Answers to Selected Exercises - UTEP

1 A18 Answers to Selected ExercisesChapter 0 Section *(2-5) (2-5)29.(3-1)/(8+6) (4+7) (3+x)-x*y^ ^3-4x^(-2)-60/(x^2-1)37.(2/3) ^(4-5)* *(1+4/100)^(-3) ^(2*x-1)+4^ ^(2x^2-x+1) *e^(-2*x)/(2-3e^(-2*x)) or4*(e^(-2*x))/(2-3e^(-2*x)) (1-(-1/2)^2)^2+1 Section 1 + a3+ (xy2)1 13x +43x (x2+1) 3 34(x2+1) 1 x3 y87. 324 x2+3 (1 x) yx 1/3103. 4105. 2/3107. 1, 1/3109. + 2x +13y+ 12x+ +2+1 1 +6x2+2x 4x3+6x2 4x+ +4y4+4y3 y23.(x+1)(2x+5)25.(x2+1)5(x+3)3(x2+x+4)2 7. x3(x3+1) x+129.(x+2) (x+1)331. (2+3x) , 2/333. (3x 1) , 1/335. a.(x 1)(x 7) , 737. a.(x 3)(x+4) , 439. a.(2x+1)(x 2) 1/2, 241. a.(2x+3)(3x+2) 3/2, 2/343. a.(3x 2)(4x+3) , 3/445. a.(x+2y) 2y47. a.(x2 1)(x2 4) 1, 2 Section 7x 4x2 2x+5x2 x+1x+ 3x2y11.(x+1)2(x+2)413. 1 (x2+1)315. (2x+y)x2(x+y)2 Section 111.(c b) 4, 1 solutions17. 5219. 121. 1, 1, 329.

2 1 5231. 1, 2, 333. , 541. 1, 1 243. 2, 1, 2, 3 Section , 33. 25. 1, 5/27. , 1, 1(x= 2isnot a solution.)13. 2, 3/2, 115. 117. 4 219. 121. 4, 1/4 Chapter 1 Section a. 85. a. 7b. (a+b) 37. +2a+3f.(x+h)2+2(x+h)+39. +1/xe.(s+h)2+1/(s+h)f.(s+h)2+1/(s+h) (s2+1/s)11. ; f(4)=63 defined15. , f( 10)=017. (2x+h) +h19. a. h(2x+h)b. (2x+h) *x^2-4*x+523.(x^2-1)/(x^2+1)25. (5)=117, P(10)=132, and P( ) 131. Approxi-mately 117 million people were employed in the on July 1,1995, 132 million people on July 1, 2000, and 131 million peoplex01 2 3 4 5 6 7 8 9 10f(x) (x) 7/17/06 11:54 PM Page 18on January 1, [5, 11].27. a.[0, 10]. t 0is not anappropriate domain because it would predict trade withChina into the indefinite future with no $280 billion; trade with China in 2004 was valued at approximately$ a.

3 (2)b.$ billion31. , ,200c.$ (0)=200: At the start of 1995,the processor speed was 200 megahertz. P(4)=500: At the startof 1999, the processor speed was 500 megahertz. P(5)=1100: Atthe start of 2000, the processor speed was 1100 through 2001c:35. a.( *t+ )*(t<8)+( * )*(t>=8) (26,000)=$730+ (26,000 7300)=$3535;T(65,000)=$4090+ (65,000 29,700)=$12,91539. a.$12, (q)=2000+100q2 500q; N(20)=$32,00041. *(1-12200/t^ ) ; (x)=4x2 2(orf(x)=4x2 2) (t)=200+10t(N=number ofsound files, t=time in days) the text reminds us: toevaluate fof a quantity (such as x+h) replace xeverywhere bythe whole quantityx+h, getting f(x+h)=(x+h)2 : Functions with infinitely many points in their domain(such as f(x)=x2) cannot be specified a. a.(I)b.(IV)c.(V)d.(VI)e.(III)f.(II) (x^3)x^ a. 21/x^2 x*(x<0)+2*(x>=0)xy24 4xy11xy11xy1 1 1115. (x^2)*(x<=0)+(1/x)* x*(x<=0)+(x+1)*(0<x) (0<x)*(x<=2)+x*(2<x) (6) 2000, f(9) 2800,f( ) 2500.

4 In 1996,2,000,000 SUVs were sold. In 1999, 2,800,000 were sold, and inthe year beginning July, 1997, 2,500,000 were (6) f(5); SUV sales increased more from 1995 to 1996than from 1999 to a.[ , ] ( ) 131, N(0) 132, N(1) 132. In July 1999, ap-proximately 131 million people were employed. In January 2000and January 2001, approximately 132 million people were [ , ]; Employment was falling during the periodJuly 2000 July a.(C)b.$ per shirt if the teambuys 70 shirts. quadratic model (B) is the best choice; the other modelseither predict perpetually increasing value of the euro or perpetu-ally decreasing value of the *(1-12200/t^ ) through 200133. a.( *t+ )*(t<8)+( * )*(t>=8) ,0003,0002,0001, 22414 Answers to Selected ExercisesA19 Answers TO Selected EXERCISESt01234 5 6 7 8 9P(t)200 275 350 425 500 1100 1700 2300 2900 3500t012345678 91011C(t) 1 (t) 7/17/06 11:54 PM Page 19A20 Answers to Selected ExercisesANSWERS TO Selected We can construct a table of values from any graph byreading off a set of In a numerically specifiedfunction, only certain values of the function are specified, givingonly certain points on the are different por-tions of the graph of the associated equation y=f(x).

5 Of g(x)is the same as the graph of f(x), but shifted 5 unitsto the value: 11; m= value: 4; m= value: 7; m=3 (x)= x/2 (0)= 5, f(x)= x linear: f(x)=4x+ linear: g(x)=2x 115. 3 4 (d b)/(c a)55. 1/3f. 1/4i. 5x+ 3x+ x+ + the corresponding successive changes xin xand0(3, 2)xy32xy083xy0 11xy(4, 5) 4xy23xy 11xy yin y, and compute the ratios y/ x. If the answer is alwaysthe same number, then the values in the table come from a linear (x)= abx+cb. Ifb=0, thenabis undefined,and ycannot be specified as a function of x. (The graph of theresulting equation would be a vertical line.) , mis positive then ywill increase as xincreases; if misnegative then ywill decrease as xincreases; if mis zero then ywill not change as slope increases, since anincrease in the y-coordinate of the second point increases ywhile leaving (x)=1500x+1200per daya.$5700b.$1500c.

6 $ cost =$8000, marginal cost =$25perbicycle5. (x)= +70, R(x)= , P(x)= (500)= 20; a loss of $ 40p+20009. p+ ; million phonesb.$1, 1 million11. :q= 60p+150; supply: q=80p 60b.$ each13. a.(1996, 125) and (1997, 135) or (1998, 140) and (1999,150). number of new in-ground pools increased mostrapidly during the periods 1996 1997 and 1998 1999, when itrose by 10,000 new pools in a +50tmilliontransactions. The slope gives the additional number of online shop-ping transactions per year, and is measured in (millions of) trans-actions per +240;Medicare spending ispredicted to rise at a rate of $ billion per yearb.$816 billion19. feet along the 6 seconds21. miles per 5 +32; 86 F; 72 F; 14 F; 7 (N)= +50, 000; N=$1, 000, 000; marginal income ism=5 per dollar of net 58; 42 ; (r)=(1/4)r+45; T(100)=70 (x)=100x 5132, withdomain [0, 405].

7 For profit, x (SP VC) (x)= 20, 000, with domainx 0; x= per day for break by$355,000 per year43. 30t+ 30t+200 if 0 t 550t 200 if 5<t (t)= 1,400t+30,000 if 0 t 57,400t 14,000if 5<t 10C(3) = 25,800 students (r)= 40r+74if r 1033if <r ;d(1)=34% per zonar; must increase by10 units each day, including the (B) number of items from the breakeven results in a profit:Because the slope of the revenue graph is larger than the slope ofthe cost graph, it is higher than the cost graph to the right of thepoint of intersection, and hence corresponds to a 7/17/06 11:54 PM Page 20 Answers to Selected ExercisesA21 Answers TO Selected EXERCISESS ection (better fit) (better fit) (best, not perfect) (worst) + ; + ; $ + ; million jobs21. acre of cultivated land produces about tons ofsoybeans23.

8 Line: y= + :The graph suggests a relationship between xand rate declines by for each $1000 increase in themedian household ; not a strong corre-lation25. + ; the first and last points lie above the regression line, whilethe central points lie below it, suggesting a 25 30 35 40 45 50 55204613y that the residuals are positive at first, then become nega-tive, and then become positive, confirming the impression fromthe line that passes through (a,b) and (c,d)gives a sum-of-squares error SSE = 0, which is the smallest regression line is the line passing throughthe given The regression line through( 1, 1), (0, 0), and (1, 1) passes through none of these 1 Review1. 13. x+ (1/2)x first line,y=x+1, is the better + , r a.(A)b.(A) Leveling off (B) Rising (C) Rising; they beginto fall after 7 months (D) Rising25.

9 Hits per not. This model predicts that Web site traffic willstart to decrease as advertising increases beyond $8500 permonth, and then drop toward 60p+ novels per monthc.$10, for a profit of $ 2 Section (2, 2)3.(3, 1)5.(6, 6)7.(5/3, 4/3)9.(0, 2)11.(x,(1 2x)/3)or 12(1 3y),y solution15.(5, 0)17.( , )19.( , )21.( , )23.( , ) quarts of vanilla and 100 quarts of servings of Mixed Cereal and 1 serving of Mango TropicalFruit29. servings of beans and 5 slices of of the variables in the solution of the system has a 5 servings of Cell-Tech and 6 servings of Ribo-Force HP for a cost of $ CSCO, 150 ED, 200 in favor and 193 7/17/06 11:54 PM Page 21A22 Answers to Selected ExercisesANSWERS TO Selected soccer games and 7 football $ : q= 4p+47; supply: q=4p 29; equilibrium price: $ pairs ofdirty socks and 11 T-shirts51.

10 $ system of threeequations in two unknowns will have a unique solution if either(1) the three corresponding lines intersect in a single point, or (2)two of the equations correspond to the same line, and the thirdline intersects it in a single Even if two lineshave negative slope, they will still intersect if the slopes cannot round both of them up, because there will not besufficient eggs and cream. Rounding both Answers down will en-sure that you will not run out of ingredients. It may be possible toround one answer down and the other up, and this should be (B)61.(B) will is very randomly chosen straight lines are unlikely to be (3, 1)3.(6, 6)5. 12(1 3y),y , solu-tion9.(1/4, 3/4) solution13.(10/3, 1/3)15.(4, 4, 4)17. 1, 3,12 19.(z, z, z), solution23.( 1, 1, 1)25.(1,z 2,z), zarbitrary27.(4+y,y, 1),yarbitrary29.(4 y/3+z/3,y,z), yarbitrary, zarbitrary31.