Please solve all parts of this question clearly and neatly
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Please solve all parts of this question clearly and neatly 1. Let S be part of the paraboloid z = 5-22-уг, z--3. Assume that the charge density of s is (x,y,2-7x +5 -z Coulombs per unit of surface ar...
PLEASE SHOW ALL WORK NEATLY! THANK YOU! (10 pts) Let F(x, y, z) = (x +...
PLEASE SHOW ALL WORK
NEATLY! THANK YOU!
(10 pts) Let F(x, y, z) = (x + y, y - 1, e), and let S be the part of the surface z = 9. 22 - y2 above the plane z=5, with downward orientation. Evaluate the flux of F across S by computing the surface integral IsF. ds.
Please show full working. Only answer if you know how. Regards (2) Let F-~itrj yk and consider the integral JTs ▽ x F·ń dS where s is the surface of the paraboloid z = 1-2.2-y2 corresponding to z >...
Please show full working. Only answer if you know how.
Regards
(2) Let F-~itrj yk and consider the integral JTs ▽ x F·ń dS where s is the surface of the paraboloid z = 1-2.2-y2 corresponding to z > 0, and n is a unit normal vector to S in the positive z-direction. (a) Apply Stokes' theorem to evaluate the integral. (b) Evaluate the integral directly over the surface S (c) Evaluate the integral directly over the new surface S...
21 Problem 20. Let S be the surface bounded by the graph of f(x,y)-2+y2 . the plane z 5; Os1; and .0sys1. In addition, let F be the vector field defined by F(x, y,z):i+ k. (1) By converting the r...
21 Problem 20. Let S be the surface bounded by the graph of f(x,y)-2+y2 . the plane z 5; Os1; and .0sys1. In addition, let F be the vector field defined by F(x, y,z):i+ k. (1) By converting the resulting triple integral into cylindrical coordinates, find the exact value of the flux integral F.n do, assuming that S is oriented in the positive z-direction. (Recall that since the surface is oriented upwardly, you should use the vector -fx, -fy, 1)...
Please, include the explanations to your solution! Begin with the paraboloid z #x2 + y2, for 0 s z s 64, and slice it with the plane y-0. Let S be the surface that remains for y 20 (including the...
Please, include the explanations to your solution!
Begin with the paraboloid z #x2 + y2, for 0 s z s 64, and slice it with the plane y-0. Let S be the surface that remains for y 20 (including the planar surface in the xz-plane) (see figure). Let C be the semicircle and line segment that bound the cap of S in the plane z 64 with counterclockwise orientation. Let F (4z 3y,4x+3z,4y+3x. Complete parts (a) through (c) below 64...
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...
rty. I 5. [16 pointsj Consider the function f(x, y,z) Let S denote the level surface consisting of all points in space such that f(,y,z)-4, and let P- (2,-2,1), which is on S. a) Calculate Vf. b) Det...
rty. I 5. [16 pointsj Consider the function f(x, y,z) Let S denote the level surface consisting of all points in space such that f(,y,z)-4, and let P- (2,-2,1), which is on S. a) Calculate Vf. b) Determine the maximum value of Daf(P), where u is any unit vector at P c) Find the angle between Vfp and PO, where O denotes the origin. d) Find an equation for the tangent plane to S at P
rty. I 5. [16...
MARK WHICH STATEMENTS BELOW ARE TRUE, USING THE FOLLOWING, Consider Vf(x, y, z) in terms of...
MARK WHICH STATEMENTS BELOW ARE TRUE, USING THE FOLLOWING, Consider Vf(x, y, z) in terms of a new coordinate system, x= x(u, v, w), y=y(u, v, w), z=z(u, v, w). Let r(s) = x(s) i+y(s) + z(s) k be the position vector defining some continuous path as a function of the arc length. Similarly for the other partial derivatives in v and w. For spherical coordinates the following must also be true for any points, x = Rsin o cose,...
Hi, I need help solving number 13. Please show all the steps, thank you. :) Consider the solid Q bounded by z-2-y2;z-tx at each point Р (x, y, z) is given by mass of Q [15 pts] 9. x-4. The density Z/...
Hi, I need help solving number 13. Please show all the steps,
thank you. :)
Consider the solid Q bounded by z-2-y2;z-tx at each point Р (x, y, z) is given by mass of Q [15 pts] 9. x-4. The density Z/m 3 . Find the center of (x, y, z) [15 pts] 10. Evaluate the following integral: ee' dy dzdx [15 pts] 11. Use spherical coordinates to find the mass m of a solid Q that lies between the...
all questions are related and need help answering! rough the surface 4. o pm) What is the value of the flux of the vector field F(x,y)j+z ioriented with upward- pointing normal vector? (A) 0 (B)...
all questions are related and need help answering!
rough the surface 4. o pm) What is the value of the flux of the vector field F(x,y)j+z ioriented with upward- pointing normal vector? (A) 0 (B) 2n/3 (C) π (D) 4T/3 (E) 2π Use Stokes, Theorem to evaluateⅡcurl F.dS, where F(x, y, z)-(x2 sin Theorem to evaluate Jceun F'.asS , where Fl.e)(', ») and 5. (5pts.) F,y, sin z, y', xy) and s is the part of the paraboloid : -...
answer all parts, please! (5) Consider the closed volume V contained by the cylinder r2+2-4 and the planes y =-2 and r +y-3. Let the surface S be the boundary of this region. Note that this boundary...
answer all parts, please!
(5) Consider the closed volume V contained by the cylinder r2+2-4 and the planes y =-2 and r +y-3. Let the surface S be the boundary of this region. Note that this boundary consists of three smooth pieces. (a) Clearly sketch and label S. (You may use GeoGebra for this.) (b) In complete sentences, verbally describe what this surface looks like. (c) Find a parametric representation for each of the three parts of the boundary S...
PLEASE SHOW ALL WORK
NEATLY! THANK YOU!
(10 pts) Let F(x, y, z) = (x + y, y - 1, e), and let S be the part of the surface z = 9. 22 - y2 above the plane z=5, with downward orientation. Evaluate the flux of F across S by computing the surface integral IsF. ds.
Please show full working. Only answer if you know how.
Regards
(2) Let F-~itrj yk and consider the integral JTs ▽ x F·ń dS where s is the surface of the paraboloid z = 1-2.2-y2 corresponding to z > 0, and n is a unit normal vector to S in the positive z-direction. (a) Apply Stokes' theorem to evaluate the integral. (b) Evaluate the integral directly over the surface S (c) Evaluate the integral directly over the new surface S...
21 Problem 20. Let S be the surface bounded by the graph of f(x,y)-2+y2 . the plane z 5; Os1; and .0sys1. In addition, let F be the vector field defined by F(x, y,z):i+ k. (1) By converting the resulting triple integral into cylindrical coordinates, find the exact value of the flux integral F.n do, assuming that S is oriented in the positive z-direction. (Recall that since the surface is oriented upwardly, you should use the vector -fx, -fy, 1)...
Please, include the explanations to your solution!
Begin with the paraboloid z #x2 + y2, for 0 s z s 64, and slice it with the plane y-0. Let S be the surface that remains for y 20 (including the planar surface in the xz-plane) (see figure). Let C be the semicircle and line segment that bound the cap of S in the plane z 64 with counterclockwise orientation. Let F (4z 3y,4x+3z,4y+3x. Complete parts (a) through (c) below 64...
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...
rty. I 5. [16 pointsj Consider the function f(x, y,z) Let S denote the level surface consisting of all points in space such that f(,y,z)-4, and let P- (2,-2,1), which is on S. a) Calculate Vf. b) Determine the maximum value of Daf(P), where u is any unit vector at P c) Find the angle between Vfp and PO, where O denotes the origin. d) Find an equation for the tangent plane to S at P
rty. I 5. [16...
MARK WHICH STATEMENTS BELOW ARE TRUE, USING THE FOLLOWING, Consider Vf(x, y, z) in terms of a new coordinate system, x= x(u, v, w), y=y(u, v, w), z=z(u, v, w). Let r(s) = x(s) i+y(s) + z(s) k be the position vector defining some continuous path as a function of the arc length. Similarly for the other partial derivatives in v and w. For spherical coordinates the following must also be true for any points, x = Rsin o cose,...
Hi, I need help solving number 13. Please show all the steps,
thank you. :)
Consider the solid Q bounded by z-2-y2;z-tx at each point Р (x, y, z) is given by mass of Q [15 pts] 9. x-4. The density Z/m 3 . Find the center of (x, y, z) [15 pts] 10. Evaluate the following integral: ee' dy dzdx [15 pts] 11. Use spherical coordinates to find the mass m of a solid Q that lies between the...
all questions are related and need help answering!
rough the surface 4. o pm) What is the value of the flux of the vector field F(x,y)j+z ioriented with upward- pointing normal vector? (A) 0 (B) 2n/3 (C) π (D) 4T/3 (E) 2π Use Stokes, Theorem to evaluateⅡcurl F.dS, where F(x, y, z)-(x2 sin Theorem to evaluate Jceun F'.asS , where Fl.e)(', ») and 5. (5pts.) F,y, sin z, y', xy) and s is the part of the paraboloid : -...
answer all parts, please!
(5) Consider the closed volume V contained by the cylinder r2+2-4 and the planes y =-2 and r +y-3. Let the surface S be the boundary of this region. Note that this boundary consists of three smooth pieces. (a) Clearly sketch and label S. (You may use GeoGebra for this.) (b) In complete sentences, verbally describe what this surface looks like. (c) Find a parametric representation for each of the three parts of the boundary S...
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