888 CHAPTER 9 Systems and Matrices 84. (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. (Modeling) Given three noncollinear points, there is one and only one circle that passes through them. Knowing that 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 given points. 85. 1-1, 32, 16, 22, and 1-2, -42 86. 1-1, 52, 16, 62, and 17, -12 87. 12, 12, 1-1, 02, and 13, 32 88. 1-5, 02, 12, -12, and 14, 32 89. Connecting Graphs with Equations x 0 (0, 3) (4, 2) (–5, –2) y 90. Connecting Graphs with Equations x 0 (4, 3) (–1, –2) (–1, 5) y (Modeling) Work each problem. See Example 8. 91. Atmospheric Carbon Dioxide Carbon dioxide concentrations (in parts per million) have been measured directly from the atmosphere since 1960. This concentration has increased quadratically. The table lists readings for three years. (a) If the quadratic relationship between the carbon dioxide concentration C and the year t is expressed as C = at2 + bt + c, where t = 0 corresponds to 1960, use a system of linear equations to determine the constants a, b, and c to four decimal places, and give the equation. (b) Predict when the amount of carbon dioxide in the atmosphere will be double its 1960 level. Year CO2 1960 317 1980 339 2018 409 Data from Scripps Institution of Oceanography. 92. Aircraft Speed and Altitude For certain aircraft there exists a quadratic relationship between an airplane’s maximum speed S (in knots) and its ceiling C, or highest altitude possible (in thousands of feet). The table lists three such airplanes. Airplane Max Speed (S) Ceiling (C) Hawkeye 320 33 Corsair 600 40 Tomcat 1283 50 Data from Sanders, D., Statistics: A First Course, Sixth Edition, McGraw Hill.
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