Verify Green's Theorem by evaluating both integrals [ 1² dx + x² oy = √ √ (2x - 3) da dA dy əx JR for the given path. C: square with vertices (0, 0), (8, 0), (8, 8), (0, 8) [x² dx + x² dy = [ le/ (x - 2) = [ dA dA əx
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- Compute the intersections of the curve xy = 1 and the lines x +y = 5/2, x+y = 2, x+y = 0, x=0 , x=1 in the affine space and then in the projective space by using homogeneous coordinates. Complex solutions are valid. Please show your steps for both affine space and in project space. Box your final answer.Verify the Cauchy-Schwarz Inequality for u = (1, −1, 3) and v = (2, 0, −1).The vectors in Z22 are [ O, O] , [ O, l], [l, O ], and [l, l ]. (How many vectors doesZn 2 contain, in general?)
- Setx = [ 0 : 4, 4,−4, 1, 1]' and y = ones(9, 1) Use the MATLAB function norm to computethe values of ||x||, ||y||, ||x + y|| and to verifythat the triangle inequality holds. UseMATLABalso to verify that the parallelogram law||x + y||2 +||x − y||2 = 2(||x||2 + ||y||2)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-planeThe diagram shows a small block B, of mass 0.2kg, and a particle P, of mass 0.5kg, which are attached to the ends of a light inextensible string. The string is taut and passes over a small smooth pulley fixed at the intersection of a horizontal surface and an inclined plane.The block can move on the horizontal surface, which is rough. The particle can move on the inclined plane, which is smooth and which makes an angle of θ with the horizontal where tanθ = 3/4The system is released from rest. In the first 0.4 seconds of the motion P moves 0.3m downthe plane and B does not reach the pulley.(a) Find the tension in the string during the first 0.4 seconds of the motion.(b) Calculate the coefficient of friction between B and the horizontal surface.
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