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(1 pt) The figure below open cylindrical can, S, standing on the xy-plane. (S has a bottom and si...
(1 point) The figure below open cylindrical can, S, standing on the xy-plane. (S has a bottom and...
(1 point) The figure below open cylindrical can, S, standing on the xy-plane. (S has a bottom and sides, but no top.) The side of S is given by x2 + y -9, and its height is 2. (a) Give a parametric equation, F(t) for the rim, C. F(t) , with tation: < fO. gC),h)>) (b)If S is oriented outward and downward, find s curl (-2yi +2xj+ 7zK) dÀ
(1 point) The figure below open cylindrical can, S, standing on...
(1 point) The figure below open cylindrical can, S, standing on the xy-plane. (S has a...
(1 point) The figure below open cylindrical can, S, standing on the xy-plane. (S has a bottom and sides, but no top.) The side of S is given by x2 + y2 = 9, and its height is 4. (a) Give a parametric equation, r(t) for the rim, C. r(t) with <t< (For this problem, enter your vector equation with angle-bracket notation: <f(t), g(t), h(t) >.) (b) If S is oriented outward and downward, find 's curl (-6yi + 6xj...
Assignment 9: Problem 3 Previous Problem List Next (1 point) The figure below open cylindrical can, S, standing on...
Assignment 9: Problem 3 Previous Problem List Next (1 point) The figure below open cylindrical can, S, standing on the xy-plane. (S has a bottom and sides, but no top.) The side of S is given by x2 +y2 = 9, and its height is 2. (a) Give a parametric equation, rt) for the rim, C r)= with (For this problem, enter your vector equation with angle-bracket notation: < f(t), g(t), h(t) >.) (b) If S is oriented outward and...
The figure below shows an open cylindrical can, S, standing on the xy-plane. (S has a bottom and sides, but no top.) 2+49 (a) Give equation(s) for the rim, C. (Enter your answers as a comma-separated...
The figure below shows an open cylindrical can, S, standing on the xy-plane. (S has a bottom and sides, but no top.) 2+49 (a) Give equation(s) for the rim, C. (Enter your answers as a comma-separated list of equations.) Cut-y7 + x7 + zk) . dA. (b) If S is oriented outward and downward, find curl(-yi + xj + zk) . dA =
The figure below shows an open cylindrical can, S, standing on the xy-plane. (S has a bottom...
Let E be the solid that lies inside the cylinder x^2 + y^2 = 1, above the xy-plane, and below the...
Let E be the solid that lies inside the cylinder x^2 + y^2 = 1,
above the xy-plane, and below the plane z = 1 + x. Let S be the
surface that encloses E. Note that S consists of three sides: S1 is
given by the cylinder x^2 + y^2 = 1, the bottom S2 is the disk x^2
+ y^2 ≤ 1 in the plane z = 0, and the top S3 is part of the plane z...
(1 point) Let F(x, y, z) = 5yj and S be the closed vertical cylinder of...
(1 point) Let F(x, y, z) = 5yj and S be the closed vertical cylinder of height 4, with its base a circle of radius 3 on the xy-plane centered at the origin. S is oriented outward. (a) Compute the flux of F through S using the divergence theorem. Flux = Flux = || F . dà = (b) Compute the flux directly. Flux out of the top = Į! Įdollar Flux out of the bottom = Flux out of...
Questions. Please show all work. 1. Consider the vector field F(x, y, z) (-y, x-z, 3x + z)and the surface S, which is the part of the sphere x2 + y2 + z2 = 25 above the plane z = 3. Let C be the...
Questions. Please show all work. 1. Consider the vector field F(x, y, z) (-y, x-z, 3x + z)and the surface S, which is the part of the sphere x2 + y2 + z2 = 25 above the plane z = 3. Let C be the boundary of S with counterclockwise orientation when looking down from the z-axis. Verify Stokes' Theorem as follows. (a) (i) Sketch the surface S and the curve C. Indicate the orientation of C (ii) Use the...
7. (16pts) Use Stokes, Theorem to find ▽ × F . nd.S where s is the surface of the cube 0 < x < 1, 0Sy, and 0szS 1 with open bottom in the ry plane. F(x, y, z)-<y, -, z > and the normal fi...
7. (16pts) Use Stokes, Theorem to find ▽ × F . nd.S where s is the surface of the cube 0 < x < 1, 0Sy, and 0szS 1 with open bottom in the ry plane. F(x, y, z)-<y, -, z > and the normal field n is oriented so that it points up on the top surface. T, zand
7. (16pts) Use Stokes, Theorem to find ▽ × F . nd.S where s is the surface of the cube...
NO.25 in 16.7 and NO.12 in 16.9 please. For the vector fied than the vecto and outgoing arrows. Her can use the formula for F to confirm t n rigtppors that the veciors that end near P, are shorter rs...
NO.25 in 16.7 and NO.12 in
16.9 please.
For the vector fied than the vecto and outgoing arrows. Her can use the formula for F to confirm t n rigtppors that the veciors that end near P, are shorter rs that start near p, İhus the net aow is outward near Pi, so div F(P) > 0 Pi is a source. Near Pa, on the other hand, the incoming arrows are longer than the e the net flow is inward,...
Consider a cylindrical capacitor like that shown in Fig. 24.6. Let d = rb − ra...
Consider a cylindrical capacitor like that shown in Fig. 24.6. Let d = rb − ra be the spacing between the inner and outer conductors. (a) Let the radii of the two conductors be only slightly different, so that d << ra. Show that the result derived in Example 24.4 (Section 24.1) for the capacitance of a cylindrical capacitor then reduces to Eq. (24.2), the equation for the capacitance of a parallel-plate capacitor, with A being the surface area of...
(1 point) The figure below open cylindrical can, S, standing on the xy-plane. (S has a bottom and sides, but no top.) The side of S is given by x2 + y -9, and its height is 2. (a) Give a parametric equation, F(t) for the rim, C. F(t) , with tation: < fO. gC),h)>) (b)If S is oriented outward and downward, find s curl (-2yi +2xj+ 7zK) dÀ
(1 point) The figure below open cylindrical can, S, standing on...
(1 point) The figure below open cylindrical can, S, standing on the xy-plane. (S has a bottom and sides, but no top.) The side of S is given by x2 + y2 = 9, and its height is 4. (a) Give a parametric equation, r(t) for the rim, C. r(t) with <t< (For this problem, enter your vector equation with angle-bracket notation: <f(t), g(t), h(t) >.) (b) If S is oriented outward and downward, find 's curl (-6yi + 6xj...
Assignment 9: Problem 3 Previous Problem List Next (1 point) The figure below open cylindrical can, S, standing on the xy-plane. (S has a bottom and sides, but no top.) The side of S is given by x2 +y2 = 9, and its height is 2. (a) Give a parametric equation, rt) for the rim, C r)= with (For this problem, enter your vector equation with angle-bracket notation: < f(t), g(t), h(t) >.) (b) If S is oriented outward and...
The figure below shows an open cylindrical can, S, standing on the xy-plane. (S has a bottom and sides, but no top.) 2+49 (a) Give equation(s) for the rim, C. (Enter your answers as a comma-separated list of equations.) Cut-y7 + x7 + zk) . dA. (b) If S is oriented outward and downward, find curl(-yi + xj + zk) . dA =
The figure below shows an open cylindrical can, S, standing on the xy-plane. (S has a bottom...
Let E be the solid that lies inside the cylinder x^2 + y^2 = 1,
above the xy-plane, and below the plane z = 1 + x. Let S be the
surface that encloses E. Note that S consists of three sides: S1 is
given by the cylinder x^2 + y^2 = 1, the bottom S2 is the disk x^2
+ y^2 ≤ 1 in the plane z = 0, and the top S3 is part of the plane z...
(1 point) Let F(x, y, z) = 5yj and S be the closed vertical cylinder of height 4, with its base a circle of radius 3 on the xy-plane centered at the origin. S is oriented outward. (a) Compute the flux of F through S using the divergence theorem. Flux = Flux = || F . dà = (b) Compute the flux directly. Flux out of the top = Į! Įdollar Flux out of the bottom = Flux out of...
Questions. Please show all work. 1. Consider the vector field F(x, y, z) (-y, x-z, 3x + z)and the surface S, which is the part of the sphere x2 + y2 + z2 = 25 above the plane z = 3. Let C be the boundary of S with counterclockwise orientation when looking down from the z-axis. Verify Stokes' Theorem as follows. (a) (i) Sketch the surface S and the curve C. Indicate the orientation of C (ii) Use the...
7. (16pts) Use Stokes, Theorem to find ▽ × F . nd.S where s is the surface of the cube 0 < x < 1, 0Sy, and 0szS 1 with open bottom in the ry plane. F(x, y, z)-<y, -, z > and the normal field n is oriented so that it points up on the top surface. T, zand
7. (16pts) Use Stokes, Theorem to find ▽ × F . nd.S where s is the surface of the cube...
NO.25 in 16.7 and NO.12 in
16.9 please.
For the vector fied than the vecto and outgoing arrows. Her can use the formula for F to confirm t n rigtppors that the veciors that end near P, are shorter rs that start near p, İhus the net aow is outward near Pi, so div F(P) > 0 Pi is a source. Near Pa, on the other hand, the incoming arrows are longer than the e the net flow is inward,...
Consider a cylindrical capacitor like that shown in Fig. 24.6. Let d = rb − ra be the spacing between the inner and outer conductors. (a) Let the radii of the two conductors be only slightly different, so that d << ra. Show that the result derived in Example 24.4 (Section 24.1) for the capacitance of a cylindrical capacitor then reduces to Eq. (24.2), the equation for the capacitance of a parallel-plate capacitor, with A being the surface area of...
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