984 CHAPTER 9 Systems and Matrices 20. (Modeling) Heart Rate In a study, a group of athletes was exercised to exhaustion. Let x represent an athlete’s heart rate 5 sec after stopping exercise and y this rate 10 sec after stopping. It was found that the maximum heart rate H for these athletes satisfied the two equations H= 0.491x + 0.468y + 11.2 H= -0.981x + 1.872y + 26.4. If an athlete had maximum heart rate H= 180, determine x and y graphically. Round to the nearest tenth. Interpret the answer. (Data from Thomas, V., Science and Sport, Faber and Faber.) 21. (Modeling) The table was generated using a function y1 = ax 2 + bx + c. Use any three points from the table to find an equation for y1. 22. (Modeling) The equation of a circle may be written in the form x2 + y2 + ax + by + c = 0. Find an equation of the circle passing through the points 1-3, -72, 14, -82, and 11, 12. Solve each system in terms of the specified arbitrary variable. 23. 3x - 4y + z = 2 2x + y = 1 (x arbitrary) 24. 2x - 6y + 4z = 5 5x + y - 3z = 1 (z arbitrary) Solve each system, using the method indicated. 25. 5x + 2y = -10 3x - 5y = -6 (Gauss-Jordan) 26. 2x + 3y = 10 -3x + y = 18 (Gauss-Jordan) 27. 3x + y = -7 x - y = -5 (Gaussian elimination) 28. 2x - y + 4z = -1 -3x + 5y - z = 5 2x + 3y + 2z = 3 (Gaussian elimination) 29. x - z = -3 y + z = 6 2x - 3z = -9 (Gauss-Jordan) 30. 2x - y + z = 4 x + 2y - z = 0 3x + y - 2z = 1 (Gauss-Jordan)
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