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Find the circulation of F = xi +8zj + 3yk around the closed path consisting of...
Find the circulation and flux of the field F around and across the closed semicircular path...
Find the circulation and flux of the field F around and across the closed semicircular path that consists of the semicircular arch r(t)=(a cost)i +(a sint)j, Ostst, followed by the line segment rz(t)=ti, -ast sa F = x’i+y? j
Find the line integrals of F=3yi + 4xj + 2zk from (0,0,0) to (1,1,1) over each...
Find the line integrals of F=3yi + 4xj + 2zk from (0,0,0) to (1,1,1) over each of the following paths. a. The straight-line path Cy: r(t) = ti + tj + tk, Osts 1 b. The curved path Cz: r(t) = Osts1 c. The path C, UC, consisting of the line segment from (0,0,0) to (1,1,0) followed by the segment from (1,1,0) to (1,1,1) (0,0,0) (1.1.1)
Given that F = ra,-xzay-ya, calculate the circulation of F around the (closed) path shown in...
Given that F = ra,-xzay-ya, calculate the circulation of F around the (closed) path shown in Figure 3.11.
a. The line integral of F over the straight-line path C1 is 3 (Type an integer or a simplified fraction) Find the line integrals of F-yi + 3xj +2zkhom (0.0.0) to (1.1.1) over each of the followin...
a. The line integral of F over the straight-line path C1 is 3 (Type an integer or a simplified fraction) Find the line integrals of F-yi + 3xj +2zkhom (0.0.0) to (1.1.1) over each of the following paths a. The straight-ine path Ct rt)-ti+j+ tk, 0sts1 ь. The curved path C2 r(t)-ti+t2jtt4k.0sts1 c. The path C3UC consisting of the line segment from (0,0.0) to (1,1,0) followed by the segment from (1.1,0) to (1,1,1 10 b. The line integral of F...
Use Green's theorem in the plane to evaluate 4 K= anti-clockwise around the closed path C given by the curves: x-0,...
Use Green's theorem in the plane to evaluate 4 K= anti-clockwise around the closed path C given by the curves: x-0, -1 2 y 2 -2 r 2, -TT/2 <0< T/2, x = 0, 2 2 yz 1, r= 1, TT/2 2 0 2 -T/2 Evaluate the line integral ass a double integral using polar coordinates. Your answer should consist of a single number accurate to five decimal digits or as an exact rational expression. For example: 10.13906368 OR rounded...
Use Green's theorem in the plane to evaluate - tv3-ry)ds+(}p2_89+12y4) dy K= anti-clockwise around the closed path...
Use Green's theorem in the plane to evaluate - tv3-ry)ds+(}p2_89+12y4) dy K= anti-clockwise around the closed path C given by the curves: x 0, -1 2 y -2 r = 2, -TT/2 < 0 < T/2. x = 0, 2 2 yz 1, r 1, TT/2 2 0 2 -TT/2 Evaluate the line integral as a double integral using polar coordinates. Your answer should consist of a single number accurate to five decimal digits or as an exact rational expression....
The value of the line integral around the closed path in the figure(Figure 1) is 1.76x10-5T...
The value of the line integral around the closed path in the figure(Figure 1) is 1.76x10-5T m. Part A What is the direction (in or out of the page) of 13? into the page O out of the page Submit Request Answer Figure < 1 of 1 Part B What is the magnitude of 13? Express your answer to two significant figures and include the appropriate units. 1 - 18 A 1. - 20 A Is = Value Units Submit...
(6) Show that F(x, y) = (x+y)i + (**)is conservative. (a) Then find such that S...
(6) Show that F(x, y) = (x+y)i + (**)is conservative. (a) Then find such that S = F (potential function). (5) Use the results in part(a) to cakulae ( F. ds along C which the curve y = a* from (0,0) to (2,16). (2) Use Green's Theorem to evaluate 1. F. ds. F(1,y) =(yº+sin(26))i + (2xy2 + cos y)and C is the unit circle oriented counter clockwise (6) Evaluate the surface integral || 9. ds. F(x,y,z) = xi +++where S...
The simulation (linked below) shows two long, straight wires wre #1 les on the z aos and carries arrent İl in the +Z direction. wre #2 is paralel to w re '1 and cames current a in the t di...
The simulation (linked below) shows two long, straight wires wre #1 les on the z aos and carries arrent İl in the +Z direction. wre #2 is paralel to w re '1 and cames current a in the t direction Wire #2 is displaced from wire #1 by distance D which is variable. By default, D = 4 m. The samulation shows a mathematical path of orular shape that lies in the xy pane and is centered at the origin....
Question 2 (30 points) Integrate f(x, y,2) xzv2-z2 - y2 over the path C, which consists of two curves, C1 and C2 from (...
Question 2 (30 points) Integrate f(x, y,2) xzv2-z2 - y2 over the path C, which consists of two curves, C1 and C2 from (1, 0, 0) to (1,0, 0), then to (-1,3, 0). Curve C1 is only half of the circle2 Curve C2 is a straight-line segment. The parametric equation for G is G: r! (t)-cos t î + sin t k, 0 π Find the line integral: Jcf(x. y,z)ds - (25 points) C2 (-1,3,0)
Question 2 (30 points) Integrate...
Find the circulation and flux of the field F around and across the closed semicircular path that consists of the semicircular arch r(t)=(a cost)i +(a sint)j, Ostst, followed by the line segment rz(t)=ti, -ast sa F = x’i+y? j
Find the line integrals of F=3yi + 4xj + 2zk from (0,0,0) to (1,1,1) over each of the following paths. a. The straight-line path Cy: r(t) = ti + tj + tk, Osts 1 b. The curved path Cz: r(t) = Osts1 c. The path C, UC, consisting of the line segment from (0,0,0) to (1,1,0) followed by the segment from (1,1,0) to (1,1,1) (0,0,0) (1.1.1)
Given that F = ra,-xzay-ya, calculate the circulation of F around the (closed) path shown in Figure 3.11.
a. The line integral of F over the straight-line path C1 is 3 (Type an integer or a simplified fraction) Find the line integrals of F-yi + 3xj +2zkhom (0.0.0) to (1.1.1) over each of the following paths a. The straight-ine path Ct rt)-ti+j+ tk, 0sts1 ь. The curved path C2 r(t)-ti+t2jtt4k.0sts1 c. The path C3UC consisting of the line segment from (0,0.0) to (1,1,0) followed by the segment from (1.1,0) to (1,1,1 10 b. The line integral of F...
Use Green's theorem in the plane to evaluate 4 K= anti-clockwise around the closed path C given by the curves: x-0, -1 2 y 2 -2 r 2, -TT/2 <0< T/2, x = 0, 2 2 yz 1, r= 1, TT/2 2 0 2 -T/2 Evaluate the line integral ass a double integral using polar coordinates. Your answer should consist of a single number accurate to five decimal digits or as an exact rational expression. For example: 10.13906368 OR rounded...
Use Green's theorem in the plane to evaluate - tv3-ry)ds+(}p2_89+12y4) dy K= anti-clockwise around the closed path C given by the curves: x 0, -1 2 y -2 r = 2, -TT/2 < 0 < T/2. x = 0, 2 2 yz 1, r 1, TT/2 2 0 2 -TT/2 Evaluate the line integral as a double integral using polar coordinates. Your answer should consist of a single number accurate to five decimal digits or as an exact rational expression....
The value of the line integral around the closed path in the figure(Figure 1) is 1.76x10-5T m. Part A What is the direction (in or out of the page) of 13? into the page O out of the page Submit Request Answer Figure < 1 of 1 Part B What is the magnitude of 13? Express your answer to two significant figures and include the appropriate units. 1 - 18 A 1. - 20 A Is = Value Units Submit...
(6) Show that F(x, y) = (x+y)i + (**)is conservative. (a) Then find such that S = F (potential function). (5) Use the results in part(a) to cakulae ( F. ds along C which the curve y = a* from (0,0) to (2,16). (2) Use Green's Theorem to evaluate 1. F. ds. F(1,y) =(yº+sin(26))i + (2xy2 + cos y)and C is the unit circle oriented counter clockwise (6) Evaluate the surface integral || 9. ds. F(x,y,z) = xi +++where S...
The simulation (linked below) shows two long, straight wires wre #1 les on the z aos and carries arrent İl in the +Z direction. wre #2 is paralel to w re '1 and cames current a in the t direction Wire #2 is displaced from wire #1 by distance D which is variable. By default, D = 4 m. The samulation shows a mathematical path of orular shape that lies in the xy pane and is centered at the origin....
Question 2 (30 points) Integrate f(x, y,2) xzv2-z2 - y2 over the path C, which consists of two curves, C1 and C2 from (1, 0, 0) to (1,0, 0), then to (-1,3, 0). Curve C1 is only half of the circle2 Curve C2 is a straight-line segment. The parametric equation for G is G: r! (t)-cos t î + sin t k, 0 π Find the line integral: Jcf(x. y,z)ds - (25 points) C2 (-1,3,0)
Question 2 (30 points) Integrate...
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