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Calculate ∂ω/∂z for ω=e -2xe((z^2)y)
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- A particle starts at the point (−4, 0), moves along the x-axis to (4, 0), and then along the semicircle y = 16 − x2 to the starting point. Use Green's Theorem to find the work done on this particle by the force field F(x, y) = 5x, x3 + 3xy2 .Why is integration used to find the work done by a variable force?Find the unit vector u along which the rate of change of the function f(x, y) = x 2 + xy3 at the point (2,1) is maximum. What is this maximum rate of change?
- Compute the work W against the earth's gravitational field required to move a satellite of mass m = l 000 kg along any path from an orbit of altitude 4000 km to an orbit of altitude 6000 km.Let Y be a uniform r.v. on the interval (0,1). find E[Y^k] using method of MGF. (Moment Generated Function Be detail. ThanksSketch the direction field of the differential equa tion.Then use it to sketch a solution curve that passes through thegiven point. y' = x - xy , (1,0)