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per minute 23. (a) 9 25. (ab)β(e) Answers will vary. (b)β(e) Answers will vary. Chapter 4 Section 4.1 (page 290) Vocabulary Check (page 290) f1x lnx x2 4 2 ln c2 ln c1 ln 1 1 k2 2 252,6061.0310t 400.88t2 1464.6t 291,782 1 k1 t 13. y1 y2 11. c 15. (a) (b) 2. angle 5. acute; obtuse 1. Trigonometry 4. radian 6. complemen... |
) (b) 330.007 145 48 3 34 48 32 83. radians 7 15 inches 47.12 inches 87. 8 3 radian 2 9 89. 3 meters 91. square inches 8.38 square inches 2 1.14 0.071 radian 4.04 93. 12.27 square feet 97. 101. (a) 728.3 revolutions per minute (b) 4576 radians per minute 95. 591.3 miles 5 12 radian 99. 103. (a) 10,400 radians per minut... |
period 2. periodic 4. odd; even csc 17 15 sec 17 8 cot 8 15 csc 13 5 sec 13 12 cot 12 5 3, 1 2 2 7. 9. 1 2, 3 2 15. 19. 1 sin 2 6 cos 3 2 6 tan 3 6 3 sin 11 1 6 2 11 3 6 2 11 3 6 3 cos tan sin 15 17 cos 8 17 tan 15 8 sin 5 13 cos 12 13 tan 5 12 2 2 2 2 0, 1, sin cos 4 4 2 2 2 2 1. 3. 5. 11. 13. 17. 21. 2 2 2 2 1 tan 4... |
β8 2 4 6 8 10 x β6 β5 β2 y 4 3 2 1 β1 β1 β2 β3 β 333200_04_AN.qxd 12/9/05 1:32 PM Page A134 A134 Answers to Odd-Numbered Exercises and Tests Section 4.3 (page 308) Vocabulary Check (page 308) (b) iv 1. (a) v 2. opposite; adjacent; hypotenuse 3. elevation; depression (c) vi (d) iii (e) i (f) ii 1. sin cos tan 3. sin co... |
r cot 1. 6. 2. csc 3. y x 4. r x 5. cos 7. reference 1. (a) sin cos tan csc sec cot 3. (a) sin cos b) sin cos tan csc sec cot (b) sin cos 15 17 8 17 15 8 17 15 17 8 8 15 17 17 417 17 tan csc sec 3 3 2 23 3 3 cot 24 25 7 25 24 7 5. sin cos tan csc sec cot 25 24 25 7 7 24 tan 1 4 csc 17 sec 17 4 cot 4 tan 3 cot 3 3 23. ... |
14 centimeter x x 95. As 91. 0.79 ampere 93. False. In each of the four quadrants, the signs of the secant function and cosine function will be the same, because these functions are reciprocals of each other. 0 y 0 cm and sin y12 decreases from 1 to 0. Thus, 90 without bound. When x y decreases from 12 cm to increases ... |
, 1 y -intercept: Horizontal asymptote: 2 y 0 Domain: all real numbers x Β±1, 0 x -intercepts: x 0 Vertical asymptote: Domain: all real numbers except x 0 x Section 4.5 (page 328) Vocabulary Check (page 328) 1. cycle 2. amplitude 3. 4. phase shift 5. vertical shift 2 b 1. Period: Amplitude: 3 7. Period: 2 3. Period: 4 A... |
minute (c) v 1.00 0.75 0.50 0.25 β0.25 β1.00 2 4 8 10 t 75. (a) Ct 56.55 26.95 cos 6 t 3.67 (b) 100 0 0 12 The model is a good fit. 100 (c) 0 0 12 The model is a good fit. 77.90; (d) Tallahassee: Chicago: The constant term gives the annual average temperature. 56.55 (e) 12; yes; one full period is one year. (f) Chicag... |
β 2Ο x β Ο x Ο 25. y 4 3 2 1 β4 4 x β Ο3 2 Ο 2 x y y y β3 β2 β1 β1 Οβ2 3 2 1 6 4 2 333200_04_AN.qxd 12/9/05 1:32 PM Page A140 Answers to Odd-Numbered Exercises and Tests 29. y 2 1 4 β4 3 β3 x Ο2 2 2 5 4 41. 7 4, 3, 4 4, A140 27. y 4 3 2 1 βΟ β1 Ο 2Ο 3Ο x 31. 35. 39. 43. 47. β.6 β6 6 β 0. 33. 5 β 2 37. 3 2 β 2 45 49. E... |
1.5 1 β1 f g the coordinate of csc x is the 43. 0.3 45. 0.1 47. 0 49. 3 5 51. 5 5 (b) As the predator population increases, the number of prey decreases. When the number of prey is small, the number of predators decreases. C : 24 months H: 24 months; 12 months; 12 months R : L: (c) 79. (a) (c) 1 month (b) Summer; winte... |
y Ο 77. β1 1 2 3 x y Ο2 Ο β Ο β2 β1 1 2 g is a The graph of horizontal shift one unit to the right of f. 79. y Ο 81. y Ο β4 β2 2 4 x β 333200_04_AN.qxd 12/9/05 1:32 PM Page A142 A142 Answers to Odd-Numbered Exercises and Tests 83. 2 85. 103. Domain: Range:, 1 1, 2, 0 0, 2 β2 4 β y Ο 2 β2 β1 1 2 x β Ο 2 87. β1 β4 0 4 β... |
7. a 3.64 c 10.64 B 70 a 49.48 A 72.08 B 17.92 13. 19.99 inches 19. (a) 5. c 11.66 A 30.96 B 59.04 11. 2.56 inches 3. 9. a 8.26 c 25.38 A 19 a 91.34 b 420.70 B 7745 15. 107.2 feet 17. 19.7 feet h x y 47Β° 40β² 50 ft 35Β° h 50tan 4740 tan 35 (b) (c) 19.9 feet (b) tan 121 2 171 3 (c) 35.8 21. 2236.8 feet 23. (a) 1 12 ft 2 ... |
82.73 83.04 83.11 8 16 cos 60 8 sin 60 83.14 8 16 cos 61 8 sin 61 8 16 cos 62 8 sin 62 83.11 83.04 (c) (d) 83.14 square feet A 641 cos sin 100 0 0 90 83.1 square feet when The answers are the same. 60 65. False. The tower is leaning, so it is not perfectly vertical and does not form a right angle with the ground. C H ... |
tan 3 csc 23 3 sec 2 cot 5 4 cot (b) (b) 22 3 15 4 51. 0.5621 (c) (c) (d) 32 4 415 15 53. 3.6722 45. (a) 3 47. (a) 1 4 49. 0.6494 57. 3 3 2 4 (d) csc 5 4 sec 5 3 cot 3 4 sin 4 5 cos 3 5 tan 4 3 sin 15241 241 cos 4241 241 csc sec 241 15 241 4 cot 4 15 82 9 csc sec 82 cot 1 9 17 4 csc sec 17 cot 1 4 61. 63. tan 15 4 sin... |
333200_05_AN.qxd 12/9/05 1:50 PM Page A147 Answers to Odd-Numbered Exercises and Tests A147 (b) 3705 feet (c) 3. (a) 4767 feet w 2183 tan 63 w 3705 feet, 3000 5. (a) (b) 3 β1 β2 2 β2 3 β1 2 Even Even h 51 50 sin8t 7. 2 9. (a) 2 E P I 7300 7380 β2 2 (b) 7348 I 7377 E P β2 (c) P7369 0.631 E7369 0.901 I7369 0.945 (b) 11.... |
. 1 cos y 39. 45. sec4 x 57. 2 csc2 x 15. d 21. b 27. 35. 1 43. 49. 55. 59. 65. 18. f 24. a 31. cos x 1 sin y 19. e 25. e 33. 41. sin2 x sec sin2 x tan2 x 47. sin2 x cos2 x 53. sin2 x 1 2 sin x cos x 63. 2 sec x 67. 3sec x tan x C H A P T E R 5 20. c 26. d 333200_05_AN.qxd 12/9/05 1:50 PM Page A148 A148 69. 1 0 0 x y1 ... |
sin 0; cos 1 79. 85. 4 sin 22; sin 2 2 ; cos 2 2 87. 0 β€ β€ lncot x 91. 95. (a) 0 β€ < 89. lncsc t sec t 93. 2, 3 2 < < 2 (b) 97. (a) 1.6360 0.6360 1 csc2 132 cot 2 132 1.8107 0.8107 1 cot2 2 csc2 2 7 7 cos90 80 sin 80 0.9848 cos 0.8 sin 0.8 0.7174 2 tan 99. 101. True. For example,, 0 103. 1, 1 107. Not an identity beca... |
.426 43. 47. 1.047, 5.236 51. 0, 2.678, 3.142, 5.820 53. 0.983, 1.768, 4.124, 4.910 55. 0.3398, 0.8481, 2.2935, 2.8018 57. 1.9357, 2.7767, 5.0773, 5.9183 59., 4 5 4, arctan 5, arctan 5 61., 3 5 3 Answers to Odd-Numbered Exercises and Tests A149 4 5 4 0.7854 3.9270 63. (a) 3 (b) 2 0 β3 Maximum: Minimum: 0.7854, 1.4142 3... |
.qxd 12/9/05 1:50 PM Page A150 A150 Answers to Odd-Numbered Exercises and Tests 3. (a) 5. (a) 2 6 4 (b) 2 1 2 1 2 (b) 3 1 2 7. sin 105 cos 105 2 4 2 4 3 1 1 3 tan 105 2 3 9. sin 195 2 4 1 3 cos 195 2 4 3 1 tan 195 2 3 11. sin cos tan 13. sin cos 3 1 2 4 2 1 3 4 11 12 11 12 11 12 17 12 17 12 17 12 tan 2 3 31. 39. 49. 16... |
sin u sin u 1 cos u 1 2 1 2 7. 8. cosu v cosu v sinu v sin u v cosu v 2 sinu v 9. 2 2 sinu v 10. 2 sinu v 2 2 333200_05_AN.qxd 12/9/05 1:50 PM Page A151 Answers to Odd-Numbered Exercises and Tests A151 3 4 cos 2x cos 4x 1. 11. 15. 17 17, 5, 12, 12, 5, 6 6 2 3 sin 2x 3. 15 17 17 13, 12 12 3 7,, 2 6 21. 11 6 4 cos 2x 9.... |
13 3 β3 95β109. Answers will vary. 113. 2 β2 3 β3 2 Ο Ο 2 x 333200_05_AN.qxd 12/9/05 1:50 PM Page A152 A152 Answers to Odd-Numbered Exercises and Tests 23.85 Review Exercises (page 420) 117. 121. (a) 2x1 x2 119. (b) 0.4482 (c) 760 miles per hour; 3420 miles per hour (d) 2 sin1 1 M u < 0, 123. False. For sin 2u sin2u 2... |
2 sec2, 1 β€ sin x β€ 1 for all 1.8431, 2.1758, 3.9903, 8.8935, 9.8820 1 cot2 csc2 y2 115. y1 x 1 (b) 113. 117. Chapter Test (page 423) 2. 1 3. 1 4. csc sec 1. sin 313 13 cos 213 13 13 3 13 2 csc sec cot 2 3 21. 2.938, 2.663, 1.170 5, tan 2u 4 sin 2u 4 23. 24. Day 123 to day 223 t 0.26 minute 25. 0.58 minute 0.89 minute ... |
.17 B 21.55, C 122.45, c 11.49 B 60.9, b 19.32, c 6.36 B 42 4, a 22.05, b 14.88 A 10 11, C 154 19, c 11.03 A 25.57, B 9.43, a 10.53 B 18 13, C 51 32, c 40.06 C 83, a 0.62, b 0.51 B 48.74, C 21.26, c 48.23 19. 21. No solution 23. Two solutions: B 72.21, C 49.79, c 10.27 B 107.79, C 14.21, c 3.30 25. (a) (c) 27. (a) b β€ ... |
x 51. sin2 x Section 6.2 (page 443) Vocabulary Check 1. Cosines 3. Heronβs Area Formula 2. (page 443) b2 a2 c2 2ac cos B 1. 3. 5. 7. 9. 11. 13. 15. A 23.07, B 34.05, C 122.88 B 23.79, C 126.21, a 18.59 A 31.99, B 42.39, C 105.63 A 92.94, B 43.53, C 43.53 B 13.45, C 31.55, a 12.16 A 14145, C 2740, b 11.87 A 27 10, C 27... |
9. x 5. v 3, 2; v 13 v 16, 7; v 305 13. v 9, 12; v 15 y 17degrees) 60.9 69.5 88.0 98.2 109.6 s (inches) 20.88 20.28 18.99 18.28 17.48 d (inches) 15 16 (degrees) 122.9 139.8 s (inches) 16.55 15.37 47. 46,837.5 square feet 51. False. For s 49. $83,336.37 to be the average of the lengths of the three s sides of the trian... |
i sin 2.62 7cos 0 i sin 0 23. Imaginary axis 253 β2 3 3+ i β3 β i 1 2 3 4 Real axis Imaginary axis Real axis β1 β2 β3 β 4 23cos 6 i sin 6 10 cos 3.46 i sin 3.46 27. y Imaginar axis 29. 5 4 3 2 1 5 + 2i Imaginary axis Real axis β10 β8 β6 β4 β2 β2 β4 β6 β8 β10 29cos 0.38 i sin 0.38 139cos 3.97 i sin 3.97 31. Imaginar y ... |
2 4 4i 125 2 608.0 144.7i 813 81 2 2 89. (a) 85. 81. i 32i 75. 1283 128i 79. 1 83. 597 122i 87. 32i 5 cos 60 i sin 60 5 cos 240 i sin 240 The absolute value of each is 1. 12cos 10 9 0.27cos 150 i sin 150 i sin 49. 3 3 47. 51. cos 200 i sin 200 (b) Imaginary axis 3 1 cos 30 i sin 30 β3 β1 1 3 Real axis 53. 55. cos 59. ... |
β6 2 4 6 Real axis A160 93. (a) (c) 95. (a) 5cos 5cos 5cos 4 9 10 9 16 9 i sin i sin i sin 4 9 10 9 16 9 (c) 101. (a) 99. (a) cos 0 i sin 0 cos cos cos cos 2 5 4 5 6 5 8 5 i sin i sin i sin i sin 2 5 4 5 6 5 8 5 β2 1, 0.3090 0.9511i, 0.8090 0.5878i, 0.8090 0.5878i, 0.3090 0.9511i 5cos 3 5cos i sin 5 5cos 3 5 3 i sin i... |
8 15 8 i sin i sin i sin i sin i sin i sin 62cos 62cos 62cos 7 12 5 4 23 12 i sin i sin i sin 7 12 5 4 23 12 Imaginary axis 1 2 β 1 2 Imaginary axis 4 Real axis β 4 β 2 2 4 Real axis β 4 Imaginary axis β 3 β 1 3 1 β 3 Imaginary axis 2 Real axis 3 β2 Real axis 2 β 2 113. True, by the definition of the absolute value of... |
12 Imaginary axis i sin i sin (b Real axis 4 (c) 113. (a) (b) i, 32 2 i, 0.7765 2.898i, 32 2 32 2.898 0.7765i, 32 2 2 0.7765 2.898i, 2.898 0.7765i 2cos 0 i sin 0 2cos 2 3 2cos 4 3 Imaginary axis 2 3 4 3 i sin i sin 3 β3 β1 1 3 Real axis β3 115. 117. i i sin i sin (c) 3cos 3cos 3cos 3cos 2, 1 3 i, 1 3 i 32 2 4 3 32 4 2... |
. 32.6; 543.9 kilometers per hour 45. 425 foot-pounds Problem Solving (page 493) 1. 2.01 feet 3. (a) A 75 mi 135Β° 15Β° y B 75Β° 30Β° x 60Β° Lost party 9. 6.7 10. 3 4 A164 4. 8 Ο2 βb) Station A: 27.45 miles; Station B: 53.03 miles (c) 11.03 miles; 5. (a) (i) 2 (iv) 1 (b) (i) 1 (iv) 1 (c) (i) 5 2 (iv) 1 (d) (i) 25 (iv) 1 5 S... |
A165 Chapter 7 Section 7.1 (page 503) Vocabulary Check (page 503) 1. system of equations 3. solving 5. point of intersection 4. substitution 2. solution 6. break-even (d) Yes (d) No 0, 0, 2, 4 (c) No (c) No (b) No (b) Yes 7. 1. (a) No 3. (a) No 2, 2 2, 6, 1, 3 5. 0, 5, 4, 3 11. 9. 0, 1, 1, 1, 3, 1 13. 20 1, 1 3, 40 21... |
, 135.47 (d) (e) The results are the same, but due to the given parameters, t 135.47 is not of significance. (f) Answers will vary. 6 meters 9 meters 75. 8 kilometers 12 kilometers 73. 77. 79. False. To solve a system of equations by substitution, you can solve for either variable in one of the two equations and then b... |
65. False. Two lines that coincide have infinitely many points (b) 41.4 bushels per acre y 0.32x 4.1 y 14x 19 59. of intersection. 69. 67. No. Two lines will intersect only once or will coincide, and if they coincide the system will have infinitely many solutions. 39,600, 398. It is necessary to change the scale on th... |
y x 2x (b) No (b) No 7. 3z 5 2z 9 3z 0 (d) Yes (d) No 2, 2, 2 1 9. 43 6, 25 6 15. First step in putting the system in row-echelon form 1, 2, 3 13. 19. No solution 23. 4, 8, 5 1 21. 3a 10, 5a 7, a 2a, 21a 2, 8a 2 25. 29. 3 2a 1 a 3, a 1, a 3a 1, a 5, 2, 0 2, 1, 3 2, 2 17. 27. 333200_07_AN.qxd 12/9/05 1:53 PM Page A167 ... |
-point kicks, and 1 field goal 53. $300,000 at 8% $400,000 at 9% $75,000 at 10% 250,000 1 2s 125,000 1 2s 125,000 s s in growth stocks in certificates of deposit in municipal bonds in blue-chip stocks 55. 59. Vanilla 2 lb Hazelnut 4 lb French Roast 4 lb X 4 lb 57. Brand Y 9 lb Brand Z 9 lb Brand Television 30 ads Radio... |
. partial fraction decomposition 3. linear; quadratic; irreducible 2. improper 4. basic equation 1. b A x 5. 2. c B x 14 3. d 4. a B x2 A x 7. B x 52 C x 53 A x 5 A x 1 x Bx C x2 1 1 x 1 Dx E x2 12 1 x 19. 2 C x 10 A 11. x 1 x 1 1 2 Bx C x2 10 1 x 1 15. 2x x2 2 1 2x 1 x2 x 1 39. 31. 1 1 x 1 x 2 4x 4 x2 1 23. x 1 x2 x2 ... |
β3 β5 (b) No (b) No (c) Yes (c) Yes (d) Yes (d) Yes (0, 1) (1, 0) 1 2 x 37. (β1, 4) (β1, 0) β 4 β 3 41. (β 2, 0 29. 31. (a) No 33. (a) Yes 35. y 3 2 β1 y (β 1, 0) β2 39. 4 1 β1 β2 β2 β1 2 3 4 x β3 β1 1 3 4 β2 β3 ( 5, 0 ( x 1 2 3 4 ( 10 333200_07_AN.qxd 12/9/05 1:53 PM Page A170 A170 43. y 3 2 1 Answers to Odd-Numbered... |
20x 15x 10x x y β₯ 300 β₯ 150 β₯ 200 β₯ 0 β₯ 0 (b) y 30 x 30 (c) Answers will vary. y 19.17t 46.61 77. (a) (b) 225 8 0 14 (c) Total retail sales h 2 a b $821.3 billion 79. True. The figure is a rectangle with a length of 9 units and a width of 11 units. 81. The graph is a half-line on the real number line; on the rectangul... |
. y 4 3 1 β1 (0, 2) (0, 0) 2 3 4 5 (5, 0) x Minimum at Maximum at 0, 0: 0 5, 0: 30 Minimum at Maximum at 0, 0: 0 0, 2: 48 4 2 (5, 3) 4 2 (5, 3) 2 4 6 8 x (10, 0) 2 4 6 8 x (10, 0) 5, 3: 35 Minimum at No maximum 21. 15 10, 0: 20 Minimum at No maximum 23. 15 20 β5 50 20 β5 50 24, 8: 104 40, 0: 160 Minimum at Maximum at 2... |
z 4x y 57. 9 2x 3, x 0 x2 2x 13 xx 2 4 ln 38 14.550 4, 3, 7 59. 63. 67., x Β±3 61. ln 3 1.099 65. 65. 1 3e127 1.851 Review Exercises (page 563) 1. 7. 11. 13. 1, 1 3. 0, 0, 2, 8, 2, 8 1.41, 0.66, 0.25, 0.625 9. 1.41, 10.66 5, 4 5. 4, 2 β6 2 β6 6 17. 23. 0, 2 96 meters 144 15. 3847 units meters 8 0, 0 0.5, 0.8 5 a 14 21.... |
) β 4 β3 1 2 3 4 x 73. 20x 12x x β 2 30y β€ 8y β€ β₯ y β₯ 24,000 12,400 0 0 75. (a) p 175 150 125 100 75 50 Consumer Surplus Producer Surplus p = 160 β 0.0001x (300,000, 130) p = 70 + 0.0002 x 100,000 200,000 300,000 x (b) Consumer surplus: $4,500,000 Producer surplus: $9,000,000 333200_07_AN.qxd 12/9/05 1:53 PM Page A173 ... |
. 89. 93. 2 14 95. 3x y 7 6x 3y 1 2x 2y 3z x 2y z x 4y z 97. An inconsistent system of linear equations has no solution. 99. Answers will vary. 7 4 1 β5 β3 β 2 β1 32 5 x β2 β5 ( ( 7, β3 (1, β3) Chapter Test 3, 4 2. 8, 4, 2, 2 1. 3. 4. (page 567) 0, 1, 1, 0, 2, 1 5. y y 8 6 4 2 β2 β4 3, 2 (3, 2) 2 4 6 10 x (β3, 0) β 9 β... |
is greater than 200 milligrams per deciliter. 50 100 150 250 x (d) LDL: 140 milligrams per deciliter HDL: 50 milligrams per deciliter Total: 190 milligrams per deciliter 50, 120; 170 50 3.4 < 4; (e) answers will vary. Chapter 8 Section 8.1 (page 582) Vocabulary Check (page 582) 2. square 1. matrix 4. row; column 7. ro... |
,, 1, 3 3 1 2 79. No 333200_08_AN.qxd 12/9/05 2:40 PM Page A175 83. 4x2 x 12x 1 85. $150,000 at 7% $750,000 at 8% $600,000 at 10% 1 x 1 3 2 x 12 x 1 y x2 2x 5 87. 89. (a) (b) y 0.004x2 0.367x 5 18 0 0 120 (c) 13 feet, 104 feet (e) The results are similar. (d) 13.418 feet, 103.793 feet (c) (b) 91. (a) 500, 0, x5 s t, 60... |
6 3 4 9 (c) (b) 1 3 6 3 4 5 11. (a), (b), and (d) not possible 0 11 3 6 1 24 1 6 0 0 2 12 (d 11 18 0 12 3 7 1 8 9 9 0 15. 19. 3.739 13.249 0.362 4.252 9.713 (c) 8 15 10 59 1.581 3 3 1 2 13 2 0 11 2 4 16 46 10 26 3 13. 17. 21. 25. 29. 24 12 17.143 11.571 23. 4 32 12 12 2.143 10.286 9 0 10 6 1 17 27. Not possible 31. 3 ... |
150 The entries represent the wholesale and retail values of the inventories at the three outlets. 0.314 0.461 0.315 0.435 0.308 0.392 P3 0.300 P4 0.250 P5 0.225 P6 0.213 P7 0.206 P8 0.203 0.308 0.486 0.311 0.477 0.305 0.492 0.175 0.433 0.392 0.188 0.377 0.435 0.194 0.345 0.461 0.197 0.326 0.477 0.198 0.316 0.486 0.199... |
. 33. 37.5 1 4.5 1 0 10 10.5 3.5 1 1.81 5 2.72 1 3 1 0.90 5 3.63 27. 175 95 14 37 20 3 13 7 1 31. 12 4 8 5 2 4 9 4 6 35. Does not exist 39. 3 19 2 19 2 19 5 19 15 59 70 59 3, 8, 11 55. No solution 7, 3, 2 16 59 4 59 41. Does not exist 43. 45. 51. 57. 61. 5, 0 2, 1, 0, 0 4, 8 5 16, 19 16a 13 5, 0, 2, 3 49. 47. 8, 6 53. ... |
1. 5 13. 72 23. (a) (b) 25. (a) (b) 27. (a) M11 C11 M11 C11 M11 M23 C11 C23 M11 M22 C11 C23 75 31. (a) 35. (a) 170 58 43. 51. 412 3. 5 11 15. 6 5, M12 5, C12 4, M12 4, C12 3, M12 4, M31 3, C12 4, C31 30, M12 26, M23 30, C12 7, C31 (b) (b) 170 30 126 45. 53. 29. (a) (b) 61. (a) 3 (b) 2 63. (a) 8 (b) 0 (c) 65. (a) 21 (b... |
8 β 4 4 8 12 x 105. Does not exist Section 8.5 (page 628) Vocabulary Check (page 628) 1. Cramerβs Rule 2. collinear x1 3. A Β± 1 2 y1 y2 y3 5. uncoded; coded x2 x3 1 1 1 4. cryptogram 67. y 6 4 2 (0, 5) (0, 0) (6, 4) ( 20 3 (, 0 x 2 4 6 Minimum at Maximum at 0, 0: 0 6, 4: 52 Review Exercises 1. 3 1 3. 1 1 5. (page 632)... |
i- 57. MEET ME TONIGHT RON cient matrix. 61. False. If the determinant of the coefficient matrix is zero, the system has either no solution or infinitely many solutions. 6, 4 1, 0, 3 63. 65. 5, 2, 0 10, 12 2a 3 2, 3, 3 x 12, y 7 1 8 13 15 8 8 20 12 5 20 7 14 42 3 31 (c) 28 44 16 8 8 (c) 35. (a) 37. (a) 39. 17 13 17 2 4... |
22 5, C32 105. 279 113. 10 x 2y 4 0 (b) 1, 1, 2 7, M21 7, C21 12, M13 19, M23 19 12, C13 19, C23 19 2, C33 107. 4, 7 115. Collinear 21, 22, 103. 130 111. 16 117. 121. Uncoded: Encoded: 109. 1, 4, 5 12 15 2 12, 5 21 6 0 20 21 99 119. 15, 15 68 30 11 2x 6y 13 0 15, 0 21 23 0 20 0, 42 60 53 8 45 102 69 123. SEE YOU FRIDAY... |
,500 Answers will vary. (b) Gold Cable Company: 30,813 subscribers Galaxy Cable Company: 39,675 subscribers Nonsubscribers: 29,513 Answers will vary. (c) Gold Cable Company: 31,947 subscribers Galaxy Cable Company: 42,329 subscribers Nonsubscribers: 25,724 Answers will vary. (d) Cable companies are increasing the numbe... |
an 57. 81, 27, 9, 3, 1 243 3n 1 24 67. 90 61. 65. 1 6 1 2 1,,,, 1 30 1 120 1 2n2n 1 9 81. 88 5 71. 79. 89. 95. i1 9 20 i1 2 3 103. 107. (a) an 2n 4 9 9 2 2 27 8,, 59. 1, 3, 63. 1, 1 2 n 1 69., 1 24, 1 720, 1 40,320 73. 35 75. 40 77. 30 85. 81 87. 47 60 93. 1i13i 6 i1 75 16 99. 101. 3 2 A3 A6 $5306.04, $5630.81, 7 9 i1... |
5, 8, 13, 21, 34, 55, 89, 144 21 13, 34 21, 55 34, 8 5,,,,, x, 125. 121. 123. 129. (a) 5 3 1, 2, 2, 3, 117. $500.95 x4 x3 x2 24 6, 2 x4 x2, x6, 720 24 2 f 1x x 3 4 8 1 2 6 18 9 7 10 3 7 4 4 2 7 42 23 194 4 1 135. 131. (a) 133. 26 4 1 (c) (c) 89 13 8, 55 119. Answers will vary. x5 120 x8 40,320, x10, x β₯ 0 127. (b) (d)... |
d) The slope of the line and the common difference of the arithmetic sequence are equal. 103. 4 105. Slope: y- 1 2; intercept: 0 107. Slope: undefined; y- intercept No y 8 6 4 2 β2 β2 β 4 β 6 β8 2 4 6 8 10 12 14 x 109. x 1, y 5, z 1 111. Answers will vary. Section 9.3 (page 669) Vocabulary Check (page 669) β4 2. an a1r... |
will vary. (b) $26,263.88 (b) $118,788.73 113. $1600 103. $7011.89 107. (a) $26,198.27 109. (a) $118,590.12 111. Answers will vary. $2181.82 115. 119. $3,623,993.23 121. False. A sequence is geometric if the ratios of consecutive 117. 126 square inches terms are the same. 123. Given a real number between r n approache... |
4, 2.2, 2.3, 0.9 (b) A linear model can be used. 2.2n 102.7 2.08n 103.9 142.3; an an (c) (d) Part b: Part c: an These are very similar. an 141.34 P7 63. True. may be false. 65. True. If the second differences are all zero, then the first differences are all the same and the sequence is arithmetic. 4x4 4x2 1 64x3 240x2 ... |
. 35. 32t 5 80t 4s 80t 3s2 40t 2s3 10ts4 s5 333200_09_AN.qxd 12/12/05 11:32 AM Page A184 A184 Answers to Odd-Numbered Exercises and Tests 41. 360 x3y2 37. 39. 45. 49. 180 55. 57. x5 10x4y 40x3y2 80x2y3 80xy4 32y5 120x7y3 1,259,712 x2y7 32,476,950,000x4y8 51. 43. 47. 1,732,104 326,592 53. 210 x2 12x32 54x 108x12 81 x 2 ... |
126 84 36 9 1 1 10 45 120 210 252 210 120 45 87. The signs of the terms in the expansion of between positive and negative. 89β91. Answers will vary. 1 10 x yn n! 3. nPr n r! 5. combinations 4. distinguishable permutations 7. 8 5. 3 9. 30 11. 30 (c) 180 (d) 600 27. 120 3. 5 15. 175,760,000 (b) 648 21. (a) 40,320 1. 6 1... |
page 709) 1. experiment; outcomes 3. probability 5. mutually exclusive 7. complement 4. impossible; certain 6. independent (b) i 8. (a) iii 2. sample space (c) iv (d) ii Answers to Odd-Numbered Exercises and Tests A185 71. y 12 10 8 4 2 73. y 2 β8 β6 β4 β2 4 6 8 x β4 β2 2 4 6 8 12 x Review Exercises (page 715) β8 β12 β... |
. 31 73. 5 2 63. 10 9 at 2 5 67. 24.85 75. 12 (b) $20,168.40 Sn n2n 7 89. 4648 93. 16, 15, 14, 13, 12 First differences: Second differences: 0, 0, 0 Linear 1, 1, 1, 1 95. 15 103. 105. 107. 115. 56 97. 56 99. 35 101. 28 x 4 16x3 96x2 256x 256 a5 15a 4b 90a3b2 270a2b3 405ab4 243b5 41 840i 117. 119. (a) 43% (b) 82% 111. 1... |
57. True. Two events are independent if the occurrence of one has no effect on the occurrence of the other. 59. (a) As you consider successive people with distinct birthdays, the probabilities must decrease to take into account the birth dates already used. Because the birth dates of people are independent events, mul... |
(a) 72 14. 26,000 18. 25% 9. Answers will vary. x4 8x3y 24x2y2 32xy3 16y4 (b) 328,440 15. 720 13. (a) 330 17. 1 15 16. 108,864 11. (b) 720,720 3.908 1010 Cumulative Test for Chapters 7β9 (page 720),, 22. 19. 20., 1 11 3, 4, 2 1 13 Jogging shoes: $358.48 million Walking shoes: $167.17 million 5, 4 1, 1 1 9 7 5 25. (a) ... |
sequence, find the differences of consecutive terms of the sequence of perfect cubes. Then find the differences of consecutive terms of this sequence. (c) 12, 18, 24, 30, 36, 42, 48; (d) To obtain the arithmetic sequence, find the third sequence obtained by taking differences of consecutive terms in consecutive sequen... |
152 2 β1 β1 β2 3537 74 53. (c) 35 8 (b) 4 (c) 8 (b) 31.0 51. 0.1003, 1054 feet 22 33.69; 56.31 49. 55. 57. True. The inclination of a line is related to its slope by m tan., then the angle is in the second quadrant, where the tangent function is negative. If the angle is greater than but less than 2 59. (a) d 4 m2 1 An... |
c 0, 0 3 21 β6 β5 β4 β3 β3 β4 333200_10a_AN.qxd 12/9/05 2:42 PM Page A188 A188 Answers to Odd-Numbered Exercises and Tests 15. Vertex: Focus: Directrix: 0, 0 0, 3 2 y 3 2 17. Vertex: Focus: Directrix: 1, 2 13 β2 β1 1 2 3 4 5 x β3 β 19. Vertex: Focus: Directrix: 2, 2 2, 3 y 1 1, 1 1, 2 21. Vertex: Focus: Directrix 321 ... |
23.67, C 121.33, c 14.89 C 89, a 1.93, b 2.33 A 16.39, B 23.77, C 139.84 B 24.62, C 90.38, a 10.88 73. 77. 79. 83. 85. 87. 89. 1 2, 5 3, Β±2 β10 2 Section 10.3 (page 750) 29. 35. 41. x2 3 2 y x2 4y x 32 y 1 31. 37. β4 x2 6y y2 8x 43. y2 8x 33. y2 9x 39. y2 4x 4 Vocabulary Check (page 750) 1. ellipse; foci 3. minor axis... |
23. Ellipse Center: Vertices: Foci: 3, 1 3, 7, 3, 5 3, 1 Β± 26 6 3 Eccentricity: y 8 4 2 β10 β8 β4 β2 2 4 x 25. Ellipse β6 y Center: Vertices: Foci: 3, 5 2, 3, 5 9, 5 2 2 3 Β± 33, 5 2 3 2 Eccentricity: y 3 2 β3 β2 β1 x 1 β1 β4 6 4 2 β2 β6 β8 2 4 6 10 x 29. Ellipse 2, 1 Center: 7 3, 1 3, 1, 5 Vertices: 15, 1 15, 1, 26 34... |
se. The 5 degree of y is 4, not 2. 69. (a) A a20 a (b) x2 196 y 2 36 1 (c) a 8 9 10 11 12 13 A 301.6 311.0 314.2 311.0 301.6 285.9 a 10, circle (d) 350 0 0 20 49. x2 48 x 22 4 y 42 64 y 22 1 1 1 The shape of an ellipse with a maximum area is a a 10 circle. The maximum area is found when so the equa(verified in part c) ... |
3 15. y2 x 17. x 12 6 y 1 6 yβ² y 2 xβ² β 6 β 4 x 2 yβ² y 6 4 2 β2 β 4 β4 2 4 x 41. xβ² β2 7 37. (a) Hyperbola (b) (c) y 6x Β± 36x2 20x2 4x 22 10 β9 6 β6 9 39. (a) Parabola (b) y 4x 1 Β± 4x 12 16x2 5x 3 8 (c) 2 β4 y 6 43. y 4 3 1 β6 β4 β2 2 4 6 x β 4 β3 β2 β1 1 3 4 x β6 β2 β3 β 4 2 47. 49. 0, 8, 12, 8 55. No solution 8, 12 ... |
Tests A193 Section 10.6 (page 776) 7. (a) Vocabulary Check (page 776) 1. plane curve; parametric; parameter 2. orientation 3. eliminating the parameter y 4 3 2 1 1. (a) (bc) y 3 x2 The graph of the rectangular equation shows the entire parabola rather than just the right half. The graph of the rectangular equation con... |
t 2 1 x t, y 1 t (b) 37. (a) 39. (a) 41. (a) 43. (a) 45. 34 x t 2, y 3t 4 (b) x t 2, y t 2 4t 4 (b) x t 2, y 1 x t 2, y t 2 4t 5 t 2 47. 6 0 β6 51. 51 6 β6 55. d 18 6 4 β4, 49. 0 0 β6 53. b 4 β4 2, 2 Domain: Range: 1, 1 Domain: Range:, 57. (a) 100 Maximum height: 90.7 feet Range: 209.6 feet Maximum height: 136.1 feet ... |
0 2, 8.64, 2, 0.78 2 2 2 0, 3 11. 2, 9. 15. 1.1340, 2.2280 22, 10.99, 22, 7.85 2, 2 6, 19. 17. 13. 2, 5 25. 4 7, 0.8571 4 6, 29. r 4 csc 33. r 3 39. r 35. 2 3 cos sin 313, 0.9828 23. 21. 27. 31. 37. 5, 2.2143 13, 5.6952 17 6, 0.4900 r 10 sec 41. r2 16 sec csc 32 csc 2 4 1 cos or r 4 1 cos r a 47. 3x y 0 y 4 57. x2 y 2... |
. For example: 3, 6, 4, 3 Points: Distance: 2.053 Points: Distance: 2.053 3, 76, 4, 43 77. 79. 2 log6 x log6 z log6 3 log6 y x ln x 2 lnx 4 3y 8 2, 3, 3 7, 88 2, 3 log7 81. 83. 35, 8 89. 93. Collinear 5 87. 85. 91. Not collinear ln xx 2 333200_10b_AN.qxd 12/9/05 2:43 PM Page A196 A196 Answers to Odd-Numbered Exercises ... |
For a graph to have polar axis symmetry, replace r,. (b) r, 59. (a) r, or by 3Ο 2 3Ο 2 Upper half of circle Lower half of circle (c) Ο 2 (d 3Ο 2 3Ο 2 Full circle Left half of circle 61. Answers will vary. 63. (a) r 2 2 2 sin cos (b) r 2 cos (c) 65. (a) r 2 sin (d) r 2 cos Ο 2 (b 3Ο 2 k 0, k 1, k 2, k 3, circle convex ... |
Ο 2 Ο 23. Ellipse Ο β4 27. Ellipse 6 3 β7 33. r 37. r 41. r 45. r 1 1 cos 2 1 2 cos 10 1 cos 20 3 2 cos 35. r 1 2 sin 39. r 43. r 47. r 2 1 sin 10 3 2 cos 9 4 5 sin 49. Answers will vary. r 9.5929 107 51. 1 0.0167 cos 9.4354 107 9.7558 107 Perihelion: Aphelion: r 1.0820 108 1 0.0068 cos miles miles 1.0747 108 1.0894 10... |
. 4 radian, 45 3. 1.1071 radians, 63.43 5. 0.4424 radian, 25.35 7. 0.6588 radian, 37.75 9. 22 11. Hyperbola 13. y 2 16x 15. y 22 12 43 5 x β4 β3 β2 β1 β2 β 3 17. 21. y 2x 2; 1, 0 x 22 y2 21 25 y 1 19. 86 meters x 22 4 y 23. y 12 1 35. Center: 3, 5 7, 5, 1, 5 3 Β± 25, 5 Vertices: Foci: Asymptotes: y 5 Β± 1 2 x 3 37. Cente... |
AM Page A200 A200 Answers to Odd-Numbered Exercises and Tests 53. t x y 3 11 2 8 1 5 0 2 19 15 11 69. 75. 81. 85. 3 2 1, 2 213, 0.9828 r2 10 csc 2 x2 y2 3x 71., 32 2 32 2 r 7 79. 77. x2 y 2 25 83. x2 y2 y23 87. 73. 2, 2 r 6 sin y 20 16 12 4 x 8 12 β 12 β 8 β 4 β 4 β 8 55. (a 57. (a 2x (b) 59. (ab) (b) y 4x x2 y 2 36 6... |
111. r 7978.81 1 0.937 cos ; 11,011.87 miles 113. False. When classifying an equation of the form Ax2 Bxy Cy2 Dx Ey F 0, its graph can be determined by its discriminant. For a graph to be a parabola, its discriminant, must equal zero. So, if C 115. False. The following are two sets of parametric equations B2 4AC, A th... |
is failure to meet the βbudget variance test.β $37,335 $37,640 $305 < $500 0.05$37,640 $1882 Because the difference between the actual expenses and the budget is less than of the budgeted amount, there is compliance with the βbudget variance test.β and less than $500 5% 65. (a) (e) 2 1. (a) 5, 1, 2 2, 2 (b) 0, 5, 1, 2... |
2 (d) $236.4 (s92.2 $195.6 $590.9 $1253.2 $1788. Year and 4 are the terms; 7 is the coefficient. 3 are the terms; and 8 are the 1 are the terms; 4 and are the coefficients. 2 6 0 (b) 0 (b) 14 2 y β₯ 6 67. 71. 73. 75. 69. x 5 β€ 3 326 351 25 miles 7x 3x2, 8x, and 11 coefficients. 4x3, x2, and 5 81. (a) is undefined. 77. 1... |
65. (a) 6x2x (b) 18z z2 67. (a) 2x 32x 2 (b) 71. (a) 2x (b) 4y 342 13x 1 (b) 69. (a) 73. (a) 75 11 81. 185x 77. 83. 5 > 32 22 2 2 87. 912 89. 532 79. 85. 91. 2 35 3 21613 93. 8134 99. (a) 3 (b) 3x 12 101. (a) 2 42 (b) 82x 103. 95. 2 x 97.57 seconds 105. (a.93 5.48 7.67 9.53 11.08 12.32 8 9 10 11 12 13.29 14.00 14.50 1... |
) (b) 2 3.077 1010 (b) 39.791 53. (a) (b) 57. (a) 7.550 (b) 200,000 4 (b) (b) 27 8 1 8 n; an; a0 2. descending 1. 3. monomial; binomial; trinomial 4. like terms 5. First terms; Outer terms; Inner terms; Last terms 6. factoring 7. completely factored 2. e 3. b 4. a 1. d 7. 11. (a) 2x3 4x2 3x 20 2x5 14x 1 5. f 15x 4 1 6.... |
. 99. 103. 107. 111. 115. 121. 125. 127. 129. 133. 137. 141. 145. 149. 153. 157. 3x3 2x 2 12z 8 4x 4 4x x 2 7x 12 x 4 x 2 1 4x 2 12x 9 x3 3x 2 3x 1 16x6 24x3 9 x2 2xy y2 6x 6y 9 1 4x2 3x 9 9x2 4 1.44x2 7.2x 9 79. 2x2 2x u4 16 83. 85. 3x 2 x2 25 x 5 89. 2xx 2 3 x 1x 6 x 3x 1 x 8 97. 2xx2 4x 10 1 2 3 x 9x 9 4x 1 4x 1 3u ... |
: P 22x 25,000 201. (a) 500r 2 1000r 500 203. (a) (b) r % 21 2 11, 11, 4, 4, 1, 1 12 2, 4 (b) $85,000 3% 4% 5001 r 2 $525.31 $530.45 $540.80 r 41 2 % 5% 5001 r 2 $546.01 $551.25 (c) The amount increases with increasing r. 205. (a) (b) V 4x3 88x2 468x x (cm) 1 2 3 cm3 V 384 616 720 207. 211. 44x 308 x 209. (a) 3x 2 8x (... |
87. Completely factor each polynomial in the numerator and in the denominator. Then conclude that there are no common factors. If n is odd, Appendix A.5 (page A56) Vocabulary Check (page A56) 2. solve ax b 0 1. equation 4. 6. quadratic equation 7. factoring; extracting square roots; completing the 3. identities; condi... |
1 2 2x 1 2x, x > 0 61. 2x3 2x2 5 x 112 1 xx h, h 0 67. 63. 1 x2 15 x7 2 x2 3x 1 3, x 0 11. 17. 21. 25. 29. 37. 41. 47. 51. 55. 59. 65. 69. 333200_App_AN.qxd 12/9/05 2:45 PM Page A207 75. 8, 16 77. 2 Β± 14 79. 1 Β± 32 2 81. 2 87. 1 Β± 83. 6 3 4, 8 85. 11 6, 11 6 89. 2 Β± 23 91. 5 Β± 89 4 93. 1 2, 1 95. 1 4, 3 4 97. 1 Β± 3 99... |
Β± 21 6 145. 151. Β±1 1, 2 147. Β± 3, Β±1 153. 50 155. 26 2, 5 167. 161. 0 163. 9 Β± 14 169. 1 171. 2, 3 2 175. 4, 5 177. 1 Β± 31 3 1 17 2 179. 3, 2 181. 3, 3 183. 3, 185. (a) 61.2 inches (b) Yes. The estimated height of a male with a 19-inch femur is 69.4 inches. (c) Height, x Female femur length Male femur length 60 70 80... |
A208 Answers to Odd-Numbered Exercises and Tests 45. 6 < x < 6 x β6 β4 β2 0 2 4 6 x 49. No solution 53. x β€ 3 2, x β₯ 3 β 3 2 β2 β1 1 0 4 < x < 5 57 43. 10.5 β€ x β€ 13.5 10.5 13.5 10 11 12 13 14 47. x < 2, x > 2 2 3 β3 51. 0 β1 β2 1 14 β€ x β€ 26 26 14 10 15 20 25 30 55. x β€ 5, x β₯ 11 11 5 10 15 β15 59. 0 β10 β5 x β€ 29 2,... |
ator and denominator separately. ax y x 9 ax y cannot be simplified. 9. 11. Divide out common factors, not common terms. 2x2 1 5x cannot be simplified. 13. To get rid of negative exponents: 1 a1 b1 1 a1 b1 ab ab ab b a. 15. Factor within grouping symbols before applying exponent to each factor. x2 5x12 xx 512 x12x 512 ... |
2n y2n 71. The two answers are equivalent and can be obtained by factoring. 1 10 2x 132 2x 13262x 1 10 2x 13212x 4 2x 1323x 1 2x 1323x 1 2x 152 1 6 1 60 1 60 4 60 1 15 2x 332x 1 2 5 (a) (b) 8 15 4 x32x 1 333200_Index_SE.qxd 12/8/05 11:32 AM Page A211 Index A Absolute value of a complex number, 470 inequality, solution ... |
nth partial sum, 657 nth term of, 654 recursion form, 654 sum of a finite, 656, 723 Associative Property of Addition for complex numbers, 164 for matrices, 590 for real numbers, A6 Associative Property of Multiplication for complex numbers, 164 for matrices, 590, 594 for real numbers, A6 Associative Property of scalar... |
variable term, A5 Coefficient matrix, 573 Cofactor(s) expanding by, 614 of a matrix, 613 Cofunction identities, 374 Collinear points, 13, 623 test for, 623 Column matrix, 572 Combination of n elements taken r at a time, 696 Combined variation, 107 Common difference, 653 Common formulas area, 7 circumference, 7 perimet... |
term, A5, A23 of variation, 105 Constraints, 552 Consumer surplus, 546 Continuous compounding, 223 Continuous function, 139, 771 Conversions between degrees and radians, 286 Convex limaçon, 789 Coordinate(s), 2 polar, 779 Coordinate axes, reflection in, 76 Coordinate conversion, 780 Coordinate system, polar, 779 Corre... |
, 447 length of, 447 magnitude, 447 terminal point, 447 Direction angle of a vector, 453 Directly proportional, 105 to the nth power, 106 Directrix of a parabola, 736 Discrete mathematics, 41 Discriminant, 767 classification of conics by, 767 Distance between a point and a line, 730, 806 between two points in the plane... |
of, 33 two-point form, 29, 33, 624 linear, 16 in one variable, A46 in two variables, 25 parametric, 771 position, 525 quadratic, 16, A49 second-degree polynomial, A49 solution of, 14, A46 solution point, 14 system of, 496 in two variables, 14 Equilibrium point, 514, 546 Equivalent equations, A47 generating, A47 expres... |
ite series, 647 First differences, 680 Fixed cost, 31 Fixed point, 397 Focal chord latus rectum, 738 of a parabola, 738 Focus (foci) of an ellipse, 744 of a hyperbola, 753 of a parabola, 736 FOIL Method, A24 Formula(s) change-of-base, 239 for compound interest, 224 double-angle, 407, 425 half-angle, 410 Heronβs Area, 4... |
of, 40, 47 rational, 184 reciprocal, 68 secant, 295, 301 sine, 295, 301 square root, 68 squaring, 67 step, 69 sum of, 84 summary of terminology, 47 tangent, 295, 301 transcendental, 218 trigonometric, 295, 301, 312 undefined, 47 value of, 42, 47 Vertical Line Test, 55 zero of, 56 Fundamental Counting Principle, 692 Fu... |
izontal shrink, 78 of a trigonometric function, 324 Horizontal stretch, 78 of a trigonometric function, 324 Horizontal translation of a trigonometric function, 325 Human memory model, 235 Hyperbola, 185, 753, 793 asymptotes of, 755 branches of, 753 center of, 753 classifying by discriminant, 767 by general equation, 75... |
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