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Chapter 2. Technical Mathematics

Signed Numbers

2-1. +7 2-8. -17 2-15. +2 2-22. +12
2-2. +4 2-9. +6 2-16. -2 2-23. +8
2-3. +2 2-10. -32 2-17. -4 2-24. -4
2-4. -2 2-11. -36 2-18. -3 2-25. 0
2-5. -10 2-12. +24 2-19. +2 2-26. +220
2-6. -33 2-13. -48 2-20. -4 2-27. +32
2-7. -5 2-14. +144 2-21. -3 2-28. -32
2-29. (a) -60C; (b) -170C; (c) 360C

2-30. (L= 2 mm[(-300C) – (-50C)] = 2 mm(-25) = -50 mm; Decrease in length.

Algebra Review

2-31. x = (2) + (-3) + (-2) = -3; x = -3 2-32. x = (2) – (-3) – (-2) = +7; x = +7
2-33. x = (-3) + (-2) - (+2) = -7; x = -7 2-34. x = -3[(2) – (-2)] = -3(2 + 2) = -12; x = -12
2-35. [pic] 2-36. [pic]
2-37. x = (-3)2 – (-2)2 = 9 – 4 = 5; x = 5 2-38. [pic]
2-39. [pic] 2-40. x = (2)2 +(-3)2 + (-2)2; x = 17
2-41. [pic] 2-42. x = (2)(-3)[(-2) – (+2)]2; x = -6(-4)2 = -96
2-43. Solve for x: 2ax – b = c; 2ax = b + c; [pic]
2-44. [pic]
2-45. [pic]
2-46. [pic]

2-47. 5m – 16 = 3m – 4 2-48. 3p = 7p - 16
5m – 3m = -4 + 16 3p – 7p = -16
2m = 12; m = 6 -4p = - 16; p = +4
2-49. 4m = 2(m – 4) 2-50. 3(m – 6) = 6
4m = 2m – 8 3m –18 = 6
2m = -8; m = -4 3m = 24; m = +8
2-51. [pic] 2-52. [pic]
2-53. [pic] 2-54. 14 = 2(b – 7); 14 = 2b – 14; b = 14
2-55. R2 = (4)2 + (3)2 = 16 + 9 2-56. [pic]
[pic] 3p = 6 + p; p = 3
2-57. V = IR; [pic] 2-58. [pic]
2-59. [pic] 2-60. s = vt + d; d = s – vt
2-61. [pic] 2-62. s = ½at2; 2s = at2; [pic]
2-63. [pic] 2-64.[pic]
2-65.[pic] 2-66. [pic]
[pic] [pic]
2-67. [pic] 2-68. [pic]
[pic] [pic]
2-69. v = vo + at; v – v0 = at 2-70. c2 = a2 + b2 ; b2 = c2 - a2
[pic] [pic]
Exponents and Radicals
2-71. 212 2-72. 3523 2-73. x10 2-74. x5
2-75. 1/a 2-76. a/b2 2-77. 1/22 2-78. a2/b2
2-79. 2x5 2-80.1/a2b2 2-81. m6 2-82. c4/n6
2-83. 64 x 106 2-84. (1/36) x 104 2-85. 4 2-86. 3
2-87. x3 2-88. a2b3 2-89. 2 x 102 2-90. 2 x 10-9
2-91. 2a2 2-92. x + 2

Scientific Notation

2-93. 4.00 x 104 2-94. 6.70 x 101 2-95. 4.80 x 102
2-96. 4.97 x 105 2-97. 2.10 x 10-3 2-98. 7.89 x 10-1
2-99. 8.70 x 10-2 100. 9.67 x 10-4 2-101. 4,000,000
2-102. 4670 2-103. 37.0 2-104. 140,0002-105. 0.0367 2-106. 0.400 2-107. 0.006
2-108. 0.0000417 2-109. 8.00 x 106 2-110. 7.40 x 104
2-111. 8.00 x 102 2-112. 1.80 x 10-8 2-113. 2.68 x 109
2-114. 7.40 x 10-3 2-115. 1.60x 10-5 2-116. 2.70 x 1019
2-117. 1.80 x 10-3 2-118. 2.40 x 101 2-119. 2.00 x 106
2-120. 2.00 x 10-3 2-121. 2.00 x 10-9 2-122. 5.71 x 10-1
2-123. 2.30 x 105 2-124. 6.40x 102 2-125. 2.40 x 103
2-126. 5.60 x10-5 2-127. –6.90 x 10-2 2-128. –3.30 x 10-3
2-129. 6.00 x 10-4 2-130. 6.40 x 106 2-131. –8.00x 106
2-132. -4.00 x 10-2
Graphs
2-133. Graph of speed vs. time: When t = 4.5 s, v = 144 ft/s; When v = 100 m/s, t = 3.1 s.
2-134. Graph of advance of screw vs. turns: When screw advances 2.75 in., N = 88 turns.
2-135. Graph of wavelength vs. frequency: 350 kHz ( 857 m; 800 kHz ( 375 m.2-136. Electric Power vs. Electric Current: 3.20 A ( 10.4 W; 8.0 A ( 64.8 W.

Geometry
2-137. 900. 1800, 2700, and 450 2-138.

2-139a. A = 170, B = 350, C = 380 2-139b. A = 500 Rule 2; B = 400 Rule 2.

2-140a. A = 500 Rule 3; B = 1300 2-140b. B = 700, C = 420 Rule 2

Right Triangle Trigonometry
2-141. 0.921 2-147. 19.3 2-153. 684 2-159. 54.20 2-165. 36.90
2-142.0.669 2-148. 143 2-154. 346 2-160. 6.730 2-166. 76.00
2-143. 1.66 2-149. 267 2-155. 803 2-161. 50.20 2-167. 31.20
2-144. 0.559 2-150. 32.4 2-156. 266 2-162. 27.10
2-145. 0.875 2-151. 235 2-157. 2191 2-163. 76.80
2-146. 0.268 2-152. 2425 2-158. 1620 2-164. 6.370
Solve triangles for unknown sides and angles (Exercises 168 – 175):
2-168. tan ( = 18/35, ( = 35.80 ;...
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