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4. Use Green's Theorem to calculate the work done by force F on a particle that...
Use Green's Theorem to calculate the work done by the force F on a particle that is moving counterclockwise around the closed path F(x,y) = (ex – 4y)i + (ey + 7x)j C: r = 2 cos(0) -11 POINTS LARCALC11 15.4.028.MI. MY NOTES ASK YOUR TEACHER Use Green's Theorem to calculate the work done by the force F on a particle that is moving counterclockwise around the closed path F(x, y) = (5x2 + y)i + 3xy?j C: boundary of...
Use Green's Theorem to calculate the work done by the force F on a particle that is moving counterclockwise around the closed path C. F(x, y) = (3x2+y)i + 3xy2jC: boundary of the region lying between the graphs of y = √x. y = 0, and x = 1
Q2: Use Green's Theorem to find the work done by the force field F (e* -y3) i+ (cosy+ x3)j particle that travels once around the circle x2 + y2 = 1 in the counterclockwise direction. on a Q3: Q2: Use Green's Theorem to find the work done by the force field F (e* -y3) i+ (cosy+ x3)j particle that travels once around the circle x2 + y2 = 1 in the counterclockwise direction. on a Q3:
12. (5 Points) Use Green's Theorem to evaluate the line integral dr +(7x + cos(y?)) dy, +5y where C is the path around the triangle with vertices (0,0), (4,0), (0,6), oriented counterclockwise. 12. (5 Points) Use Green's Theorem to evaluate the line integral dr +(7x + cos(y?)) dy, +5y where C is the path around the triangle with vertices (0,0), (4,0), (0,6), oriented counterclockwise.
Select statements that are correct. Green's Theorem calculate the circulation in R^2 which convert the line integral into a double integral over the region Din R^2 formed by the simple and closed curve C To compute the work done by a vector field in moving a particle around a simple and closed curve Cin R^2, we apply the Green's Theorem U line integral of a vector field computes the work done to move a particle along a space curve C...
5. Let F (y”, 2xy + €35, 3yes-). Find the curl V F. Is the vector field F conservative? If so, find a potential function, and use the Fundamental Theorem of Line Integrals (FTLI) to evaluate the vector line integral ScF. dr along any path from (0,0,0) to (1,1,1). 6. Compute the Curl x F = Q. - P, of the vector field F = (x4, xy), and use Green's theorem to evaluate the circulation (flow, work) $ex* dx +...
QUESTION 10 (a) Verify that the force field F = yi+zj+4k s conservative. By finding its potential function ф, evaluate the work done by F in moving a particle over the path from (6 marks) Apply Green's Theorem to evaluate the line integral фу2dr+x2dv in which C is (b) the boundary of a triangle made by x-0, x+y-1, y-0 (6 marks)
Please solve this. (Calc 3) Using Green's Theorem, compute the counterclockwise circulation of F around the closed curve C. F=(x+y) i + (x-y)j; C is the rectangle with vertices at (0,0), (7,0), (7,3), аnd (0,3) ОА. – 42 Ов. о Ос.
F(x, y, z)-(y-re)it(cos(2y2)-x)/ 1s the force field acting on a particle moving around the rectangular path from A(0.1) to B(0,3) depicted in Figure 1 Figure 1. Rectangular path of the particle. Compute the work done by the force in this field; Using line integral (if the integral is difficult to evaluate, then use Matlab) b. Also using Green's Theorem without computer aid. Compare your results. a. F(x, y, z)-(y-re)it(cos(2y2)-x)/ 1s the force field acting on a particle moving around the...
(a) (15 F-(1+9) 9. points) Apply Green's theorem to evaluate φ F.nds, where (x2 +y)j, of a triangle with vertices (1,0), (0,1). (-1,0) oriented in the counterclockwise direction n is the outward-pointing normal vector on , and C is the boundary (b) (15 points) Evaluate directly the line integral p F- nds in part (a). (a) (15 F-(1+9) 9. points) Apply Green's theorem to evaluate φ F.nds, where (x2 +y)j, of a triangle with vertices (1,0), (0,1). (-1,0) oriented in...