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- 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 = (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 =Match the vector fields: ? curl(F)=0 ? curl(F)=2 V 2. div(F)=0, ? curl(F)=0 ? V 3. div(F)=-1, 1. div(F)=4, ? curl(F)=1 V 4. div(F)=-2, V 5. div(F)=-2, curl(F)=-1 ? curl(F)=3 6. div(F)=2, A D B E C 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 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 IncorrectDefine two vector functions 7(t) = 8 sin(t)i + 6 cos(t)+ (t - 2)k ü(t) = 6 sin(t)i + 8 cos(t)j + (t – 2)k Compute 7 (t) ü(t)If r(t) = acoswt+bsinwt, where a and b are constant vector, show that r(t)xr'(t)=wa x b
- Calculate the integration of (A" - dlP2P1 from point P1 (2,1, -1) to P2 (8,2, -1) of the vector function given as A° = ye"x + xe¯y on the line joining the two points.Please solve thisShow that the vector-valued function shown below describes the function of a particle moving in a circle of radius 1 centered at a point (5,5,3) and lying in the plane 3x+3y-6z = 12
- 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 - z?, y > 0, and oriented in the positive y- direction. (Use symbolic notation and fractions where needed.) v • dS = IncorrectA 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 = Incorrect4. Determine the directional derivatives of +V3 sin" xy $(x, y) =tan at the point (1,1) in the direction of the vector 31-2j .
