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hw5sol

Course: MAT 135, Fall 2009
School: Princeton
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Word Count: 1005

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135 Math Intermediate Algebra Homework 5 Solutions 8 - 1 2 3 -4 - 1 8 8 - 5.1: Problems 9-25, 33-55, 61-73 9. terms: 5x3 , -x2 , -6x, 7; coefficients: 5, -1, -6, 7 11. terms: 4n, 2 -n ; 3 1 2 1 -4 - 4 2 -2 - 1 +7 = 2 1 -2 - +7 = 2 -1 - 1 + 1 + 7 = 6 43. 3x + 9 + 2x2 - 4x + 1 = 2x + (3x - 4x) + (1 + 9) = 2x2 - x + 10 45. (a3 - 5a3 + 3) - (5a2 + a - 3) = a3 - 5a2 + 3 - 5a2 - a + 3 = a3 + (-5a2 - 5a2 ) -...

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135 Math Intermediate Algebra Homework 5 Solutions 8 - 1 2 3 -4 - 1 8 8 - 5.1: Problems 9-25, 33-55, 61-73 9. terms: 5x3 , -x2 , -6x, 7; coefficients: 5, -1, -6, 7 11. terms: 4n, 2 -n ; 3 1 2 1 -4 - 4 2 -2 - 1 +7 = 2 1 -2 - +7 = 2 -1 - 1 + 1 + 7 = 6 43. 3x + 9 + 2x2 - 4x + 1 = 2x + (3x - 4x) + (1 + 9) = 2x2 - x + 10 45. (a3 - 5a3 + 3) - (5a2 + a - 3) = a3 - 5a2 + 3 - 5a2 - a + 3 = a3 + (-5a2 - 5a2 ) - a + (3 + 3) = a3 - 10a2 - a + 6 2 coefficients: 4, -1 3 13. terms: 3a2 , -8ab, 5b2 ; coefficients: 3, -8, 5 15. Polynomial of degree 3 17. Binomial of degree 2 19. Trinomial of degree 4 21. Monomial of degree 5 23. -3x2 + 9x + 2; leading term: -3x2 25. 5x + 8x - 2x - x + 10; leading term: 5x 33. -2x2 + 10x - 9 35. 3n3 + n2 + 2n 37. -6x4 - 1 x2 + 6 39. 2x2 - 7x + 6 a. 2(2) - 7(2) + 6 8 - 14 + 6 2 9 8 5 4 3 5 4 4 47. (3x4 - 7x3 + x2 + 8x - 10) + (8x3 - 1) + (10 - 9x - 7x2 + x4 ) = (3x + x ) + (-7x + 8x3 ) + (x2 - 7x2 ) + (8x - 9x) + (-10 - 1 + 10) = 4x4 + x3 - 6x2 - x - 1 49. (12p5 - 2p3 + 4p2 - 11p) - (13p5 + p4 + 2p3 - 3p2 - 11p - 1) = (12p5 - 13p5 ) - p4 + (-2p3 - 2p3 ) + 3 = = 0 (4p2 + 3p2 ) + (-11p + 11p) + 1 = -p5 - p4 - 4p3 + 7p2 + 1 51. b. 2(-3)2 - 7(-3) + 6 18 + 21 + 6 41. 8x3 - 4x2 - 2x + 7 a. 8 3 3 -4 2 2 27 9 8 -4 8 4 3 = = 45 (x2 + 5xy + 6y 2 ) + (9x2 y - 2xy 2 - 3xy + x2 - y 2 ) + (2x2 y - 12xy 2 ) = (9x2 y + 2x2 y) + (-2xy 2 - 12xy 2 ) + (x2 + x2 ) + (5xy - 3xy) + (6y 2 - y 2 ) = 11x y - 14xy 2 + 2x2 + 2xy + 5y 2 2 3 +7 = 2 3 -2 +7 = 2 27 - 9 - 3 + 7 = 22 -2 2 53. -y 3 + 6y 3 +5y 3 -3y 2 +8y 2 +5y 2 +4y -3y +y +2 +2 b. 55. 3p4 - 3p4 -2p2 +p2 -3p2 -10p +10p -5 +21 71. R(n) = = = = 18n + 3.5n2 - 0.005n3 18 100 + 3.5 1002 - 0.005 1003 1800 + 35000 - 5000 31800 -26 R(100) 61. (3x2 - 7x + 5) - (5x - 8x2 ) + (2 + 6x - 9x2 ) = (3x + 8x - 9x ) + (-7x - 5x + 6x) + (5 + 2) = 2x2 - 6x + 7 63. (12n3 + 16) - (11n3 - 9n2 + 3n + 8) - (-10n - 13) = (12n - 11n ) + 9n + (-3n + 10n) + (16 + 13 - 8) = n + 9n + 7n + 21 65. f (x) + g(x) = (2x - 8) + (2x2 + 7x + 5) = (2x2 + 2x2 ) + 7x + (-8 + 5) = 4x2 + 7x - 3 f (x) - g(x) = (2x - 8) - (2x + 7x + 5) = (2x2 - 2x2 ) - 7x + (-8 - 5) = -7x - 13 67. f (x) + g(x) = (-5x4 + 6x2 - 3) + (4x4 - 3x3 + 2x2 - x) = (-5x4 + 4x4 ) - 3x3 + (6x2 + 2x2 ) - x - 3 = -x4 - 3x3 + 8x2 - x - 3 f (x) - g(x) = (-5x4 + 6x2 - 3) - (4x4 - 3x3 + 2x2 - x) = (-5x4 - 4x4 ) + 3x3 + (6x2 - 2x2 ) - x - 3 = -9x4 + 3x3 + 4x2 + x - 3 69. t 0: 1: 2: 3: h(t) = -16t + 520 -16 02 + 520 = 520 -16 12 + 520 = 504 -16 22 + 520 = 456 -16 32 + 520 = 376 29. 2 2 2 2 3 2 3 3 2 2 2 2 73. (8t4 - 82t3 + 245t2 - 303t + 38, 387) + (25t2 + 93t + 14, 783) = 8t4 - 82t3 + (245t2 + 25t2 ) + (-303t + 93t) + (38, 387 + 14, 783) = 8t4 - 82t3 + 270t2 - 210t + 53, 170 5.2: Problems 1-19, 29-49, 67-77, 101, 103, 109-115 1. (6n3 )(-5n3 ) = (-5 6)(n3 n3 ) = -30n6 3. 2 2 (- 3 rt2 )(-9r3 t) = (- 3 -9)(r r3 )(t2 = t) 6r4 t3 5. (10x5 )(-x3 )(-2x4 ) = (10 -1 -2)(x5 x3 x4 ) = 20x12 7. (-3pr) 2p3 q q 2 = (-3 2)(p p3 )(q q 2 )r = -6p4 q 3 r 9. (-4ab5 )3 = (-4ab5 )(-4ab5 )(-4ab5 ) = -64a3 b15 11. (-2x)(5) + (-2x)(-4x) = -10x + 8x2 13. (4n2 )(6n) + (4n2 )(-1) = 24n3 - 4n2 15. (-3x)(x2 ) + (-3x)(-4x) + (-3x)(5) = -3x3 + 12x2 - 15x 17. 1 ( 2 n3 )(12m2 ) + ( 1 n3 )(8n) = 6n3 m2 + 4n4 2 19. (7x5 )(4x2 y 4 ) + (-4x3 )(4x2 y 4 ) + (1)(4x2 y 4 ) = 28x7 y 4 - 16x5 y 4 + 4x2 y 4 (x + 2)(x + 4) = x + 4x + 2x + 8 = 2 x2 + 6x + 8 (9p + 10q)(2p - q) = 31. (n - 6)(n - 3) = n - 3n - 6n + 18 = n2 - 9n + 18 33. (5 - a)(a + 7) = 5a + 35 - a - 7a = -a2 - 2a + 35 35. (y + 7)2 = (y + 7)(y + 7) = y + 7y + 7y + 79 = y 2 + 14y + 49 37. (2x - 1)(x + 4) = 2x2 + 8x - x - 4 = 2x2 + 7x - 4 39. (3 - 2x)(2 + 3x) = 6 + 9x - 4x - 6x2 = -6x2 + 5x + 6 41. (5x + 3)(6x + 5) = 30x + 25x + 18x + 15 = 30x2 + 43x + 15 43. (4x - 9)2 = (4x - 9)(4x - 9) = 16x2 - 36x - 36x + 81 = 16x2 - 72x + 81 45. (a - b)(2a + 3b) = 2a2 + 3ab - 2ab - 3b2 = 2a2 + ab - 3b2 47. 113. a. Longest panel: (x + 0.1) inches by (x + 0.1) inches. Shortest panel: (x - 0.1) inches by (x - 0.1) inches. b. (x2 + 18x + 72) - 72 = x2 + 18x x4 +x3 -45x2 +18x 109. pV2 - pV1 111. a. (6 + x)(12 + x) = 72 + 6x + 12x + x2 = x2 + 18x + 72 2 2 2 2 18p - 9pq + 20pq - 10q 2 = 18p2 + 11pq - 10q 2 49. (7x - 11y)(8x - 7y) = 56x - 49xy - 88xy + 77y 2 = 56x2 - 137xy + 77y 2 67. t2 - 100 69. x2 + 16x + 64 71. 16n2 - 9 73. 4n2 - 20n + 25 75. b2 - 2 ab + 1 a2 3 9 77. 25x2 - y 2 101. (3x2 - 1)(5x + 2) = 15x3 + 6x2 - 5x - 2 103. x2 x2 -6x3 x4 7x3 -42x2 -3x2 +7x -6x 18x -3 2 2 b. (x + 0.1)2 - (x - 0.1)2 = (x + 0.2x + 0.01) - (x - 0.2x + 0.01) = 0.4x 23. 115. Volume = length width height = (18 - 2x) (12 - 2x) x = (216 - 36x - 24x + 4x2 ) x = 216x - 60x2 + 4x3 5.3: Problems 1-15, 21-27, 39, 51, 53 1. 6x4 6 x4 = 3 = 3x4-3 = 3x 3 2x 2 x 3. 20 y 5 20y 5 = = -5y 5-3 = -5y 2 -4y 3 -4 y 3 5. -9x5 y 2 -9 x5 y 2 = = 3x5-1 y 2-1 = 3x4 y -3xy -3 x y 7. 6x3 9x2 6x3 + 9x2 = + = 2x2 + 3x 3x 3x 3x 9. 24n3 - 10n2 + 4n 24n3 -10n2 4n = + + = -4 -4 -4 -4 5 -6n3 + n2 - n 2 11. 54a5 - 6a4 + 36a3 54a5 -6a4 36a3 = + + = 9a2 - a + 6 3 3 3 6a 6a 6a 6a3 13. 16t4 + 10t3 - 18t2 - 8t 16t4 10t3 -18t2 -8t = + + + = 2 2 2 2 -2t -2t -2t -2t -2t2 4 -8t2 - 5t + 9 + t 15. 8p2 - 16pq + 28q 2 8p2 -16pq 28q 2 = 2 + + = 2 4q 4q 4q 2 4q 2 2p2 4p - +7 q2 q 51. a. 7.95 + 0.05x 7.95 = + 0.05 x x b. x is the number of monthly minutes, and 5 hours of calls is equal to 5 60 = 300 minutes, so x = 300. 7.95 + 0.05 0.08 = 8 cents 300 53. a. -30, 000r3 + 30, 000 = 30, 000r2 + 30, 000r + 30, 000 -r + 1 b. r = 1.04, cumulative earnings = \$93,648 (requires a calculator) 39. x4 - x3 + 5x2 - 3x + 6 = x2 - x + 2 x2 + 3 25. 3x3 - 8x2 - 39x + 11 9 = -3x2 - 7x + 4 - -x + 5 5-x 27. 5x2 - 11x - 12 =x-3 5x + 4 n3 + 5n2 - n - 5 = n2 + 4n - 5 n+1 2 2 21. x2 - 4x + 4 =x-2 x-2
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Allan Hancock College - CS - 9315
Disks and Files Storing Data: Disks and FilesChapter 9 (3rd Edition) DBMS stores information on (&quot;hard&quot;) disks. This has major implications for DBMS design!READ: transfer data from disk to main memory (RAM). WRITE: transfer data from RAM to disk. B
Allan Hancock College - CS - 9315
Relational OperationsWe will consider how to implement:Evaluation of Relational OperationsChapter 14 (3rd Edition) , Part A (Joins)Selection ( ) Selects a subset of rows from relation. Projection ( ) Deletes unwanted columns from relation. Joi
Allan Hancock College - CS - 9315
Using an Index for SelectionsCost depends on # qualifying tuples, and clustering.Evaluation of Relational Operations: Other TechniquesChapter 14 (3rd Edition)Cost of finding qualifying data entries (typically small) plus cost of retrieving reco
Allan Hancock College - CS - 9315
Physical Database DesignChapter 20 (3rd Edition)COMP9315: Database Systems Implementation1OverviewAfter ER design, schema refinement, and the definition of views, we have the conceptual and external schemas for our database. The next step
Allan Hancock College - CS - 9315
External SortingChapter 13 (3rd Edition)COMP9315 Database Systems Implementation1Why Sort?A classic problem in computer science! Data requested in sorted order e.g., find students in increasing gpa orderSorting is first step in bulk lo
Allan Hancock College - CS - 9315
Storing Data: Disks and FilesChapter 9 (3rd Edition)COMP9315 Database Systems Implementation1Disks and Files DBMS stores information on (&quot;hard&quot;) disks. This has major implications for DBMS design! READ: transfer data from disk to main m
Allan Hancock College - CS - 9315
TreeStructured IndexesChapter 10 (3rd Edition)COMP9315 Database Systems Implementation1IntroductionAs for any index, 3 alternatives for data entries k*: Data record with key value k &lt;k, rid of data record with search key value k&gt; &lt;k,
Allan Hancock College - CS - 9315
Overview of Query EvaluationChapter 12 (3rd Edition)COMP9315 Database Systems Implementation 1Overview of Query EvaluationPlan: Tree of R.A. ops, with choice of alg for each op.Each operator typically implemented using a `pull' interfac
Allan Hancock College - CS - 9315
SQL query parse parse tree convert logical query planheuristic based q.o.Query Optimization answer executecostbased q.o.apply laws statistics &quot;improved&quot; l.q.pPiestimate result sizes l.q.p. +sizespick best{(P1,C1),(P2,C2).}consider