Precalculus With Limits, Answers To Section 8.1 1
333202CB08 AN.qxd4/13/065:32 PMPage 1Precalculus with Limits, Answers to Section 8.11 Chapter 8122. 12Section 8.1 (page 582)Vocabulary Check (page 582)1.4.7.9.matrix2. square3. main diagonalrow; column5. augmented 6. coefficientrow-equivalent8. reduced row-echelon formGauss-Jordan elimination2 16324 3429 1002 32 32124 7 4623. Add 5 times Row 2 to Row 1.24. Add 3 times Row 1 to Row 2.25. Interchange Row 1 and Row 2.Add 4 times new Row 1 to Row 3.26. Add 2 times Row 1 to Row 2.1. 1 24. 3 47. 14 19. 52 110. 7311. 19712. 9013.15.Copyright Houghton Mifflin Company. All rights reserved.16.17.18.2. 1 45. 2 2 3310 31 80 1 578.5 158 311Add 5 times Row 1 to Row 3. 4 9 8 3820 1310 20 5x 2y 714. 7x 5y 08x 3y 2 2x 3y 4 5z 12y 2z 76x 3y 2 2x4x 5y z 18 11x 6z 253x 8y 29 6x 2y z 5w x 7z 3w4x y 10z 6w8y z 11w 25 7 23 21121. 00145 23 20 120.4 2 83 3 6114 101 526503204 164 123(b) 0 5 100 5 101 2 3(d) 0 1 20 0 0 1 0 1(e) 0 120 00The matrix is in reduced row-echelon form.7 11 5150 20 20228. (a)(b)(c)0 19 3 4 3 4171 57 1 151 0010 1(e)(f )0190 00 340 0The matrix is in reduced row-echelon form.29. Reduced row-echelon form1502(d)0 190 3431. Not in row-echelon form 0 10 4 10432 1 221512327. (a) 0 5 1031 1123(c) 0 5 1000030. Reduced row-echelon form9x 12y 3z 2x 18y 5z 2wx 7y 8z3x 2z1019. 206 510 82 25 512 2403. 3 16. 2 3 32. Row-echelon form133. 0011002150 1134. 00 1 2135 1135. 00 110 160130136. 00 310010 720137. 00010001 210138. 00300010 1040.00 010000100001 1001022 6 39. 100020000100001041. 1001321612 42.
333202CB08 AN.qxd4/13/065:32 PMPage 2Precalculus with Limits, Answers to Section 8.1290. (a) y 0.188t 2 2.75t 12.9(b) 28(Continued)43. x 2y 4y 3 2, 3 44. x 5y 0y 1 5, 1 45. x y 2z 4y z 2z 246. 8, 0, 2 x 2y 2z 1y z 9z 3 31, 12, 3 47. 3, 4 48. 6, 10 49. 4, 10, 4 50. 5, 3, 0 51. 3, 2 52. 1, 3 53. 5, 6 54. 9, 13 55. 1, 4 56. 2, 1 57. Inconsistent58. 3a 5, a 59. 4, 3, 2 60. 8, 10, 6 61. 7, 3, 4 62. 6, 8, 2 63. 4, 3, 6 64. 5, 1, 2 180(c) 8.9 million. This model is not very accurate whencompared with the actual value of 6.3 million.(d) 24.3 million; answers will vary.91. (a) x1 s, x 2 t, x 3 600 s, x 4 s t,x 5 500 t, x6 s, x 7 t(b) x 1 0, x 2 0, x 3 600, x 4 0, x 5 500,x6 0, x 7 0(c) x1 0, x 2 500, x 3 600, x 4 500,x 5 1000, x6 0, x 7 50067. 4 5b 4a, 2 3b 3a, b, a 92. (a) x1 500 s t, x 2 200 s t, x3 s,x4 350 t, x5 t(b) x1 100, x2 200, x3 50, x4 0, x5 350(c) x1 150, x2 150, x3 0, x4 0, x5 35068. 3b 96a 100, b, 52a 54, a 93. False. It is a 2 4 matrix.66. 32a 32, 13a 13, a 65. 2a 1, 3a 2, a 69. Inconsistent70. Inconsistent71. 0, 2 4a, a 72. 5a, a, 3 73. 1, 0, 4, 2 74. 1, 1, 3, 1 75. 2a, a, a, 0 76. 2a, a, a, a 77. Yes; 1, 1, 3 1381. 013274001 78. No 41 32 , 02 031079. No121 3 1280. No 82. I1 2, I2 3, I3 1Copyright Houghton Mifflin Company. All rights reserved.783.4x2132 x 1 2 x 1 x 1 x 1 x 1 22648x 284. x 1 2 x 1 x 1 x 1 x 1 285. 150,000 at 7% 750,000 at 8% 600,000 at 10%86. 100,000 at 9% 250,000 at 10% 150,000 at 12%87. y x 2 2x 588. y x2 2x 889. (a) y 0.004x 2 0.367x 5(b) 1894. False. A matrix is in reduced row-echelon form if (1) allrows consisting entirely of zeros occur at the bottom ofthe matrix, (2) for each row that does not consist entirelyof zeros, the first nonzero entry is 1, (3) for two successive nonzero rows, the leading 1 in the higher row isfarther to the left than the leading 1 in the lower row, and(4) every column that has a leading 1 has zeros in everyposition above and below its leading 1.95. False. Gaussian elimination reduces a matrix until a rowechelon form is obtained; Gauss-Jordan eliminationreduces a matrix until a reduced row-echelon form isobtained.96. Answers will vary. For example:x y 7z 1x 2y 11z 02x y 10z 3 97. (a) There exists a row with all zeros except for the entryin the last column.(b) There are fewer rows with nonzero entries than thereare variables and no rows as in (a).98. Interchange two rows.Multiply a row by a nonzero constant.Add a multiple of a row to another row.99. They are the same.01200(c) 13 feet, 104 feet(d) 13.418 feet, 103.793 feet(e) The results are similar.100. A matrix in reduced row-echelon form has zeros abovethe leading 1s. A matrix in row-echelon form may haveany real numbers above the leading 1s.
333202CB08 AN.qxd4/13/065:32 PMPage 3Precalculus with Limits, Answers to Section 8.13104.(Continued)y101.10y88664422x 8 62468 2 4x246810 2 6 8105.y102.y432142x 8 6 4 2 2246x 2 1 18213456 2 3 4103.106.yy584634221Copyright Houghton Mifflin Company. All rights reserved. 2 1xx1 12342 246810
333202CB08 AN.qxd4/13/065:32 PMPage 4Precalculus with Limits, Answers to Section 8.2412. (a), (b), and (d) not possible9(c)6 3Section 8.2 (page 597) Vocabulary Check (page 597)1. equal5. (a) iii6. (a) ii2. scalars3. zero; O4. identity(b) iv(c) i (d) v(e) ii(b) iv(c) i(d) iii1. x 4, y 222. x 13, y 123. x 2, y 34. x 4, y 93 25. (a)17 1 1(d)8 19 0 9 20310 177. (a)1 2 3915 16 11(d)82 11 5(b) 244 1 5 1 55(b)3 4 Copyright Houghton Mifflin Company. All rights reserved.(c)12 61224 31 5 2 10 2 06 3 180(b)21 5 3 4(d)35 5 6 1211. (a), (b), and (d) not possible180 9(c) 3 12 0 366318(c)6 9 31215 495 615 53 10 40 39150 12(c) 44 20 52 (b) 02 2463329(c) (d) 3 3 12 3 533 2119. (a) 257 6 8 110 11(b) 4 3 1166 66 303(c) 33 60 3 44 1 23(d) 9 5 24 12 11 81515. 24 12 43217. 8919.8. (a)10. (a)(c) 3 336 69(d) 26. (a) (b) 1313. 36 516 223020 5 17.14311.571 220 1 104 3.739 13.249 0.362 623. 117 90 10226. 55 506 41646329. 1026 190 22 2.14310.286 1194 270140 40132. 0001000033. 0000000035. 7260 4142 1015137. 5164724.16. 19218. 6 23111 3132 8 1 440 4954951375 1686060 13222. 108 348 20 24 33005 721 2 13211225.75 2525279 20Order: 3 3Order: 3 3 725456072 4838787Order: 2 4 028. Not possibleOrder: 3 31012 52Order: 3 2 3Order: 3 2 92 7227. Not possible00 1072 220. 514. 2 331. 0034. 1212 10 59 1.58121. 4.2529.71330. 12136 2 7 1 252 3036. 298 452217 18038. Not possible
333202CB08 AN.qxd4/13/065:32 PMPage 5Precalculus with Limits, Answers to Section 8.25(b) B 3.50 6.00 The entries represent the profits per bushel of each crop.(c) BA 1037.50 1400 1012.50 The entries represent the profits from both crops ateach of the three outlets.(Continued)39. Not possible 41. (a) 061512(b) 42. (a) 12 123 (b) 3 15 0043. (a) 10 (b) 10 10044. (a) (b) 3 10004 224745. (a)8 178 1 1416 247. 45 48. 12 450.2028 53. (a) 54. (a) 52. (a)55. (a) 36 615 (c) 68 68 (c) 02 20 42630027 6 6 27 51 2158. (a) 10 13 660120 405 15,77063. 26,500 21,260 49. 43 11x14 0x2 1014(b) 48 (b) (b) (b)(b)x19x2 6x3 50(b)3 22 15x1 20x2 8x3 16 1(b)3 2x117x2 11x340 75125 110444(b) 5299227766 18,300 29,250 24,150 The entries represent the wholesale and retail values of theinventories at the three outlets. 23 76 23 3531 12 30160. 3084 (c) Not possible 1 262. 916,500 885,500 The entries represent the costs of the three models of theportable CD players at the two warehouses.(c) Not possiblex15 10x2 3 x1 4 1 x2 369 x1 13 3 x212 23 x193 1 x2 6 55 x317157. (a) 30 24(c) 2 31 4 26 411 1212 159.4 2 (b) 13 51. (a)156. (a) 118442 8 166 21014 06(b) 9046. (a) 12 Copyright Houghton Mifflin Company. All rights reserved. 249 42 417124 104284232 176520 2296(c)31 1412 1240. 3366125 10061. (a) A 100 175The entries represent the numbers of bushels of eachcrop that are shipped to each outlet. 0.4064. 0.280.320.150.530.320.150.170.68 P 2 gives the proportions of the voting population thatchanged parties or remained loyal to their parties from thefirst election to the third. 0.30065. P3 0.3080.3920.1750.4330.3920.1750.2170.6080.250P4 0.3150.4350.1880.3770.4350.1880.2480.5650.225P5 0.3140.4610.1940.3450.4610.1940.2670.5390.213P6 0.3110.4770.1970.3260.4770.1970.2800.5230.206P7 0.3080.4860.1980.3160.4860.1980.2880.5140.203P8 0.3050.4920.1990.3090.4920.1990.2920.508 Approaches the matrix0.2 0.2 0.20.3 0.3 0.30.5 0.5 0.5 18.10 15.4066. 29.80 25.40 59.20 50.80The entries represent the labor costs at each plant for eachsize of boat.
333202CB08 AN.qxd4/13/065:32 PMPage 6Precalculus with Limits, Answers to Section 8.2671. True. The sum of two matrices of different orders isundefined.(Continued)67. (a) Sales Profit (b) 464 447115624.5161731.2188The entries represent the total sales and profits for eachtype of milk.68. (a) Sales Profit(b) 1868.8035416162297394.44929858.4The entries represent the total sales and profits for eachtype of gasoline.69. (a) 2 0.5 3 (b) 120 lb 150 lb 473.5 588.5 The entries represent the total calories burned.694.321725.3610.4125.8870. (a) A: 451.8(b) 11.31187.76 29.69489.481248.12 9.79 24.96 683.911699.48B: 463.11217.45499.271273.08Each entry representsthe cost of a plan.57.86 143.78(c) A: 37.6598.9840.79 104.01 Copyright Houghton Mifflin Company. All rights reserved.56.99B: 38.5941.61 141.62101.45106.09 60.17(d) 39.1642.42 72. False. For most matrices, AB BA.73. Not possible 74. Not possible 75. Not possible76. 2 277. 2 278. Not possible79. 2 380. 2 381. AC BC 82. AB 3 0083. AB is a diagonal matrix whose entries are the products ofthe corresponding entries of A and B.A385. 8,02344388. 0, 9, 1 0 1 and i 1. i0 and i i.0 i 1 0 and i 1.0 1 10 I, the identity matrix.01 84. (a) A2 (b) B 2 2AB O and neither A nor B is O.A4149.53102.94108.17 00 2 3 1 386. ,4 25391. 7, 12 89. 4, 15i392. 1, 3 87. 0,90. 5 45, 237693. 3, 1 94. 4, 1
333202CB08 AN.qxd4/13/065:32 PMPage 7Precalculus with Limits, Answers to Section 8.37 247 10338. 29712 3Section 8.3 (page 608)Vocabulary Check (page 608)1. square3. nonsingular; singular2. inverse4. A 1B39. 42. 1–10. AB I and BA I11. 14. 33 19 4 7 120013 17. Does not exist12. 15. 1218. 45 15 6 52 21 16. 01 1 1 3525 21 111 19. Does not exist 4 31 3 213.121. 3320. Does not exist 1322.12 57 3 1 1212 30023. 3414 1401525.Copyright Houghton Mifflin Company. All rights reserved.27.29.31. 000010001400 15 17537 1395 20714 31 1.51.54.5 3.5 1100 12 4 80 5 2 41 31 9 4 6 26.1 32 4012100 12000 28. 102 13 30. 17 8 0 1.81 0.9033. 10 5510 2.72 3.63 41 5 4 29 2 18 2 20 18 1037.2001011010 76116594 5915597059 41. Does not exist44. 32 14360143811439143 46. 6, 3 47. 8, 6 48. 7, 4 49. 3, 8, 11 50. 1, 7, 9 51. 2, 1, 0, 0 52. 32, 13, 37, 15 53. 2, 2 54. 12, 13 55. No solution56. 6, 2 57. 4, 8 58. 12, 10 516 a 13 1916 , 16 a60. 5, 8, 2 1116 , a 62. 2a 1, 3a 2, a 65. 5, 0, 2, 3 68. 4000 in AAA-rated bonds 2000 in A-rated bonds 4000 in B-rated bonds 69. 9000 in AAA-rated bonds 1000 in A-rated bonds 2000 in B-rated bonds 70. 200,000 in AAA-rated bonds 100,000 in A-rated bonds 200,000 in B-rated bonds71. (a) I1 3 amperesI2 8 amperesI3 5 amperes 1.25 1.375 2.535. Does not exist27 10 16536. 174 72 4343.86167. 7000 in AAA-rated bonds 1000 in A-rated bonds 2000 in B-rated bonds32. Does not exist3.75034. 3.4583 14.160 59 126166. 6.21, 0.77, 2.67, 2.40 135 451101501 1 1340.5 6163. 7, 3, 2 64. 10, 3, 5 27 535 1 8.510 29 45. 5, 0 61.24. Does not exist 1821951959. 1, 3, 2 1720 3192 19 2 1 21103 10102 72. (a)(b) I1 2 amperesI2 3 amperesI3 5 amperes27a 561.2 27b3b 251a 5068(b) y 2.15t 167.7 (c) 195.65 million(d) The value is close to the estimate. (e) 200873. True. If B is the inverse of A, then AB I BA.74. True. If A and B are both square matrices and AB I n , itcan be shown that BA I n .75. Answers will vary.
333202CB08 AN.qxd4/13/065:32 PMPage 8Precalculus with Limits, Answers to Section 8.38(Continued)x 10 9 8 7 6 5 476. (a) Answers will vary.(b) A 1 Copyright Houghton Mifflin Company. All rights reserved.77. x 5 1a 1100.001a 220.0001a 33.0 . 0.1a nn00or x 9 78. 1 x 2x 2 179.02 ln 315ln 381. 26.512310.47290.51083. Answers will vary.480. 5 ln82.151 528.0471.618
333202CB08 AN.qxd4/13/065:32 PMPage 9Precalculus with Limits, Answers to Section 8.49Section 8.4 (page 616)Vocabulary Check (page 616)1. determinant3. cofactor2. minor4. expanding by cofactors1. 52. 83. 54. 116. 147. 08. 09. 612. 3413. 7214. 1815.5. 2711. 910. 011616.17. 0.00218. 0.02219. 4.84220. 11.21721. 022. 2010923. (a) M11 5, M12 2, M21 4, M22 3(b) C11 5, C12 2, C21 4, C22 324. (a) M11 2, M12 3, M21 0, M22 11(b) C11 2, C12 3, C21 0, C22 1125. (a) M11 4, M12 2, M21 1, M22 3(b) C11 4, C12 2, C21 1, C22 326. (a) M11 2, M12 7, M21 5, M22 6(b) C11 2, C12 7, C21 5, C22 627. (a) M11 3, M12 4, M13 1, M21 2, M22 2,M23 4, M31 4, M32 10, M33 8(b) C11 3, C12 4, C13 1, C21 2, C22 2,C23 4, C31 4, C32 10, C33 8Copyright Houghton Mifflin Company. All rights reserved.28. (a) M11 38, M12 8, M13 26, M21 4,M22 4, M23 2, M31 5, M32 5, M33 5(b) C11 38, C12 8, C13 26, C21 4,C22 4, C23 2, C31 5, C32 5, C33 529. (a) M11 30, M12 12, M13 11, M21 36,M22 26, M23 7, M31 4, M32 42, M33 12(b) C11 30, C12 12, C13 11, C21 36, C22 26,C23 7, C31 4, C32 42, C33 1230. (a) M11 36, M12 42, M13 85, M21 82,M22 12, M23 68, M31 24,M32 28, M33 51(b) C11 36, C12 42, C13 85, C21 82,C22 12, C23 68, C31 24, C32 28,C33 5131. (a) 75 (b) 7532. (a) 151(b) 15133. (a) 9634. (a) 650(b) 650(b) 96(b) 2(c) 200 3 (d) 662. (a) 0(b) 1(c) 24 510 (d) 063. (a) 8(b) 0(c) 414 1 (d) 064. (a) 17(b) 6(c) 14222065. (a) 217(b) 19 (c) 8766. (a) 23(b) 1 9(c) 544 10 116 1(d) 2367. (a) 2(b) 61(c) 10402330(d) 1268. (a) 0(b) 7 19 37(c) 8669–74. Answers will vary. 4 6 278. 2, 380. 3x2 3y281. e 5x82. e 2x83. 1 ln x84. x87. Answers will vary.88. (a) For an n n matrix n 2 with consecutive integerentries, the determinant appears to be 0.(b) Answers will vary.89. A square matrix is a square array of numbers. The determinant of a square matrix is a real number.90. Yes. 2A 8 A 8 5 4091. (a) Columns 2 and 3 of A were interchanged.A 115 B(b) Rows 1 and 3 of A were interchanged.A 40 B41. 942. 543. 5844. 245. 3046. 6647. 16848. 108 49. 050. 054. 22392. (a) Add 5 times Row 1 to Row 2.A 17 B(b) Add 2 times Row 2 to Row 1.A 11 B58. 744193. (a) Multiply Row 1 by 5.60. 48(d) 086. True. If a square matrix has two columns that are equal,then elementary column operations can be used to createa column with all zeros.40. 259. 410(d) 39985. True. If an entire row is zero, then each cofactor in theexpansion is multiplied by zero.39. 057. 336 77. 1, 436. (a) 116756. 105931579. 8uv 138. 352. 100 53. 1264 3976. 1, 337. 051. 412(d) 10275. 1, 435. (a) 170 (b) 17055. 0(b) 116761. (a) 3(b) Multiply Column 2 by 4 and Column 3 by 3.
333202CB08 AN.qxd4/13/065:32 PMPage 10Precalculus with Limits, Answers to Section 8.410102.(Continued)y(b) 1094. (a) 28(c) 12; Answers will vary.295. All real numbers x 4x 2296. All real numbers x97. All real numbers x such that 4 x 4 498. All real numbers x except x 6 699. All real numbers t such that t 1100. All real numbers s103. 104. 101.y12 421 1 43x4812 14106. 14 12Copyright Houghton Mifflin Company. All rights reserved.5612 105. Does not exist4 814 14161213 13153
333202CB08 AN.qxd4/13/065:32 PMPage 11Precalculus with Limits, Answers to Section 8.51150. 58 122 139 1 37 95 40 67 55 23 17 19 4788 88 14 21 11Section 8.5 (page 628)Vocabulary Check (page 628)51. HAPPY NEW YEAR1. Cramer’s Rule2. collinearx1 y1113. A x2 y24. cryptogram12x3 y315. uncoded; coded52. BRONCOS WIN SUPER BOWL53. CLASS IS CANCELED54. HAVE A GREAT WEEKEND2. 3, 5 1. 2, 2 3. Not possible 85, 8310 4. 7, 5 5.7. 1, 3, 2 8. 5, 8, 2 9. 2, 1, 1 10. 0, 3, 2 11. 0, 12, 12 12. 3, 1, 2 13. 1, 2, 1 14. Cramer’s Rule does not apply.32 307, 715. 716.33217. 1420. 5521.5222.6.18.25231223. 2819.33824.23225. y 165 or y 026. y 19 or y 327. y 3 or y 1128. y 6 or y 029. 250 square miles30. 3100 square feet31. Collinear32. Not collinear33. Not collinear34. Collinear35. Collinear36. Not collinear37. y 338. y 339. 3x 5y 040. x y 041. x 3y 5 042. 7x 6y 28 043. 2x 3y 8 0Copyright Houghton Mifflin Company. All rights reserved.44. 3x 2y 6 045. Uncoded: 20 18 15 , 21 2 12 , 5 0 9 , 14 0 18 , 9 22 5 , 18 0 3 , 9 20 25 Encoded: 52 10 27 49 3 34 49 13 27 94 22 54 1 1 7 0 12 9 121 41 5546. Uncoded: 16 12 5 , 1 19 14 4 0 , 13 15Encoded: 43 6 9 38 45 42 47 14 44 55 65 205 , 0 19 5 ,14 , 5 25 0 1316 10 49 9 1247. 6 35 69 11 20 17 6 16 58 46 79 6748. 13 19 10 1 33 77 3 2 144 1 9 5 25 47 4 1 949. 5 41 87 91 207 257 11 5 41 40 8084 76 177 22755. SEND PLANES56. RETURN AT DAWN57. MEET ME TONIGHT RON 3c 3b 5a 27,5473c 5b 9a 27,9885c 9b 17a 46,800(b) y 9.5t 2 201.5t 8965(c) 12,000(d) 200458. (a)08,000859. False. The denominator is the determinant of the coefficient matrix.60. True. If the determinant of the coefficient matrix is zero,then the solution of the system would result in division byzero, which is undefined.61. False. If the determinant of the coefficient matrix is zero,the system has either no solution or infinitely manysolutions.64. 5, 12 62. Answers will vary.63. 6, 4 65. 1, 0, 3 66. 2, 2, 5 67.68.yy166(0, 5)12(6, 4)482(203 , 0((0, 0)4(0, 8)(3, 4)(15, 0)x246Minimum at 0, 0 : 0Maximum at 6, 4 : 52x4812Minimum at 3, 4 : 46No maximum
333202CB08 AN.qxd4/13/065:32 PMPage 12Precalculus with Limits, Answers to Review Exercises121. 3 15.7.8. 13. 3 1054 21.210311 Copyright Houghton Mifflin Company. All rights reserved. 110. 00x 2y 3z 9y 2z 2z 0 5, 2, 0 12. 14.x 5y 4z 1y 2z 3z 4 40, 5, 4 21041070 x 3y 9z 4y z 10z 2 38, 8, 2 x 8y 2y z 7z 1 50, 6, 1 16. 9, 4 717. 15, 10 19. 5, 2, 6 20. 12, 13, 1 35, 12 2a 32, 2a 1, a 22. Inconsistent 31 5 1342 , 14 , 84 24. Inconsistent25. 2, 3, 3 27. 2, 3, 1 28. 6, 2, 0 29. 2, 6, 10, 3 31. x 12, y 730. Inconsistent32. x 8, y 033. x 1, y 11 1835. (a)15 138 8(c)12 2034. x 12, y 2 936. (a) 1326 164232 95 12 3 7 28(d) 39 29 (b) 1 8(b) 27 38 4 28168817 40(d) 53 12256 92537. (a) 3317144251(b) 11 10 9 381688 (d)5 135 3871 122 42432 48 1815515441. 2 4 333 48. 242. 13 3011 54644. 11 44 8542 136 1 13 176103 46. 49. 14 47 1745. 17 2 133 1034 5 263 1630 3051 12 1740 23113347. 431030 47050. Not possible. The number of columns of A does not equalthe number of rows of B.51. 1001284220 4212 1453. 143652. [30] 2 10 1284048 54. Not possible. The number of columns of the first matrixdoes not equal the number of rows of the second matrix.4 6344424 855.56. 0 6 1057.20836 120 06 58. 4 10 59. 22 41 66 76 114 13338 95 761461. 194263. 20(c) 284420(c) 284412202643.13x 16y 7z 3w 2x 21y 8z 5w 124x 10y 4z 3w 123. 1, 0, 4, 3 26. 152215. 10, 12 18.3. 1 14. 1 58 74 6. 3 52 53 3 5x y 7z 94x 2y 109x 4y 2z 319. 0011.2. 2 417 1738. (a), (b), and (d) not possible39.132(c) 24 20 28 40. Not possible. The matrices are not of the same order. Revi
(Continued) 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55. 56. 57. Inconsistent 58. 59. 60. 61. 62. 63. 64.
PreCalculus Student Solutions Manual- Precalculus 6th Ed Sullivan 1 PreCalculus Precalculus: Enhanced with Graphing Utilities 3rd Ed (Instructor Ed) M.Sullivan, M. Sullivan III 1 PreCalculus Precalculus 8 Sullivan
answers, realidades 2 capitulo 2a answers, realidades 2 capitulo 3b answers, realidades 1 capitulo 3a answers, realidades 1 capitulo 5a answers, realidades 1 capitulo 2b answers, realidades 2 capitulo 5a answers, realidades capitulo 2a answers, . Examen Del Capitulo 6B Answers Realidades 2 Realidades 2 5a Test Answers Ebook - SPANISH .
Precalculus with Limits, Answers to Section 12.1 3 (Continued) 21. Does not exist. Answers will vary. 22. 23. 24
Speak with a Precalculus Program Director if you have any questions or concerns. Learning Resources in the Precalculus Program Below is a list of resources available to help you succeed in the Precalculus Program. e-text Contains the course objec
PACKET FOR PRECALCULUS STUDENTS Summer, 2017 Congratulations. You've made it to Precalculus! INSTRUCTIONS: . PRECALCULUS SUMMER ASSIGNMENT Name:_ SHOW ALL WORK NEATLY ON THE SEPARATE ANSWER SHEET. b. 44 hr d. 22 hr Solve the problem.57. Brandon can paint a fence in 12 hours and Elaine can paint the same fence in 11 hours. .
Honors PreCalculus Summer Review Packet This packet is a review of information you learned in Algebra, Geometry, & Advanced Algebra. You need to know this information to be successful in PreCalculus. Therefore, this packet is due on your FIRST DAY IN PRECALCULUS. It is to be completed CORRECTLY, NEATLY, and on SEPARATE sheets of paper.
Unit II. Limits (11 days) [SC1] Lab: Computing limits graphically and numerically Informal concept of limit Language of limits, including notation and one-sided limits Calculating limits using algebra [SC7] Properties of limits Limits at infinity and asymptotes Estimating limits num
Precalculus with Limits, Answers to Review Exercises 29 (Continued) 9. 10. Vertex: Vertex: Axis of symmetry:
