Week9 Calculus - Section 9.1: 6. Because it is a comparison...

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Unformatted text preview: Section 9.1: 6. Because it is a comparison of immigration vs. time and a model which is a constant is used. x =1 4 x - 5 y = -11 4 x - 5(5 - 2 x) = -11 2x + y = 5 y 5 2x = - 10. 4(1) - 5 y = - 11 y = 3 Answer (1,3) 16. A 2 x - 3 y = -7 5 x + 4 y = 17 18. -23 y = -69 Answer (1,3) (5) 10 x - 15 y = -35 - 2) -10 x - 8 y = -34 ( y 3, 2 x 3(3) -7 x D 1 = - = = 3x y 3x y + = -2 (-1) - - = 2 2 2 2 2 x y x y + = 0 + = 0 - x = 2 x = -2 2 2 24. 2 2 -2 y + =0 y 2 = 2 2 Answer (-2, 2) 3 x + 2 y = 5 (2) 6 x + 4 y = 10 32. 6 x + 4 y = 8 8 10 InconsistentSystem Section 9.5: x 2 + y 2 = 45 (3) 2 + (-6) 2 = 45 & (-6) 2 + (3) 2 = 45 4. x + y = -3 - 6 3 - 3 & 3 - 6 - 3 + = + = y = ( x +& 3) 2 2 12. x + 2 y = -3 x + 2( x + 3) 2 = -2 2 x 2 + 13 x + 20 = 0 (2 x + 5)( x + 4) = 0 y 1 = x= -5 or - 4 2 -5 1 + 2 y = - 2 y = or - 4 + 2 y = -2 2 4 -5 1 SolutionSet , ), (-4,1) ( 2 4 x 2 + 2 y 2 =& 9 3 2 x 2 + 4 y 2 = 18 3x 2 - 4 y 2 = 27 y = 0, (-3) 2 + 2 y 2 = 9 y 0 = 5 x 2 = 45 (2) x2 = 9 x= 3 22. 3 x 2 - 4 y 2 = 27 (3) 2 + 2 y 2 = 9 SolutionSet { (3, 0), (-3, 0)} x + y = 10 2 2 x = (10 - y ) y=4 x - y = 20 (10 - y ) 2 - y 2 = 20 52. x + 4 = 10 x = 6 SolutionSet ( 6, 4 ) y = x2 x 2 + y 2 =& 90 x 2 + ( x 2 ) 2 =* 90 x 4 + x 2 - 90 = 0 y = 10i ( x 2 + 10)( x 2 - 9) = 0 y = i 10) 2 *( 58. x =i 10 x= 3 y=9 SolutionSet i 10,10i , -i 10,10i , ( 3,9 ) , ( -3,9 ) {( )( ) } Section 9.2: 2 - 5 6 16 -37 0 4 4. -1 2 4 - 1 2 7 1 3 3 7 1 8. 4 x - 2 y + 3z - 4 = 0 3x + 5 y + z - 7 = 0 5x - y + 4 z - 7 = 0 4 2 3 4 5 1 7 3x4 3 1 4 7 5 10. 2 1 3 12 -3 0 10 4 0 -4 -11 5 2 x + y + 3 z = 12 4 x - 3 y = 10 5 x - 4 z = -11 2 x - 5 y - 10 = 0,3 x + y - 15 = 0 2 -5 10 1 ( R1 ) 3 20. 1 -15 2 5 ( R2 ) + R1 2 1 0 5 0 1 0 -5 1 2 3 1 5 - ( 3R1 ) R2 + ~ -15 -5 1 2 5 2 ( R2 ) 17 0 17 0 2 -5 1 2 5 0 1 0 ( 5, 0 ) x + y = 1, 2 x - z = 0, y + 2 z = -2 1 1 1 0 1 1 1 0 0 -1 0 swapR2 & R3 1 1 2 -2 0 0 1 28. 1 0 -2 3 (- R2 ) + R1 & ( R2 ) + R3 1 2 - 2 0 0 1 -3 0 Section 9.7: 0 1 2 - 2 ( 1R1 ) R3 - + -1 0 (2 R3 ) R1 & ( 2 R3 ) R2 + - + 1 1 0 1 0 1 2 - 2 -1 -1 -1 0 1 0 0 -3 e 0 1 0 4 e e (-3, 4, -3) 0 1 -3 e 0 0 5 - 2. 1 3 1 4 x w + 3 6 0 y + 2 1 = - 3 0 x = 6, y = -2, w = 2, z = 8 z 4 1 8 - 9 6 2 8. 2 x3 4 1 8 9 - 4 3 2 6 6 + = 16. - - - 8 2 4 7 12 9 5 - 4k - 8 y k + 6 y k - 14 y 2 6 z - 3x z + 5 x 4 z - 8 x - = 20. 2k + 5a k + 6a -2k - a 4 - 4 - 4 m + 2 n m - 2 n 8m + 4 n - 6 1 5 x 30. -1(6) + 5(2), 7(6) + 0(2) 7 2 0 4 42 2 - - 9 2 1 16 x - + - + + + = 36. 1 - 9(2) 2( 1) 1(4),3(2) 0 0 3 6 0 0 4 4 - - -2 5 4 1 20 10 -8 x = 44. 3 0 - 1 3 6 15 15 9 1 0 56a. 4 0 4 3 3 1 1 4 0 2 0 1 4 1 4 1 1 3 1 5 5 47.5 57.75 8 10 27 38.75 0 12 x 10 = 95 81 1 15 12 15 12 5 6 0 1 0 b. 4 0 4 3 3 1 1 4 0 2 0 1 4 1 4 1 1 3 1 0 ( 20 200 50 60 ) = ( 220 890 150 125 70 ) x 1 0 5 5 1100 8 7120 10 = 1500 10 c. ( 220 890 150 125 70 ) x 12 12 1500 15 5 6 350 1100 8900 1800 1875 420 1 1 1 ( + 1 1 1 62. 1 1 1 + 1 ( 1 1 1 1 2 1 2 1 ) = + + 1 1 2 1 2 1 1 1 1 1 1 2 + ) + 1= 1 1 1 1 2 1 3 3 = 1 3 3 2 3 3 = 3 2 3 Section 9.3: 6. y 8 2 = y ( y ) - (2)(8) = y 2 - 16 y 2 -1 4 10. 3 0 1 -2 1 4 M 12 (12 - 2)( 1)3 - 14 = - - = M 22 = (8 - -8)(-1) 4 =* 16 M 32 = (2 - 12)(-1)5 = 10 3 2 0 0 1 x 18. 2 0 0 M 13 = (0 - 2)(-1) 4 = -2 M 23 = (0 - 4)(-1)5 = 4 M 33 = (3 - 0)(-1)6 = 3 -2(0) + 4( x) + 3(0) = 4 x 4 3 0 2 0 1 = 5 26. -3 x -1 M 13 = (2 x + 3)(-1) 4 = (2 x + 3) M 23 = (4 x + 9)(-1)5 = -4 x - 9 x = -2 M 33 = (-6)(-1)6 = -6 0(2 x + 3) + 1(-4 x - 9) + (-1)(-6) = -4 x - 3 - 4 x 3 5 - = -4 1 4 2 0 1 C3- 2)* C1 ( + 40. 0 2 4 -12 1 D = (1) (-1)5 = 16 -8 2 -12 1 4 0 0 1 -8 2 4 R3allzeroexceptC3 4 x + 3 y = -7, 2 x + 3 y = -11 46. x= D = (12 - 6) = 6, Dx = (-21 - (-33)) = 12 Dy = (-44 - (-14)) = -30 D 12 D -30 = = 2, y = = = -5 (2, -5) Dx 6 Dy 6 2 x - y + 4 z = -2,3 x + 2 y - z = -3, x + 4 y + 2 z = 17 2 -1 4 -2 -1 4 2 -2 4 D = 3 2 -& D =63; Dx = - 2 - 1 3 1 Dx= - 189; Dy= 3 - 3 - 1 Dy = 252; 1 4 2 17 4 2 1 17 2 54. 2 -1 -2 -189 252 126 Dz = 3 2 -3 Dz = 126 x = = -3; y = = 4; z = = 2 ( -3, 4, 2 ) 63 63 63 1 4 17 x + 2 y = 10,3 x + 4 z = 7, - y - z = 1 1 2 0 10 2 0 1 10 0 1 2 10 D = 3 0 4 = 10; Dx = 7 0 4 = 62; Dy = 3 7 4 = 19; Dz = 3 0 7 = -29 64. 0 -1 -1 1 -1 -1 0 1 -1 0 -1 1 x= 62 19 -29 ; y = ;z = 10 10 10 ( 62 19 -29 , , ) 10 10 10 Section 9.6: 26. D 6x + y (1,5) 6(1) 5 11 + = (6,8) 6(6) 8 44 + = + = 63. (1, 2) 6(1) 2 8 (9,1) 6(9) 1 55 + = Minimum (1, 2) Maximum (9,1) ...
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