SOLUTIONS MANUAL
For
C ALCULUS WITH A PPLICATIONS ,
B RIEF V ERSION
TWELFTH EDITION
By
Margaret L. Lial
Raymond N. Greenwell
Nathan P. Ritchey
Part 2: Instructor's Manual: Page 2-70
Part 1: Solutions Manual: Page 71-1126
, Part 2
Complete Instructor Answers
Answers to selected writing exercises are provided.
Answers to Prerequisite Skills Diagnostic Test
1. 20% 2. 3. x + y = 75 4. s Ú 4p 5. - (Sec. R.4) 6. - (Sec. R.4) 7. 1-2, 54 (Sec. R.5)
8. x … -3 (Sec. R.5) 9. y Ú - (Sec. R.5) 10. p 7 (Sec. R.5) 11. -y 2 + 4y - 6 (Sec. R.1)
12. x 3 - x 2 + x + 3 (Sec. R.1) 13. a2 - 4ab + 4b2 (Sec. R.1) 14. 3pq11 + 2p + 3q2 (Sec. R.2)
15. 13x + 521x - 22 (Sec. R.2) 16. 1a - 62/ 1a + 22 (Sec. R.3) 17. 1x 2 + 5x - 22/ 3x1x - 121x + 124 (Sec. R.3)
18. 1-2 ± 172/ 3 (Sec. R.4) 19. 1-∞, -32 ∪ 31, ∞2 (Sec. R.5) 20. x 6y / 4 (Sec. R.6) 21. p2q2 (Sec. R.6)
22. 1m - k2/ 1km2 (Sec. R.6) 23. 1x 2 + 12-1/213x 2 + x + 52 (Sec. R.6) 24. 4b2 (Sec. R.7) 25. 14 + 2102/ 3 (Sec. R.7)
26. y - 5 (Sec. R.7)
Chapter R Algebra Reference
Exercises R.1 (page R-5–R-6) For exercises . . . 1–8 9, 10 11–16 17–24 25–28
Refer to example . . . 2 3 4 5 6
1. -x 2 + x + 9 2. -6y 2 + 3y + 10 3. z 2 + z + 2
4. t 2 + t + 5. -16q2 + 4q + 6 6. 9r 2 - 4r + 19 7. -0.327x 2 - 2.805x - 1.458
8. 0.8r 2 + 3.6r - 1.5 9. -18m3 - 27m2 + 9m 10. -12x 4 + 30x 2 + 36x 11. 9t 2 + 9ty - 10y 2
12. 18k 2 - 7kq - q2 13. 4 - 9x 2 14. 36m2 - 25 15. y 2 + yz + z 2
16. r 2 - rs - s 2 17. 27p3 - 1 18. 15p3 + 13p2 - 10p - 8 19. 8m3 + 1
20. 12k 4 + 21k 3 - 5k 2 + 3k + 2 21. 3x 2 + xy + 2xz - 2y 2 - 3yz - z 2 22. 2r 2 + 2rs - 5rt - 4s 2 + 8st - 3t 2
23. x 3 + 6x 2 + 11x + 6 24. x 3 - 2x 2 - 5x + 6 25. x 2 + 4x + 4 26. 4a2 - 16ab + 16b2
27. x 3 - 6x 2y + 12xy 2 - 8y 3 28. 27x 3 + 27x 2y + 9xy 2 + y 3
Exercises R.2 (page R-9) For exercises . . . 1–4 5–15 16–20 21–32
Refer to example . . . 1 2,3 3, 2nd CAUTION 4
1. 7a21a + 22 2. 3y1y 2 + 8y + 32 3. 13p2q1p2q - 3p + 2q2
4. 10m216m2 - 12mn + 5n22 5. 1m + 221m - 72 6. 1x + 521x - 12 7. 1z + 421z + 52 8. 1b - 721b - 12
9. 1a - 5b21a - b2 10. 1s - 5t21s + 7t2 11. 1y - 7z21y + 3z2 12. 13x + 721x - 12 13. 13a + 721a + 12
14. 15y + 2213y - 12 15. 17m + 2n213m + n2 16. 61a - 1021a + 22 17. 3m1m + 321m + 12 18. 212a + 321a + 12
19. 2a214a - b213a + 2b2 20. 12x 21x - y212x + 5y2 21. 1x + 821x - 82 22. 13m + 5213m - 52
23. 101x + 421x - 42 24. Prime 25. 1z + 7y22 26. 1s - 5t22 27. 13p - 422 28. 1a - 621a2 + 6a + 362
29. 13r - 4s219r 2 + 12rs + 16s 22 30. 31m + 521m2 - 5m + 252 31. 1x - y21x + y21x 2 + y 22
32. 12a - 3b212a + 3b214a2 + 9b22
Exercises R.3 (page R-12) For exercises . . . 1–12 13–38
Refer to example . . . 1 2
1. v / 7 2. 5p / 2 3. 4. t + 22 5. x - 2 6. 41y + 22 7. 1m - 22/ 1m + 32
8. 1r + 22/ 1r + 42 9. 31x - 12/ 1x - 22 10. 1z - 32/ 1z + 22 11. 1m2 + 42/ 4 12. 12y + 12/ 1y + 12 13. 3k / 5
14. 25p 15. c2 16. 2 17. 18. 19. 21a + 42/ 1a - 32 20. r + 22 21. 1k - 22/ 1k + 32
22. 1m + 62/ 1m + 32 23. 1m - 32/ 12m - 32 24. 212n - 12/ 13n - 52 25. 1 26. 16 + p2/ 12p2 27. 112 - 15y2/ 110y2
28. m2 29. 13m - 22/ 3m1m - 124 30. 1r - 62/ 3r12r + 324 31. a - 124 32. k - 224
33. 17x + 12/ 31x - 221x + 321x + 124 34. 1y 2 + 12/ 31y + 321y + 121y - 124 35. k1k - 132/ 312k - 121k + 221k - 324
36. m13m - 192/ 313m - 221m + 321m - 424 37. 14a + 12/ 3a1a + 224 38. 15x 2 + 4x - 42/ 3x1x - 121x + 124
Exercises R.4 (page R-17) For exercises . . . 1–8 9–26 27–37
Refer to example . . . 2 3–5 6,7
1. -12 2. 3. 12 4. - 5. - 6. - 7. 4 8. - 9. -3, -2
10. -1, 3 11. 7 12. -2, 13. -, 14. 2, 5 15. -3, 3 16. -4, 17. 0, 4
18. 15 + 2132/ 6 ≈ 1.434, 15 - 2132/ 6 ≈ 0.232 19. 12 + 2102/ 2 ≈ 2.581, 12 - 2102/ 2 ≈ -0.581
20. 1-1 + 252/ 2 ≈ 0.618, 1-1 - 252/ 2 ≈ -1.618 21. 5 + 25 ≈ 7.236, 5 - 25 ≈ 2.764
22. 14 + 262/ 5 ≈ 1.290, 14 - 262/ 5 ≈ 0.310 23. 1, 24. No real number solutions
25. 1-1 + 2732/ 6 ≈ 1.257, 1-1 - 2732/ 6 ≈ -1.591 26. -1, 0 27. 3 28. 12 29. - 30. 6 31. 3 32. -
33. 34. 1 35. 2 36. No solution 37. No solution
Exercises R.5 (page R-22) For exercises . . . 1–14 15–26 27–38 39–42 43–54
Refer to example . . . Figure 1, Example 2 2 3 4 5–7
1. 1-∞, 42
0 4
2. 3-3, ∞2 3. 31, 22
–3 0 0 1 2
A-9
Copyright © 2022 Pearson Education, Inc.
,A-10 Complete Instructor Answers
4. 3-2, 34 5. 1-∞, -92 6. 36, ∞2
–2 0 3 –9 0 0 6
7. -7 … x … -3 8. 4 … x 6 10 9. x … -1 10. x 7 3 11. -2 … x 6 6 12. 0 6 x 6 8 13. x … -4 or x Ú 4
14. x 6 0 or x Ú 3 15. 1-∞, 24 16. 1-∞, 12
0 2 0 1
17. 13, ∞2 18. 1-∞, 14 19. , ∞2
0 3 0 1 01 1
5
20. , ∞2 21. 1-4, 62 22. , 44
0 1 1 –4 0 6 0 7 4
3 3
23. 3-5, 32 24. 3-1, 24 25. 3-, ∞2
–5 0 3 –1 0 2 – 17 0
7
26. 1-∞, 27. 1-5, 32
0 50 –5 0 3
9
28. 1-∞, -64 ∪ 31, ∞2 29. 11, 22
–6 0 1 0 1 2
30. 1-∞, -42 ∪ , ∞2 31. 1-∞, -42 ∪ 14, ∞2
–4 01 –4 0 4
2
32. 3-, 54 33. 1-∞, -14 ∪ 35, ∞2
–3 0 5 –1 0 5
2
34. 3-, 35. 1-∞, -12 ∪ , ∞2
–1 0 2 –1 01
2 5 3
36. 1-∞, -22 ∪ , ∞2 37. 1-∞, -34 ∪ 33, ∞2
–2 0 5 –3 0 3
3
38. 1-∞, 02 ∪ 116, ∞2 39. 3-2, 04 ∪ 32, ∞2
0 16 –2 0 2
40. 1-∞, -44 ∪ 3-3, 04 41. 1-∞, 02 ∪ 11, 62
–4 –3 0 0 1 6
42. 1-1, 02 ∪ 14, ∞2 43. 1-5, 34 44. 1-∞, -12 ∪ 11, ∞2 45. 1-∞, -22
–1 0 4
46. 1-2, 47. 3-8, 52 48. 1-∞, - ∪ 3-, ∞2 49. 32, 32 50. 1-∞, -12 51. 1-2, 04 ∪ 13, ∞2
52. 1-4, -22 ∪ 10, 22 53. 11, 54. 1-∞, -22 ∪ 1-2, 22 ∪ 34, ∞2
Exercises R.6 (page R-26) For exercises . . . 1–8 9–26 27–36 37–50 51–56
Refer to example . . . 1 2 3,4 5 6
1. 2. 3. 1 4. 1 5. - 6. 7. 36 8.
9. 10. 85 11. 8 12. 7 13. x 2 14. 1 15. 8k 3 16. z 72 17. x y 32 18. m 19. a3b6
20. c 6d 42 21. 1a + b2/ 1ab2 22. 11 - ab22/ b2 23. 21m - n2/ 3mn1m + n224 24. 13n2 + 4m2/ 1mn22
25. xy / 1y - x2 26. y xy - 122 27. 11 28. 3 29. 4 30. -25 31. 32. 33. 34. 35.
36. 37. 9 38. 3 39. 64 40. 1 41. x 4 / y 4 42. b / a3 43. r 44. 123 / y 8 45. 3k 3/ 46. p22
47. a2/3b2 48. y x 1/6z 5/42 49. h1/3t 1/5 / k 2/5 50. m3p / n 51. 3x1x 2 + 3x221x 2 - 52 52. 6x1x 3 + 721-2x 3 - 5x + 72
53. 5x1x 2 - 12-1/21x 2 + 12 54. 316x + 22-1/2127x + 52 55. 12x + 521x 2 - 42-1/214x 2 + 5x - 82
56. 14x 2 + 1212x - 12-1/2136x 2 - 16x + 12
Exercises R.7 (page R-30) For exercises . . . 1–22 23–26 27–40 41–44
Refer to example . . . 1,2 3 4 5
1. 5 2. 6 3. -5 4. 5 22 5. 20 25 6. 4y 2 22y 7. 9 8. 8
3 3 3
9. 7 22 10. 9 23 11. 9 27 12. -2 27 13. 5 2 2 14. 3 2 5 15. xyz 2 22x 16. 4r 3s 4t 6 210rs 17. 4xy 2z 3 2 2y 2
18. x yz 2y z 19. ab 2ab1b - 2a + b 2 20. p 2pq1pq - q + p 2 21. 2a 22. b 2b 23. 4 - x
2 2 4 3 3 2 3 2 4 2 6 5 2 4
24. 3y + 5 25. Cannot be simplified 26. Cannot be simplified 27. 5 28. 29. - 30. 22
31. -311 + 222 32. -512 + 262/ 2 33. 312 - 222 34. 15 - 2102/ 3 35. 1 2r + 232/ 1r - 32
36. 51 2m + 252/ 1m - 52 37. 2y + 25 38. 1z + 25z - 2z - 252/ 1z - 52 39. -2x - 2 2x1x + 12 - 1
40. 3p2 + p + 2 2p1p2 - 12 - 14/ 1-p2 + p + 12 41. - - 2224 42. + 232
43. -x - 2 2x1x + 12 + 14 44. p + 2p1p - 224
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, Complete Instructor Answers A-11
Chapter 1 Linear Functions
For exercises . . . 5–8 9–12 17,33,34 18,35–38 19–21 22,31 23–28 29,30 32 49–64 65–79
Exercises 1.1 (page 13–17)
Refer to example . . . 1 3 8 9 4 7 5 2 6 11,12 10,13
W1. -3 W2. y = -2x - 13
W3. y = x +
W4. y = x -
1. False 2. True 3. False 4. False 5. 6. - 7. Not defined 8. 0 9. 1 10. 3 11. 12. -
13. Not defined 14. 0 15. 0 16. 0 17. 2 18. - 19. y = -2x + 5 20. y = -x + 6 21. y = -7 22. x = -8
23. y = - x + 24. y = -x + 7 25. y = 6x - 26. y = x + 27. x = -8 28. y = 3
29. x + 2y = -6 30. 2x - y = -4 31. x = -6 32. y = 7 33. 3x + 2y = 0 34. 2x - y = 9 35. x - y = 7
36. 3x + 2y = 6 37. 5x - y = -4 38. 3x + 6y = -2 39. No 40. (a) k = - (b) k = - 43. (a) 44. (f)
45. -4 46. 48. (a) y = - 1b / a2x + b (b) a and b
49. 50. y 51. 52. y
5 y = 4x + 5
6
y = –6x + 12
1
0 x 0 6 x
–1
53. 54. y 55. y 56. y
3x – y = –9
9
0 x 2 5y + 6x = 11
3
0 x 0 4 x
3
3y – 7x = –21
–7
57. 58. y 59. 60. y
0 x
x=4
0 4 x
y+8=0
–8
61. 62. y 63. 64. y
y = –5x 3
1
0 x
0 5 x
3x – 5y = 0
–5
65. (a) 12,000; y = 12,000x + 3000 (b) 8 years 1 month 66. (a) 0.9; each additional cupcake costs $0.90
(b) y = 0.9x + 36 (c) $198
67. (a) y Yes (b) y = 598t + 25,522; the slope indicates that the annual cost of tuition and fees at
40,000
private four-year colleges is increasing by about $598 per year. (c) The year 2035
Tuition and fees
35,000 is too far in the future to rely on this equation to predict costs; too many other factors
30,000 may influence these costs by then.
25,000 t
8 10 12 14 16 18 20
Years after 2000
68. (a) y The number of subscribers appears to be increasing at a nearly linear rate.
400 (b) y = 15.729t + 138.67 (c) y = 15.688t + 139.42
Subscribers
300
(e) 390.33 million; 390.43 million
200
100
0 t
0 5 10 15 20
Years after 2000
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