Stitz-Zeager_College_Algebra_e-book

2 systems of linear equations augmented matrices 469

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Unformatted text preview: −2, −4 − 11 √ Asymptotes y = ± 30 5 (x + 2) − 4 y 2 x2 − =1 9 16 (x − 6)2 (y − 5)2 (d) − =1 256 64 (c) 5. Sasquatch is located at the point (−0.9629, −0.8113). 6. By placing Station A at (0, −50) and Station B at (0, 50), the two second time difference x2 y2 − = 1 with foci A and B and center (0, 0). Placing Station C yields the hyperbola 36 2464 at (−150, −50) and using foci A and C gives us a center of (−75, −50) and the hyperbola (x + 75)2 (y + 50)2 − = 1. The point of intersection of these two hyperbolas which is closer 225 5400 to A than B and closer to A than C is (−57.8444, −9.21336) so that is the epicenter. 7. (b) y2 x2 − = 1. 9 27 Chapter 8 Systems of Equations and Matrices 8.1 Systems of Linear Equations: Gaussian Elimination Up until now, when we concerned ourselves with solving different types of equations there was only one equation to solve at a time. Given an equation f (x) = g (x), we could check our solutions geometrically by finding where the graphs of y = f (x) and y = g (x) intersect. The x-coordinates of these intersection points correspond to the solutions to the equation f (x) = g (x), and the y coordinates were largely ignored. If we modify the problem and ask for the intersection points of the graph...
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This note was uploaded on 05/03/2013 for the course MATH Algebra taught by Professor Wong during the Fall '13 term at Chicago Academy High School.

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