Use Green's Theorem to find the counterclockwise circulation and outward flux for the field F = (x-4y)i + (5y - 4x)j and curve C: the square bounded by x = 0, x = 2, y = 0, y = 2. The flux is (Simplify your answer.) The circulation is (Simplify your answer.)
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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 + 3, z²) and the net is decribed by the equation y = √1-x²-2², y ≥ 0, 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+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 + 7, z?) and the net is decribed by the equation y = V1 – x? – z?, y 2 0, and oriented in the positive y- V = direction. (Use symbolic notation and fractions where needed.) v • dS =
- Use Green's Theorem to find the counterclockwise circulation and outward flux for the field F = The flux is (Simplify your answer.) (4y2-9x2)i+ (9x² + 4y2) j and curve C: the triangle bounded by y = 0, x=3, and y=x.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 =(b) Use Green's theorem to calculate the circulation of F around the triangle with verticcs (2, 0), (0, 3), (–2,0) oricntcd counterclockwisc where F = (2x²+3y)i+ (2.x + 3y²)j.
- Use Green's Theorem to find the counterclockwise circulation and outward flux for the field F = (y² - 5x²)i + (5x² + y²) j and curve C: the triangle bounded by y=0, x= 3, and y = x. The flux is (Simplify your answer.)Fill in the table and then sketch the vector field. y F(x, y) = -2 -2 -2 2 -2 -2 -2 3- -2- 2. /- 2.Use Green's Theorem to find the counterclockwise circulation and outward flux for the field F = (2y² - 9x²)i + (9x² + 2y²) j and curve C: the triangle bounded by y = 0, x= 3, and y=x. The flux is. (Simplify your answer.)
- The scalar product 0v is 0.The figure shows a vector field F and three paths from P (-3,0) to Q= (3,0). The top and bottom paths T and B comprise a circle, and the middle path M is a line segment. Determine whether the following quantities are positive, negative, or zero, or answer true or false. Be sure you can explain your answers. (Click on graph to enlarge) (a) F dr is ? (b) F- dř is ? F. dr is ? (c) F-dr is 2 () (e) ? v True or False: F- dr () ? v True or False F is a gradient field.