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Numbers

Bob Jones PPT Notes -- Chapter 3b

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Measurements Reporting 1 how close a measurement or the average of several measurements is to the established or theoretical value accuracy Accuracy How close you are to the correct answer Small percent error ? 100% Percent Error O ? A A percent error = Your answer is 2351. The correct answer is 2048. What is your percent error? 2351 ? 2048 2048 ? 100 = 14.79% Sample Problem how close several measurements of the same event are to each other how reproducible the results are precision precise but not accurate 9.75 sec 9.74 sec 9.73 sec 9.75 sec Electronic Gate Timer Hand Timers Avg: 9.7425 9.0241sec accurate but not precise 9.51 sec 9.20 sec 8.52 sec 8.85 sec Electronic Gate Timer Hand Timers Avg: 9.0200 9.0241sec precise and accurate 9.02 sec 9.01 sec 9.03 sec 9.02 sec

AHSME 1983

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USA AIME 1983 1 Let x, y, and z all exceed 1 and let w be a positive number such that logxw = 24, logy w = 40, and logxyz w = 12. Find logz w. 2 Let f(x) = |x? p|+ |x? 15|+ |x? p? 15|, where 0 < p < 15. Determine the minimum value taken by f(x) for x in the interval p ? x ? 15. 3 What is the product of the real roots of the equation x2 + 18x+ 30 = 2 ? x2 + 18x+ 45? 4 A machine-shop cutting tool has the shape of a notched circle, as shown. The radius of the circle is ? 50 cm, the length of AB is 6 cm, and that of BC is 2 cm. The angle ABC is a right angle. Find the square of the distance (in centimeters) from B to the center of the circle. A B C 5 Suppose that the sum of the squares of two complex numbers x and y is 7 and the sum of
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