6. Find the circulation and outward flux of the velocity field = sin yi + cos y) over the square cut from the first quadrant by the lines and y = .
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- 5. The electric potential is V volts at any point (x, y) in the xy = e=2# cos(2y). Distance is measured in feet. plane and V (a) Find the rate of change of the potential at the point (0, x) in the direction of the unit vector cos T î + sin r ĵ. (6) Find the direction and magnitude of the greatest rate of change of V at (0. Įr).Find Components of the Acceleration For the curve defined by 7(t) = (e-t cos(t), eʻ sin(t)) find the unit tangent vector, unit normal vector, normal acceleration, and tangential acceleration at t = 3 T(플) - N(플) - 3 3 AN =Calculate directional derivatives and gradients in three dimensions. Find an equation for the tangent plane to the surface z + 4 = xy° cos(2) at the point (4, 1, 0).
- Sketch the curve with the vector equation r(t) = cos(t)i − cos(t)j + sin(t)k. Show the direction of increasing t with an arrow drawn on your curve.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 = Incorrect6) Let f(xxx)=3xy²-x² be a potential function of a fluid velocity field. a) Find the magnitude of the greatest rate of change for f(x,y) at (1,3). Please provide a physical interpretation. b) Find the direction angles for this greatest rate of change. Express angles in degrees. Please provide a physical interpretation.
- show full and complete procedure HANDWRITTEN onlyd Compute : CSC Csclevx dx - csc cot e А. 2/x В. cSC cot evx). evx csc С. 2 evt D. -csc cot 2/xA bee with a velocity vector r' (t) starts out at (7, -3, 7) at t = 0 and flies around for 6 seconds. Where is the bee located at time t = 6 if [°r' (Use symbolic notation and fractions where needed.) r' (u) du = 0 location: