82 CHAPTER R Review of Basic Concepts 97. 41x2 - 123 + 8x1x2 - 124 161x2 - 123 98. 1014x2 - 922 - 25x14x2 - 923 1514x2 - 926 99. 212x - 321/3 - x - 1212x - 32-2/3 12x - 322/3 100. 713t + 121/4 - 1t - 1213t + 12-3/4 13t + 123/4 (Modeling) Distance from the Origin of the Nile River The Nile River in Africa is about 4000 mi long. The Nile begins as an outlet of Lake Victoria at an altitude of 7000 ft above sea level and empties into the Mediterranean Sea at sea level (0 ft). The distance from its origin in thousands of miles is related to its height above sea level in thousands of feet (x) by the following formula. Distance = 7 - x 0.639x + 1.75 For example, when the river is at an altitude of 600 ft, x = 0.6 (thousand), the distance from the origin is Distance = 7 - 0.6 0.63910.62 + 1.75 ≈3, which represents 3000 mi. (Data from The World Almanac and Book of Facts.) 101. What is the distance from the origin of the Nile when the river has an altitude of 7000 ft? 102. What is the distance, to the nearest mile, from the origin of the Nile when the river has an altitude of 1200 ft? (Modeling) Cost-Benefit Model for a Pollutant In situations involving environmental pollution, a cost-benefit model expresses cost in terms of the percentage of pollutant removed from the environment. Suppose a cost-benefit model is expressed as y = 6.7x 100 - x , where y is the cost in thousands of dollars of removing x percent of a certain pollutant. Find the value of y for each given value of x. 103. x = 75 175%2 104. x = 95 195%2 R.8 Radical Expressions ■ Radical Notation ■ 6LPSOLıHG 5DGLFDOV ■ Operations with Radicals ■ Rationalizing Denominators Radical Notation Previously, we used rational exponents to express roots. An alternative notation for roots is radical notation. Index Radical symbol 2 n a Radicand Radical Notation for a1/n Let a be a real number, n be a positive integer, and a1/n be a real number. !n a =a1/n
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