8) Show that the graph of +692 +9z²&exy 6x z-12yz-2x - 4y +6z+1=0 is degenerate quadric...
3. (20 p.) Let 2x-2y + 6z = 18 , 3y =-6x + 15 and -9z + x +2y-7-0. Solve this linear equation system for variable y by using Cramer rule.
8) Find the circulation of F =(6x+5 y,4y+3z, 2x+1z) around a square of side 7, centered at (1,2,1), lying in the plane 4x+1y+6z = 12 , and oriented clockwise when viewed from the origin 8) Find the circulation of F =(6x+5 y,4y+3z, 2x+1z) around a square of side 7, centered at (1,2,1), lying in the plane 4x+1y+6z = 12 , and oriented clockwise when viewed from the origin
): Classify and sketch the quadric surface x2 +2x+92-.2+22+1 = 0, labeling at least 3 points on the surface. Show the trace of the graph in 3 planes. ): Classify and sketch the quadric surface x2 +2x+92-.2+22+1 = 0, labeling at least 3 points on the surface. Show the trace of the graph in 3 planes.
Define T : R3 → R2 by T(x,y,z) = (2x +4y +3z,6x) Show that T is linear.
Minimize the objective function 1/2x+3/4y subject to the constraints (In graph form please) 2x+2y>=8 3x+5y>=16 x>=0, y>=0
For 18-20 graph the following equations. 18. [6] 2x-4y+3z = 12 19. [6] x2 +4y2 +9z2 =1 20. [6] z 2x2 + y7 For 18-20 graph the following equations. 18. [6] 2x-4y+3z = 12 19. [6] x2 +4y2 +9z2 =1 20. [6] z 2x2 + y7
Find the volume of the solid by subtracting two volumes, the solid enclosed by the parabolic cylinders y = 1 − x2, y = x2 − 1 and the planes x + y + z = 2, 6x + 4y − z + 16 = 0.
Show that the line with equation 2x-5y-1=0 is perpendicular to the line with equation 4y+10x=3.
Consider the vector field F(x, y, z) = 8x^2 + 3y, −5x^2y − 4y^2, 6x^2 + 7y − 8 which is defined on all of double-struck R3, and let F be the rectangular solid region F = {(x, y, z) | 0 ≤ x ≤ a, 0 ≤ y ≤ b, −1 ≤ z ≤ 1} where a > 0 and b > 0 are constants. Determine the values of a and b that will make the flux of F...
Please solve all questions 1. Let 0 : Z/9Z+Z/12Z be the map 6(x + 9Z) = 4.+ 12Z (a) Prove that o is a ring homomorphism. Note: You must first show that o is well-defined (b) Is o injective? explain (c) Is o surjective? explain 2. In Z, let I = (3) and J = (18). Show that the group I/J is isomorphic to the group Z6 but that the ring I/J is not ring-isomorphic to the ring Z6. 3....