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Calculus with Applications by Margaret Lial, Ray Greenwell, Nathan Ritchey

By Margaret Lial, Ray Greenwell, Nathan Ritchey

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EXAMPLE 5 Using Point-Slope Form to Find an Equation Find an equation of the line through 1 5, 4 2 and 1 210, 22 2 . SOLUTION Begin by using the definition of slope to find the slope of the line that passes through the given points. Slope 5 m 5 22 2 4 26 2 5 5 210 2 5 215 5 Either 1 5, 4 2 or 1 210, 22 2 can be used in the point-slope form with m 5 2 / 5. If 1 x1, y1 2 5 1 5, 4 2 , then y 2 y1 5 m 1 x 2 x1 2 2 1x 2 52 5 5y 2 20 5 2 1 x 2 5 2 Multiply both sides by 5. 5y 2 20 5 2x 2 10 Distributive property y245 YOUR TURN 4 Find the equation of the line through (2, 9) and (5, 3).

2 2 "6 2 1 "2 1 34. "5 1 "2 5 "y 2 "5 38. "x 2 "x 1 1 40. 6 "r 2 "3 y25 "x 1 "x 1 1 36. "5 "m 2 "5 "z 2 1 "z 2 "5 "p 1 "p2 2 1 "p 2 "p2 2 1 Simplify each root, if possible. 23. "16 2 8x 1 x2 Rationalize each numerator. Assume that all radicands represent positive real numbers. 25. "4 2 25z2 41. 24. "9y2 1 30y 1 25 26. "9k2 1 h2 Rationalize each denominator. Assume that all radicands represent positive real numbers. 27. 29. 5 "7 23 "12 28. 30. 5 "10 4 "8 43. 1 1 "2 2 "x 1 "x 1 1 "x 2 "x 1 1 YOUR TURN ANSWERS 1.

An alternative notation for a1/n uses radicals. Radicals If n is an even natural number and a . 0, or n is an odd natural number, then a 1/n 5 "a. n R-26 CHAPTER R Algebra Reference The symbol " is a radical sign, the number a is the radicand, and n is the index of 2 the radical. a. n EXAMPLE 1 Radical Calculations 4 5 161/4 5 2 (a) "16 (b) "232 5 22 5 3 (c) " 1000 5 10 (d) 64 2 5 Å 729 3 6 With a1/n written as "a, the expression am/n also can be written using radicals. n am/n 5 1 "a 2 m n or am/n 5 "am n The following properties of radicals depend on the definitions and properties of exponents.

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