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- Consider z = z (x, y) Find (∂z / ∂x )and (∂z / ∂y )by implicit derivation and confirm that the result obtained1. 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).△XYZ is given with X(2, 0), Y(0, −2), and Z(−1, 1). Which of the following can be used to prove that △XYZ is isosceles?
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- Find the angle between the planes 3x – 2y + z + 4 = 0 and x + 4y – 3z – 3 = 0. Express your answers in DMS.Integrate H(x, y, z) = x2sqrt(5 - 4z), over the parabolic dome z = 1 - x2 - y2, z>=0.A _____ is the set of points (x, y) in a plane such that the difference in distances between (x, y) and two fixed points (called _____) is a positive constant.