Glencoe Solution Manual

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28. 3(x 2 2x 3)dx 1 1 3 x 3 2 1 2 x 2 3x 3 37. 0 (x 4 x 3 )dx11 1 3 x 3 x 2 3x 3 1 115 x 5 1 4 x 4 0 1 13 3 3 3 2 3 3 1 3 1 3 1 2 9 3 1 0 2 9 1 1 3 or 1 0 9or 2 063units 238. 2(x 3 x 1)dx29. 1(x 3 x)dx 1 4 x 4 1 2 x 2 1 000 1 4 1 4 1 2 1 2 1 4 0 4 1 2 0 2 3 4 0 or 3 4 unit 2 8 0 or 830. 3 (x 3 8x 10)dx39. 5 (x 2 3x 8)dx1 1 4 x 4 8 1 2 x 2 10x 3 2 1 3 x 3 3 1 2 x 2 8x 512 1 4 x 4 4x 2 10x 3 1 3 x 3 3 2 x 2 8x 512 1 4 3 4 4 3 2 10 3 1 3 5 3 3 2 5 2 8 5 1 4 (1) 4 4 (1) 2 10 1 1 3 (2) 3 3 2 (2) 2 8 2 34 54 2 34 or 92 units 2 26 56 7 43 31. 76x 2 dx 6 1 3 x 3 7 26 56 14 86or 41 3600 2x 3 7 40. 3(x 3)(x 1)dx01 (2 7 3 ) (2 0 3 ) 3(x 2 2x 3)dx 686 0 or 686132. 43x 4 dx 3 1 5 x 5 4 1 3 x 3 2 1 2 x 2 3x 3 122 3 5 x 5 4 1 3 x 3 x 2 3x 3 12 3 5 4 5 3 5 2 5 30 725 9 65or 29 9 5763 or 3 23533. 3 (x 4)dx 1 2 x 2 4x 3 41. 3(x 1) 3 dx 3(x 3 3x 2 3x 1)dx2211 1 1 2 3 2 4 3 1 2 (1) 2 4 4 1 x 4 3 1 3 x 3 3 1 2 x 2 x 3 2 3 32 7 2 1 4or 20 x 4 x 3 3 2 x 2 x 3 234. 5(3x 2 2x 1)dx 3 1 3 x 3 2 1 2 x 2 x 5 1 4 3 4 3 3 3 2 3 2 311 x 3 x 2 x 5 1 4 2 4 2 3 3 2 2 2 21 1 5 (5 3 5 2 5) (1 3 1 2 4 0 or 1 45 1) 105 1 or 10442. 1 x2 x 2x dx2 1 (x 2)(x 1)x dx20035. 3(x 3 x 2 )dx 1 4 x 4 1 3 x 3 3 1(x 1)dx110 1 4 3 4 1 3 3 3 1 4 1 4 1 3 1 3 1 2 x 2 x 1 4 05 14 1 2 1 1 35112 1 2 or 3 2 1 2 1 1 2 0 2 043 336. 12 (x 4 2x 2 1)dx043. 2x(4x 2 1)dx 2(4x 3 x)dx 1 5 x 5 2 1 3 x 3 x 1 000 4 1 1 5 x 5 2 3 x 3 x 1 4 x 4 1 2 x 2 2 00 1 5 1 5 2 3 1 3 1 1 5 0 5 2 3 0 3 0 2 815 0 or 2 815 18 0 or 18 1 5 0 5 1 4 0 4 1 5 (1) 5 1 4 (1) 4 1 4 x 4 1 2 x 2 x 2 0 1 4 2 4 1 2 2 2 2 1 4 0 4 1 2 0 2 0 1 3 3 3 3 2 3 3 1 3 1 3 1 2 3 1 x 4 1 2 x 2 2 02 4 1 2 2 2 0 4 1 2 0 2 489 Chapter 15
44. 1 (x 1)(3x 2)dx49a.1 1 (3x 2 5x 2)dx1 3 1 3 x 3 5 1 2 x 2 2x 1 1 x 3 5 2 x 2 2x 1 11 3 5 2 1 2 2 1(1) 3 5 2 (1) 2 2 1 1 21 1 2 or 645a. 20.5x 3 dx 1 4 x 4 20.500 1 4 20.5 4 1 4 0 4 44,152.52 0 or 44,152.52 20i 3 202 (20 1)24i1 400 (441)40or 44,10045b. 100.5x 2 dx 1 3 x 3 100.500 1 3 100.5 3 1 3 0 3 338,358.38 0 or 338,358.38100 i 2 100(100 1)(2 100 1) 6i1 100(10 1)(201)6or 338,35046. 2490,000 xdx 490,000 1 2 x 2 2 00 245,000 x 2 2 0 (245,000 2 2 ) (245,000 0 2 ) 980,000 0 or 980,000 J47a. Since the graph is below the x-axis, f(x) isnegative. Each f(x i ) is negative and x isnpositive, so each term in the sum f(xi1 i )x isnegative. Therefore, the sum is negative. since b f(x)dx is a limit of negative sums, it is alsoanegative.47b. 2(x 2 5)dx0 1 3 x 3 5x 2 0 1 3 2 3 5 2 1 3 0 3 5 0 2 2347c. Since the function is negative, the integral inpart b gives the opposite of the area of theregion. The area is 2 23.48. yThe integral represents the108642O2 1 2 3 4 5x4 y 3x 66area of a right triangle. Thevalue is 1 2 (3)(9) 2 72.110100908070605040302010149b. 6 0 60 75 8x 1 2 x 2 dx 1 6 75x 8 1 2 x 2 1 2 1 3 x 3 6 0 1 6 75x 4x 2 1 6 x 3 6 0 1 6 75 6 4 6 2 1 6 6 3 75 0 4 0 2 1 6 1 6 (558 0) $93 0 3 149c. 12 6 1275 8x 1 2 x 2 dx6 1 6 75x 8 1 2 x 2 1 2 1 3 x 3 1250. R ROf(x) 1 6 75x 4x 2 1 6 x 3 12 1 6 75 12 4 12 2 1 6 12 2 75 6 4 6 2 1 6 1 6 (1188 558) $1056 6 3 (R 2 x 2 )dx R 2 x 1 3 x 3 R RR 2 R 1 3 R 3 R 2 R 1 3 (R) 3 2 3 R 3 2 3 R 3 4 3 R 3f(x) 75 8x 1x 2251a. 1000 k(6.4 10 6 ) 211000 k 40.96 10 124.1 10 16 k; 4.1 10 16 Nm 23.8 10851b. 4.1 6.4 10 6 1016 x 2 dx 4.1 10 16 (1)x 1 3.8 4.1 10 16x 10 86 10 86.4 10 6 3.8 6.4 10 6 4 . 1 13.8 016 4 . 1 11086 . 4 016 106 1.1 10 8 64.1 10 8 6.3 10 9 JxChapter 15 490
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Copyright © by The McGraw-Hill Com
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16b.Weight(lb)300280260240220200180
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54e. t(30,000) 95 0.005(30,000)55
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15. [f g](x) f(g(x)) f(x 4) (x
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4. Sample answer: Both graphs are l
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24. 9x 5 09x 5x 5 9 The y-interc
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27b. Using sample answer from part
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13. y 7x 5 0 y 7x 9 0y 7x 5
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4b. Sample answer: using (1995, 229
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19. The y-intercept is 1.The slope
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22.x f(x)5 63 01 60 91 63 05 623. S
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8a. c(m) 45 0.4m8b. c(m)7014.y605
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Chapter 1 Study Guide and Assessmen
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37. 7x 2y 5y7x 2y 5O38. The y-in
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Page 61 Applications and Problem So
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Chapter 2 Systems of Linear Equatio
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32b. S 4V 0 S V 30,000S 4V 4V
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9. 7(x 3y 2z) 7(16) x 3y 2z 1
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23. x yz 2y xz 2z xy 2x yz
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26. 2 w 5 x z 16 43y 8 6 2x 8
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2 351a. a b 2 34 5 c d 4 52(a)
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4. See students’ work for graphs.
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18a. 4 0 2 6 6 6 2 6 4 131222F(
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c 1 1,where c is the number of squa
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4 1 23 5 y 2420. 4 2 1 (1) 0 1
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52. Let x represent Jessi’s first
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13.14.y 0.5x 1O 3 5 , 3 1 5 ,
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28a. 3 is $3 profit on each batch o
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13e. $77614a. Let x the number of
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Pages 120-122 Skills and Concepts11
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2 545. x 11 3 y 21 3 5 1 3 52
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6. Start by simplifying the fractio
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18. f(x) 7x 5 8x12. ⏐y⏐ x 3
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33. y 2 3x 0 → b 2 3a 0x-axis
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9a. translated up 3 units, portion
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37c. 0.642a. (1) y x 2 (2) y x 3(
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19. y x 2 y x 20 ? 0 2 4 ? 1
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53. Student A 15Student B 1 3 (
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14b. r 1 1 or 0.0323; 3.23%Pages 1
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30. f(x) x 2 4x 3y x 2 4x 3x
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47d. C 1 (x) (x 2) 2 3C 1 (1) (
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28.33b. Since f is odd, its graph m
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6. {all real numbers x⏐x 6 or x 2
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23. rel. max.: (1, 1); rel. min.: (
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3-7Pages 185-1861.Graphs of Rationa
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26. The parent graph is translated
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56. Let x the width of each card a
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The correct choice is D.Chapter 3 S
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42.52. x 1 y x x1y x x x x
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3a. Sample answer:(2, 1)y(0, 0)O3b.
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Chapter 4 Polynomial and Rational F
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43. 3; n 3 9n 0n(n 2 9) 0n(n 3
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65. [f g](x) f(g(x)) f 1 2 x 6
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29. x 2 3x 28 0(x 7)(x 4) 0x
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Pages 226-228 Exercises14. 7⏐ 1 2
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6. p: 1, 3q: 1, 2 P q : 1, 3, 1 2
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24b. V() 2 3 9 2 42208 2 3 9 2
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11b. V w h 1.5V 1.5(3750)V 25
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37a. f (x)100,00080,00060,00040,000
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18. 1 1 1aa a 11 aa a 11(1 a)
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1 1 832. 2b 1 b 1 1 51 1 8 2b
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53b. Let x short answer questions
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21. a1 2 1 a2 1a 21 2a1 2 1
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38c. No; it is not a linear functio
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23b. Sample answer:f(x) 0.109x 2
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29. p: 1, 3q: 1, 2 p q : 1, 3, 1
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50. 3 4a 1 8 5 Check: 3 4a 1
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8. You can solve this problem using
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40. 217° 360k; Sample answers:217
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Pages 287-288 Check for Understandi
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31c. 87.5° 40.5° 47°49.5° 25
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23. terminal side — Quadrant IIre
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36. r x 2 y r x 2 y r 56) 2 (
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3. ∠DCB; ∠ABC; the measures are
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34.yOy |x 2|x35. Let x the cost
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35. — 1 2 — (14) 7base angles:
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2. Sample answer:Cb35˚A103. Area o
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34. x90° 63° 27°55˚ 63˚ 180
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9. Since 130° 90°, consider Case
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27. Since 47° 90°, consider Case
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41. tan 22° 7 4. Sample answers:
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15. b 2 a 2 c 2 2ac cos B13.7 2
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C could also equal 180 76.27180414
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34. r x 2 y 2 r 5 2 0 2 43. a 2
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58. b 2 a 2 c 2 2ac cos By 2 1b
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Chapter 6 Graphs of Trigonometric F
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60. 3.5 km 350,000 cms rv350,000
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38b. lighter child: v rqv 9(1.2)v
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32. y1y cos xO 8 9133.y cos x5 43
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2 x60. x 2 2 x 2 4x x2 41(x 2
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13. ⏐A⏐ 7 2 k 3 2A 7 k o
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50. sine curve A 0.5 36. ⏐A⏐
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71. y 14.7x 140.1y 14.7(20) 140
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5; 18. 4; y 424. ⏐5⏐A 5; 2 1
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42. y349. f(x) y xx 133y x 123
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12b. y 23.5 sin 6 t 2 3 47.
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8. 1 4 24. ; 4 4 n, where
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46d. 34.3 N52. C 180° (62°31 7
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10. Let v Cos 1 22 .Cos v 22v
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43d. A 3.675 2 k 12.4 h 7.05
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42. 3 2 Page 417 Applications
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10. Notice that the triangles are n
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20. Sample answer: 30°sec 2 x 1
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48. sin x cos x sec x cot x sin x
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1cosx6. tan x sec x sin x 11cosx
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32. Sample answer: sin x 1 2 1
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5. cos 165° cos (45° 120°)10.
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29. sec x tan 2 x 1 5 3 2 cos y
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48b. tan A tan B tan C tan A tan
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7-4Double-Angle and Half-AngleIdent
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20. tan 2v 1 1 c osv cos v1 1
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tan A 2 sin 2A 2 1 cos 2 A 2
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4. Each type of equation may requir
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34. cot 2 x csc x 1csc 2 x 1 cs
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62. cot 67.5° cot 13 5°12cot v
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10. 2x 2y 62x 2y 6 0A B 2 2
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33b. p 1.25, f 45°x cos (45°)
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7. 3x 5y 1 When x 2, y 1. Use (
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31. m 1 432. 73 1or 3 4 y 7
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125. cos y se c y1sin y 1 s co2
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51. y 1 3 x 6 → x 3y 18 0d
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7. Simplify the fraction. One metho
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21. 324˚u26.tur5.5 cmr3.5 cm22˚r
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50. v o volume of original boxv n
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45a.30˚Shore1545b. sin 30° ⏐V
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20. u TM 1 0, 4 6, 3 3 or 1, 2,
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u10. AB (0.65, 0, 0.3) (0, 0, 0)
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36a.F45˚36b. W ⏐F u ⏐⏐d u
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8. u F1 (33 cos 90°)iu (33 sin 9
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38. *4 *(3) (4 3 4) [(3) 3 (3)
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37a. target drone:x 3 (1)t y 4
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If the magnitude of the initial vel
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6b. Sample answer: If the original
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23. The first transformation reflec
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40. 1, 0, 4 5, 2, 1 0uiu juk1 0 45
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2. In order to write the equation o
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Chapter 9 Polar Coordinates and Com
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38. 120˚90˚ 39. 60˚120˚150˚30
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7.2 2 338.5665623236Pages 565-567 E
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34a. r cos 2 r cos 7 r cos 4
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13a.150˚180˚120˚90˚210˚330˚24
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49. sin 2 A cos A 11 cos 2 A co
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19. 4 r cos v 4 0 r cos v cos
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7. x 2 y 2 36x 2 y 2 36r 6 or
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39b. z 0 1 0iz 1 (0.5 0.866i)(1
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13.5623i2363(2, 2)01 2 3 4 19. 20.i
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46a. 40∠30° 40(cos 30° j sin
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13. r 5(2) or 10 v 3 4 4 4
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3. Rewrite 1 i in polar form as 2c
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27. x 5 1 → x 5 1Find the fifth
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Find c.cos 81°15 2 c8c cos 828
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48. r 4 2 0 2 v 0 16 or 44(cos
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Chapter 10 Conics10-1Introduction t
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24. Let the vertices of thequadrila
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34b. The two regions are closest be
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13. midpoint of diameter:18. (x h)
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30. x 2 y 2 Dx Ey F 0(2) 2 7
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42d. center: (h, k) (4, 2)radius:
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7. center: (h, k) (0, 0)a 2 36 b
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22. (h, k) (0, 0)a 2 9 b 2 4 c
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32. The major axis contains the foc
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47. The target ball should be place
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2. Sample answer: The graph will sh
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transverse axis: horizontal (x h)
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23. 25y 2 9x 2 100y72x269025(y 2 4y
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38. center: (h, k) (3, 1)a distan
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48b. They are the same lines.48c.
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10. (y k) 2 4p(x h)(1 5) 2 4p[
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20. y 2 2y 12x 13 0y 2 2y 12x
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32. opening: upwardh x 1 x 22 1
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41.5676 12 cos 2 (r, )0 12 (12, 0)
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10. vertex: (h, k) (5, 1)(x h) 2
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15. A 1, C 3; since A and C have d
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26. x cos 2t y sin 2tcos 2 2t si
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41a. A 2, C 5; since A and C have
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3. y90° or 270°y 2 1y 2x 2 125
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20. B 2 4AC 0 4(2)(2)16A C; cir
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42. 9x 2 4xy 6y 2 2039. 8x 2 5x
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52.WN5S53. cos 70° 0.34cos 170°
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12a. Let x side length of flowerbe
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21. x 2 y 3 0x 2 y 3x 2 4y 2
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38c. (h, k) (0, 3)(x, y) (6, 0)(x
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5c. SHADE(((36X 2 )/9),((36X 2 )/9)
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24. (h, k) (4, 1)a 9b 6 (y k) 2
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36. vertex: (h, k) (1, 3)(y k) 2
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57. x 2 4x 4y 461. 62.x 2 b b2
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6. For a quadratic equation in the
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19. A r 2 r 3.875 10 7 mA (3.87
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69d. If the exponent is less than 0
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5. x y1 1 9 0 11 32 9yy 3 x11. x
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25b. y28d. Sample answer: A borrowe
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11a. Annually: I 100[(1 0.08) 1
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11-4Pages 722-723Logarithmic Functi
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54. x y1 02 34 655. x y2 06 156. x
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11-5Common LogarithmsPage 730 Check
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54.[10, 1] scl:1 by [2, 10] scl:155
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12. 10 5e 5k2 e 5kln 2 5k ln e33
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59. 1800 5000 ln r68. 2x 5y 3 01
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23b. The result of part a indicates
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54. 1 4 3x 6 x23x log 1 4 (x
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6. C D9. A is the arithmetic mean
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23. d n 5n or 6x7n (6n) 13n 13n
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67. x 1x 3x 2 4x 2(x 2 3x)x 2
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37. r —5or 343a. r 5 5. 50 3
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n 1n→n1d. lim limn→ n n 1 0
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1 9 36. r — or 1 6 S n 2 3 2
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14. Let x 3 , then x 3 1 x .
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2216. a n (n 1),(n 2)a n1 (n 2)2
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10. 5001 0. 124 515a 1 515, r
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53. 322 a 1 2 51322 4a 182 a 182
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Binomial Theorem to find the 4th te
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39. If you add the numbers on the d
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15. f(0.1) 2(0.1) 2 0.10.08f(0.08
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40. n 1 sin I n 2 sin r1.00 sin 42
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13. Step 1: Verify that the formula
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Chapter 12 Study Guide and Assessme
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Page 439 and 440: Chapter 13 Combinatorics and Probab
Page 441 and 442: 47. C(3, 1) C(4, 1) C(6, 1) C(14
Page 443 and 444: uiu u j k44. u v u w 2 0 3 2 5 0
Page 445 and 446: 42a. P 179,820 151,32284,475 3273
Page 447 and 448: 34. P(all red cards) 2 652 2 5
Page 449 and 450: 5. P(queen ⏐ face card) 45 2— 1
Page 451 and 452: 42d. Sample answer: A chip from Cyb
Page 453 and 454: 25. P(half answers correct) C(10,
Page 455 and 456: 20. There are P(5, 5) ways to arran
Page 457 and 458: 10.12The probability that a dart th
Page 459 and 460: 10e. Sample answer:Grams of Fat Fre
Page 461 and 462: 3. Write the stems 9, 10, 11, 12, 1
Page 463 and 464: 28a.stem leaf0 1 1 1 1 1 1 1 2 2 2
Page 465 and 466: 8c. Los AngelesLas Vegas8d. Los Ang
Page 467 and 468: Page 917 Mid-Chapter Quiz1. Sample
Page 469 and 470: 15b.2015Frequency10500 1 2 3 4 5 6N
Page 471 and 472: 7. A1% confidence level is given wh
Page 473 and 474: 4. range5. measure of central tende
Page 475 and 476: 9.To find the median of Set A, firs
Page 477 and 478: x2 25x→5x 519. lim lim (x 5)(
Page 479 and 480: 153. csc 270° sin 270° 1 y 1
Page 481 and 482: 20. f(x) 8xf(x) 8 1x 11 821. f(x
Page 483 and 484: 57. x 2 y 2 Dx Ey F 02 2 (1)
Page 485 and 486: 12. 2 x 2 dx 0 x 2 dx 2x 2 dx1
Page 487 and 488: 27. 30 1 2 x 3 dx lim n→ n 1
Page 489: 7. 0 (4 x 2 )dx 4x 1 3 x 3 0
Page 493 and 494: 23. f(x) lim f(x h ) f(x)h→0h
Page 495 and 496: 2. Let x represent the length of th
Page 497 and 498: 5. 2x 1 02x 1x 1 2 f(x)f(x) 2
Page 499 and 500: 6. 8x 2y 2 → 16x 4y 43x 4y 2
Page 501 and 502: 4 0 16. 5 3625 265 2 2 2 4(36) 0(2
Page 503 and 504: 6. y 2 2 x 2 17→ b 2 2 a 2
Page 505 and 506: Lesson 3-5Page A311. Yes; the funct
Page 507 and 508: 4. 4⏐ 1 2 7 3 44 8 4 41 2 1 1⏐
Page 509 and 510: 6. x 2x x 4x 6(x 6)(x 2) x(x
Page 511 and 512: 3. r x 2 y 2 (1) 2 ) (22 5sin v
Page 513 and 514: 4. C 180° (45° 85°) or 50°a
Page 515 and 516: Lesson 6-4Page A361. ⏐2⏐ 2; 2
Page 517 and 518: 5. csc (930°) sin (16. t sin van
Page 519 and 520: 3. tan 12 tan 6 7. 7 2 2 2
Page 521 and 522: Lesson 7-7Page A391. 3 (2) 2( 1)
Page 523 and 524: Lesson 8-6Page A411. x 2, y 3 t1
Page 525 and 526: 5.120˚90˚60˚Lesson 9-6150˚180˚
Page 527 and 528: 3. x 2 49 y 2 → x 2 y 2 49y8
Page 529 and 530: Lesson 10-6Page A451. A 1, C 1; s
Page 531 and 532: 3.yOLesson 11-3xy 3 x 1Page A461.
Page 533 and 534: 7. a n a 1 (n 1)da 16 2 (16 1
Page 535 and 536: n228. a n n ,2a n1 n (n 12 n 1
Page 537 and 538: 2. Step 1: Verify that the formula
Page 539 and 540: Lesson 13-5Page A521. P(second clip
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5f.Lesson 14-4Page A541a. 25% corre
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6. 60(x 2)dx 1 2 x 2 2x 6 0
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20a.20b. Sample answer: Using (47,
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222. y x 2 → b a 2x-axis b a22b
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14. Sample answer: 1; 219. 2x 2 3
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12. cos A b c cos ° 4 c2 42c
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20. 6 5 mi1 ho lesur 52 80feet1 h
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Chapter 8 TestPage A631. 2.5 cm, 60
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21. (2 5i) (2 4i) (2 (2)) (5i
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13. A 3, C 16; since A and C have
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14. log 5 (2x) log 5 (3x 4)2x 3x
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610. P(2 white) 1 0 5 9 4. Sampl
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21. 3(x 2 x 6) dx 1 3 x 3 1
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