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- 1. Solve by Cramer’s rule 3x + y + 4z = 11 4x – 4y + 6z = 11 6x – 6y = 3 2. Find the volume of tetrahedron given the following (1, 0, 1), (0, 1, 0), (0, 0, 1), and (1, 1, 1).what local linearizatoin of the function f(x,y) sin(xy) + cos(x/y) at (pie/4, 1) (show all steps please)How would I solve ∭xzdV, where E is bounded by the planes z = 0, z=y, and the cylinder x2 + y2 = 1 in the half-space y ≥ 0 ? Thanks for you help in advance. :)
- True or False and explain1- For any two non parallel and non orthogonal vectors a and b with angle θ between them, it holds that cosθ(a.b) = sinθ(axb). 2- Ifr(t)=⟨−4cos(2t),3sin(3t),ln(2t)⟩,then the ∫r(t)dt is equal to⟨−2sin(2t),−cos(3t),tlnt−t⟩+C,where C is a vector constant of integration.How would I solve ∭xzdV, where E is bounded by the planes z = 0, z=y, and the cylinder x2 + y2 = 1 in the half-space y ≥ 0 ? Any help would be greatly appreciated. :)Show that except in degen-erate cases, (u * v) * w lies in the plane of u and v, whereas u * (v * w) lies in the plane of v and w. What are the degenerate cases?
- IntegrateF(x, y, z) = z, over the portion of the plane x + y + z = 4 that lies above the square 0<= x <= 1, 0<=y<=1, in the xy-planeFind the work done by the force field 2 2, , , 3 , x y z z z y z z x F in moving a particle along the line segment from (0, 2, 0) to (−4, 3, 2).Suppose R3 has the Euclidean inner product. Apply the Cauchy Schwarz inequality to the vectors u = (a, b) and v = (cos θ, sin θ) to show that | a cos θ + b sin θ |2 ≤a2 + b2. Note: Do not skip any step to arrive at the result, apply the Cauchy Schwarz inequality to arrive at the result (In the image the enunicoado is better seen)
- Suppose the JPDF of X, Y is f(x,y)={1K(x2+y2)0<x<2,0<y<20otherwisef(x,y)={1K(x2+y2)0<x<2,0<y<20otherwise Find K so that fXY(x,y)fXY(x,y) is a valid JPDFFind the particular number of orthogonal transectories of x2+cy2=1 passing through the point (2,1)Let u = (2, -3, 4) and v = (-2, 1,3). What is the projection of u onto v (proj v u) and the scalar of u onto v (scalv u)? What is the cross product u x v? What is the area of a parllelogram that has two adjacent sides u and v?