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- Plot the vector field F = (y,sinx) using the viewing window (-2pi,2pi)x(-2pi,2pi).F = (x² - y)i + + (4z)j + (x²)k Find the curl (curl calculation) of the vector field?A net is dipped in a river. Determine the flow rate of water across the net if the velocity vector field for the river is given by v=(x-y,z+y+7,z2) and the net is decribed by the equation y=1-x2-z2, y20, and oriented in the positive y- direction. (Use symbolic notation and fractions where needed.)
- A net is dipped in a river. Determine the flow rate of water across the net if the velocity vector field for the river is given by v = (x - y, z + y + 6, z? ) and the net is decribed by the equation y = 1 – x - z', y 2 0, and oriented in the positive y- direction. (Use symbolic notation and fractions where needed.) · dS = IncorrectA charged particle begins at rest at the origin. Suddenly, a force causes the particleto accelerate according to the vector function a(t) = ⟨ sin(t) , 6t , 2cos(t)⟩Find functions for the velocity, speed and position of the particle at time tConsider the vector field. F(x, y, z) = (sex sin(y), 2e sin(z), 6e² sin(x)) (a) Find the curl of the vector field. curl F = (b) Find the divergence of the vector field. div F =
- Consider the vector field. F(x, y, z) = (9ex sin(y), 2e sin(z), 4e² sin(x)) (a) Find the curl of the vector field. curl F = (b) Find the divergence of the vector field. div F =Find the curl of the vector fieldF (6y cos(x), 7x sin(y)) curl F =A net is dipped in a river. Determine the flow rate of water across the net if the velocity vector field for the river is given by = (x - y, z + y + 9, z) and the net is decribed by the equation y = V1-x - z, y 2 0, and oriented in the positive y- direction. (Use symbolic notation and fractions where needed.) V. dS =
- Using a graphic calculator, plot the vector field F(x, y) = j. Explain briefly with words why the plot x²+y? has this shape.A net is dipped in a river. Determine the flow rate of water across the net if the velocity vector field for the river is given by v = (x - y, z + y + 9, z?) and the net is decribed by the equation y = V1 - x² – z7, y > 0, and oriented in the positive y- direction. (Use symbolic notation and fractions where needed.) v · dS = 10n IncorrectFind the curl of the vector field F = (2y cos(x), 4x sin(y)) curl F =