) 5097 1606 sh (2) 1794 2997 sh (2) 1794 3872 sh (3) 3697 2895 sh (935) 3985 2895 sh (835) 3839 3429 sh (85) 4967 3136 sh (7) 5447 3136 sh (0) 6379 3136 sh (40) 6667 3136 sh 384 /Symbol f1 (=) 617 505 sh (=) 1975 505 sh (-) 3172 505 sh (=) 4270 505 sh (-) 4584 505 sh (=) 616 1606 sh (=) 1974 1606 sh (-) 3187 1606 sh (=) 4285 1606 sh (-) 4599 1606 sh (=) 829 3136 sh (+) 1786 2463 sh (+) 1786 3338 sh (=) 3363 3136 sh (-) 4757 3136 sh (=) 5855 3136 sh (-) 6169 3136 sh 384 /Symbol f1 (D) 1339 264 sh (D) 1358 798 sh (D) 1338 1365 sh (D) 1357 1899 sh (D) 2727 2895 sh (D) 2746 3429 sh 384 /Times-Roman f1 (.) 2513 264 sh (\() 3030 505 sh (.) 3766 505 sh (\)) 4053 505 sh (.) 4986 505 sh (.) 2500 1365 sh (\() 3045 1606 sh (.) 3781 1606 sh (\)) 4068 1606 sh (.) 5001 1606 sh (.) 3889 2895 sh (\() 4615 3136 sh (.) 5351 3136 sh (\)) 5638 3136 sh (.) 6571 3136 sh (.) 7051 3136 sh end MTsave restore dMATHY E p97 =PQDQDP=4.11820(-85.7)=-0.43E p98 =PQDQDP=3.76850(-85.7)=-0.38E pAVE =P 97 +P 98 2Q 97 +Q 98 2DQDP=3.935835(-85.7)=-0.40. E p97 =PQDQDP=4.11820(-85.7)=-0.43E p98 =PQDQDP=3.76850(-85.7)=-0.38E pAVE =P 97 +P 98 2Q 97 +Q 98 2DQDP=3.935835(-85.7)=-0.40. Equationdt0 %   .  & Ole10FmtProgID  _1011084213 F`F3}B`F3}BOle  PIC  dMETA  RPICT  CompObj KObjInfo PSymbolw@Z Vzww0-!D Timesw@~ zww0-!Q PSymbolw@Z Wzww0-!DTimesw@~ zww0-!P -  PSymbolw@Z Xzww0-!=Timesw@~ zww0-!75 /PSymbolw@Z Yzww0-!- =Timesw@~ zww0-!70 F!10 !.,!35/PSymbolw@Z Zzww0-!-=Timesw@~ zww0-!10E!.Q!48T  _PSymbolw@Z [zww0-!=d!-nTimesw@~ zww0-!5 ~!0w!.}!13 v PSymbolw@Z \zww0-!=!-Timesw@~ zww0-!38!.!5!. & 'dxpr MTHU Grphbj " currentpoint " + D)Q(D)P" (=( /75)-) 70( 10) .)35)-)10) .)48" ?(d=) -( ~5(w0).)13" v(=) -)38) .)5)./MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 5920 div 896 3 -1 roll exch div scale currentpoint translate 64 39 translate /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 406 moveto 558 0 rlineto stroke 984 406 moveto 2054 0 rlineto stroke 3729 406 moveto 700 0 rlineto stroke /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 384 /Symbol f1 (D) 30 264 sh (D) 49 798 sh 384 /Times-Italic f1 (Q) 265 264 sh (P) 284 798 sh 384 /Symbol f1 (=) 666 505 sh (-) 1900 264 sh (-) 1906 798 sh (=) 3146 505 sh (-) 3460 505 sh (=) 4537 505 sh (-) 4851 505 sh 384 /Times-Roman f1 (75) 1448 264 sh (70) 2194 264 sh (10) 974 798 sh (35) 1454 798 sh (10) 2165 798 sh (48) 2645 798 sh (5) 3989 264 sh (0) 3752 798 sh (13) 4040 798 sh (38) 5061 505 sh (5) 5541 505 sh 384 /Times-Roman f1 (.) 1358 798 sh (.) 2549 798 sh (.) 3944 798 sh (.) 5445 505 sh (.) 5733 505 sh end MTsave restore dMATH^ DQDP=75-7010.35-10.48=-50.13=-38.5.x| FMathType Equation1ELO EquationOle10Native Ole10FmtProgID  _1014533622 F`F3}B`F3}BOle   DQDP=75-7010.35-10.48=-50.13=-38.5. Equationdf Xf B   .PIC  dMETA  PICT  CompObj K                        # $ ( * + , - . / 0 1 2 3 4 5 6 7 8 9 : ; < = > ? @ A B C E F G H I J K L M N O P Q R S T U V W X Y Z [ \ ] ^ _ ` b e f j l m n o p q r s t u v w x y z { | } ~    & Timesw@! 9zww0-!ETimesw@u zww0-!p Timesw@! :zww0-!97 PSymbolw@u zww0-!=Timesw@! ;zww0-!P !Q-  'PSymbolw@u zww0-!D +Timesw@! zww0-!10 I!. U!35 X!75Q I c!(fPSymbolw@u zww0-!-jTimesw@! ?zww0-!38q!.}!5!)PSymbolw@u zww0-!=!-Timesw@! @zww0-!5!.!31 & ' dxpr MTHU Grphbj " currentpoint " +E +p( 97 + =( P(Q" ( +D)Q(,D)P" *(?=( I10) .)35(Q75" I(f()-)38) .)5)))=) -)5).)31/MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 5696 div 960 3 -1 roll exch div scale currentpoint translate 64 39 translate /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 935 406 moveto 310 0 rlineto stroke 1309 406 moveto 558 0 rlineto stroke 2293 406 moveto 862 0 rlineto stroke /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 384 /Times-Italic f1 (E) 6 505 sh (P) 982 264 sh (Q) 952 798 sh (Q) 1574 264 sh (P) 1593 798 sh 224 ns (p) 254 601 sh 224 /Times-Roman f1 (97) 265 333 sh 384 ns (10) 2283 264 sh (35) 2763 264 sh (75) 2541 798 sh (38) 3553 505 sh (5) 4033 505 sh (5) 4961 505 sh (31) 5249 505 sh 384 /Symbol f1 (=) 617 505 sh (=) 1975 505 sh (-) 3343 505 sh (=) 4437 505 sh (-) 4751 505 sh 384 /Symbol f1 (D) 1339 264 sh (D) 1358 798 sh 384 /Times-Roman f1 (.) 2667 264 sh (\() 3201 505 sh (.) 3937 505 sh (\)) 4220 505 sh (.) 5153 505 sh end MTsave restore dMATH E p97 =PQDQDP=10.3575(-38.5)=-5.31۠ FMathType Equation1ELO Equation E p97 =PQDQDP=10.3575(-38.5)=-5.31 Equationd XObjInfo! Ole10Native" Ole10FmtProgID % _1014533654 F`F3}B`F3}BOle & PIC ' dMETA ) PICT D - B   .  & Timesw@u zww0-!ETimesw@D zww0-!p Timesw@u zww0-!98 PSymbolw@D zww0-!=Timesw@u zww0-!P !Q-  'PSymbolw@D zww0-!D +Timesw@u zww0-!Q 3PSymbolw@D zww0-!D,Timesw@u zww0-!P3 * ;PSymbolw@D zww0-!=?Timesw@u zww0-!10 I!. U!48 X!70Q I c!(fPSymbolw@D zww0-!-jTimesw@u zww0-!38q!.}!5!)PSymbolw@D zww0-!=!-Timesw@u zww0-!5!.!76 & '-dxpr MTHU Grphbj " currentpoint " +E +p( 98 + =( P(Q" ( +D)Q(,D)P" *(?=( I10) .)48(Q70" I(f()-)38) .)5)))=) -)5).)76#/MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 5728 div 960 3 -1 roll exch div scale currentpoint translate 64 -1062 translate /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 934 1507 moveto 310 0 rlineto stroke 1308 1507 moveto 558 0 rlineto stroke 2292 1507 moveto 863 0 rlineto stroke /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 384 /Times-Italic f1 (E) 6 1606 sh (P) 981 1365 sh (Q) 951 1899 sh (Q) 1573 1365 sh (P) 1592 1899 sh 224 ns (p) 254 1702 sh 224 /Times-Roman f1 (98) 265 1434 sh 384 ns (10) 2282 1365 sh (48) 2762 1365 sh (70) 2533 1899 sh (38) 3553 1606 sh (5) 4033 1606 sh (5) 4961 1606 sh (76) 5249 1606 sh 384 /Symbol f1 (=) 616 1606 sh (=) 1974 1606 sh (-) 3343 1606 sh (=) 4437 1606 sh (-) 4751 1606 sh 384 /Symbol f1 (D) 1338 1365 sh (D) 1357 1899 sh 384 /Times-Roman f1 (.) 2666 1365 sh (\() 3201 1606 sh (.) 3937 1606 sh (\)) 4220 1606 sh (.) 5153 1606 sh end MTsave restore dMATH! E p98 =PQDQDP=10.4870(-38.5)=-5.76m FMathType Equation1ELO Equation E p98 =PQDQDP=10.4870(-38.5)=-5.76 EquationCompObja KObjInfoc Ole10Natived Ole10FmtProgID g _1004703214F`F3}B4}BOle h PIC i LPICT k B L L B7dxpr MTHU7Grphbj 7"7 currentpoint " +E +p( AVE +=( *P +97 ( 9+) P +98 (:2" (((%'Q +97 (%9+) Q +98 (6:2")&,"%. (WD)Q((WD)P"V(k=(t10) .)415(({72) .)5"u(()-)38) .)5)))=) -)5).)52) .=/MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 7392 div 1760 3 -1 roll exch div scale currentpoint translate 64 58 translate /thick 0 def /th { dup setlinewidth /thick exch def } def 8 th 1243 403 moveto 1294 0 rlineto stroke 1179 1278 moveto 1422 0 rlineto stroke 16 th 1147 835 moveto 1486 0 rlineto stroke 2697 835 moveto 558 0 rlineto stroke 3681 835 moveto 1054 0 rlineto stroke /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 384 /Times-Italic f1 (E) 6 934 sh (P) 1281 261 sh (P) 2094 261 sh (Q) 1196 1136 sh (Q) 2073 1136 sh (Q) 2962 693 sh (P) 2981 1227 sh 224 ns (p) 254 1030 sh (AVE) 281 762 sh 384 /Symbol f1 (=) 829 934 sh (+) 1786 261 sh (+) 1786 1136 sh (=) 3363 934 sh (-) 4923 934 sh (=) 6017 934 sh (-) 6331 934 sh 224 /Times-Roman f1 (97) 1449 357 sh (98) 2262 357 sh (97) 1449 1232 sh (98) 2326 1232 sh 384 ns (2) 1794 795 sh (2) 1794 1670 sh (10) 3671 693 sh (415) 4151 693 sh (72) 3881 1227 sh (5) 4361 1227 sh (38) 5133 934 sh (5) 5613 934 sh (5) 6541 934 sh (52) 6829 934 sh 384 /Symbol f1 (D) 2727 693 sh (D) 2746 1227 sh 384 /Times-Roman f1 (.) 4055 693 sh (.) 4265 1227 sh (\() 4781 934 sh (.) 5517 934 sh (\)) 5800 934 sh (.) 6733 934 sh (.) 7213 934 sh end MTsave restore dMATH( E pAVE =P 97 +P 98 2Q 97 +Q 98 2DQDP=10.41572.5(-38.5)=-5.52.mFMathType Equation 3.6+DNQEEquation.DSMT36 E pAVE =P 97 +P 98 2Q 97 +Q 98 2DQDP=10.41572.5(-38.5)=-5.5CompObj WObjInfo Ole10Native Ole10FmtProgID  2. 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