430 CHAPTER 3 Polynomial and Rational Functions 76. Concept Check This rational function has two holes and one vertical asymptote. ƒ1x2 = x3 + 7x2 - 25x - 175 x3 + 3x2 - 25x - 75 (a) What are the x-values of the holes? (b) What is the equation of the vertical asymptote? (Modeling) Solve each problem. 77. Environmental Pollution In situations involving environmental pollution, a costbenefit model expresses cost as a function of the percentage of pollutant removed from the environment. Suppose a cost-benefit model is expressed as C1x2 = 6.7x 100 - x , where C1x2 is cost in thousands of dollars of removing x percent of a pollutant. (a) Graph the function in the window 30, 1004 by 30, 1004. (b) How much would it cost to remove 95% of the pollutant? Round to the nearest tenth. 78. Antique-Car Competition Antique-car owners often enter their cars in a concours d’elegance in which a maximum of 100 points can be awarded to a particular car based on its attractiveness. The function C1x2 = 10x 491101 - x2 models the cost, in thousands of dollars, of restoring a car so that it will win x points. (a) Graph the function in the window 30, 1014 by 30, 104. (b) How much would an owner expect to pay to restore a car in order to earn 95 points? Round to the nearest tenth. Solve each inequality. Give the solution set in interval notation. 79. 12x - 121x + 52 60 80. -5x2 + 28x … -12 81. 1x - 421x - 121x + 22 70 82. 2x4 - 9x3 - 5x2 + 57x - 45 … 0 83. -x4 + 3x2 74x3 - 18x 84. x + 7 2x + 1 60 85. x2 - x - 2 x2 + 4x + 4 … 0 86. 4 x + 6 7 2 x - 1 Solve each problem. 87. If x varies directly as y, and x = 20 when y = 14, find y when x = 50. 88. If x varies directly as y, and x = 12 when y = 4, find x when y = 12. 89. If t varies inversely as s, and t = 3 when s = 5, find s when t = 20. 90. If z varies inversely as w, and z = 10 when w = 1 2 , find z when w = 10. 91. ƒ varies jointly as g2 and h, and ƒ = 50 when g = 5 and h = 4. Find ƒ when g = 3 and h = 6. 92. p varies jointly as q and r2, and p = 100 when q = 2 and r = 3. Find p when q = 5 and r = 2.
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