hwsol_6 - Homework Assignment 6(10.5(10.6 Solutions Page...

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Unformatted text preview: Homework Assignment 6- (10.5)(10.6) - Solutions Page 834: 41*, 52*, 53, 54*, 57, 58* 41. x ! y ! z " 4 1 2 3 4 z 1 2 3 4 y 1 2 3 4 x x ! y ! z " 4 in the 1st octant 2 4 6-2-1 1 2 y-2-1 1 2 x 52. z " ! 2 x ! 1 0.5 1 0.5 1 y 0.4 x z " ! 2 x ! 1 in the first octant-1 1 3-1-0.5 0.5 1 y-1-0.5 0.5 1 x z " ! 2 x ! 1 54. 3 x ! y ! z " 2, and 2 x ! 3 y ! z " ! 1 Add two equations: 5 x ! 2 y " 1, and solve y in terms of x : y " 1 2 ! 5 x ! 1 " " 5 2 x ! 1 2 Solve z in terms of x from the 1st equation: z " 3 x ! y ! 2 " 3 x ! 1 2 ! 5 x ! 1 " " 11 2 x ! 1 2 . The parametric equations of the line: x " t y " ! 1 2 ! 5 2 t z " ! 1 2 ! 11 2 t 58. P ! 1,3,0 " , plane: 3 x ! y ! 5 z " 2 Pick a point in the plane: Q 0, 2, 0 . Form the vector QP "# 1,1,0 $ . The normal vector of the plane is: n % "# 3,1, ! 5 $ . 1 d % " comp n % QP " QP # n % || n % || " |3 ! 1| 3 2 ! 1 ! 5 2 " 4 35 Page 845: without using a calculator: 6. z " 4 ! y 2 (trace: x " 2) When x " 2, the curve is a parabola: z " 4 ! y 2 ....
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hwsol_6 - Homework Assignment 6(10.5(10.6 Solutions Page...

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