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HW #5 MAT 110 Name______________________________ Part I Due Tuesday, April 20 (1) Solve the system of linear equations: x 4 y 2 z 15 2 x y 3z 2 3x 2 y z 3 (2) Find the solutions of the non-linear system: y x2 4x 2 y x 12 (3) Decompose into the sum of partial fractions: x 2 x 3 x 10 (4) Graph the solution set of the system of linear inequalities: x 2 y 8, 3x y 6 (5) Graph the solution set of the non-linear inequality: ( x 3)2 ( y 4)2 9 (6) Find the maximum value of the function P 6 x 8 y subject to the constraints: 2 x y 12, x 3 y 21, x 0, y 0 Part II Due Thursday, April 22 (1) Solve the system of linear equations: x 6 y 4 z 6, 4 x 3 y 4 z 1, 5 x 9 y 8 z 13 (2) Find the equation of the form y ax 2 bx c whose graph passes through the points (2,3), (-2,7) and (1,-2). (tip plug these points into the equation, then solve the resulting system for a, b, and c. (3) Find the solutions of the non-linear system using elimination: 2 2 x y 5 2 2 3 x 2 y 19 (4) Decompose into the sum of partial fractions: 2x 1 x2 4 (5) Graph the solution set of the system of inequalities: y x2 2x 1 (6) A farmer has 10 acres to plant in wheat and rye. He has to plant at least 7 acres. However, he has only $1200 to spend and each acre of wheat costs $200 to plant and each acre of rye costs $100 to plant. Moreover, the farmer has to get the planting done in 12 hours and it takes an hour to plant an acre of wheat and 2 hours to plant an acre of rye. If the profit is $500 per acre of wheat and $300 per acre of rye how many acres of each should be planted to maximize profits?