197 58. (Modeling) Airplane Landing Speed To determine the appropriate landing speed of a small airplane, the formula D= 0.1s2 - 3s + 22 is used, where s is the initial landing speed in feet per second and D is the length of the runway in feet. If the landing speed is too fast, the pilot may run out of runway. If the speed is too slow, the plane may stall. If the runway is 800 ft long, what is the appropriate landing speed? Round to the nearest tenth. 59. (Modeling) U.S. Government Spending on Health Care The amount spent in billions of dollars by the U.S. government on health care programs during the period 1990–2017 can be approximated by the equation y = 0.865x2 + 8.87x + 159, where x = 0 corresponds to 1990, x = 1 corresponds to 1991, and so on. According to this model, about how much was spent by the U.S. government on health programs in 2017? Round to the nearest tenth of a billion. (Data from U.S. Office of Management and Budget.) 60. Dimensions of a Right Triangle The shortest side of a right triangle is 7 in. shorter than the middle side, while the longest side (the hypotenuse) is 1 in. longer than the middle side. Find the lengths of the sides. Solve each inequality. Give the solution set using interval notation. 83. -9x + 3 64x + 10 84. 11x Ú 21x - 42 85. -5x - 4 Ú 312x - 52 86. 7x - 21x - 32 … 512 - x2 87. 5 … 2x - 3 … 7 88. -8 73x - 5 7 -12 89. x2 + 3x - 4 … 0 90. x2 + 4x - 21 70 91. 6x2 - 11x 610 92. x2 - 3x Ú 5 93. x3 - 16x … 0 94. 2x3 - 3x2 - 5x 60 95. 3x + 6 x - 5 70 96. x + 7 2x + 1 … 1 97. 3x - 2 x - 4 70 98. 5x + 2 x + 1 60 99. 3 x - 1 … 5 x + 3 100. 3 x + 2 7 2 x - 4 x – 7 x + 1 x CHAPTER 1 Review Exercises Solve each equation. 61. 4x4 + 3x2 - 1 = 0 62. x2 - 2x4 = 0 63. 2 x - 4 3x = 8 + 3 x 64. 2 - 5 x = 3 x2 65. 10 4x - 4 = 1 1 - x 66. 13 x2 + 10 = 2 x 67. 1x - 422/5 = 9 68. 1x2 - 6x21/4 = 2 69. 1x - 222/3 = x1/3 70. 22x + 3 = x + 2 71. 2x + 2 - x = 2 72. 2x - 2x + 3 = -1 73. 24x - 2 = 23x + 1 74. 5x - 15 - 2x + 1 = 2 75. 2x + 3 - 23x + 10 = 1 76. 25 2x = 25 3x + 2 77. 23 6x + 2 - 23 4x = 0 78. 2x2 + 3x - 2 = 0 79. x x + 2 + 1 x + 3 = 2 x2 + 2x 80. 2 x + 2 + 1 x + 4 = 4 x2 + 6x + 8 81. 12x + 322/3 + 12x + 321/3 - 6 = 0 82. 1x + 32-2/3 - 21x + 32-1/3 = 3
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