Set up and then compute the fhux of the vector feld Flx.y.)(2 y, 3n) on the sphere given
(a) Set up a double integral for calculating the flux of the vector field F(x, y, z) = z2k through the upper hemisphere of the sphere x2 + y2 + z2 = 4, oriented away from the origin. If necessary, enter P as rho, 8 as theta, and o as phi. B D Flux IT do de А A= B= C = D= (b) Evaluate the integral. Flux = F.dĀ= SI S
(1) Let G(,y, z) = (x,y, z). Show that there exists no vector field A : R3 -> R3 such that curl(A) Hint: compute its divergence G. (2) Let H R3 -> R3 be given as H(x,y, z) = (1,2,3). Find a vector potential A : R3 -> R3 such that curl(A) smooth function = H. Show that if A is a vector potential for H, then so is A+ Vf, for any f : R5 -> R (3) Let...
Math 2177 4) For vector field f(x, y) = (xy, 2-y): i set up the line integral along the following paranie trized curves. G: gradient of any function f(x, y). Horizontal E vertical - Ellipse (9,14) (7,11) (13,7) ii) show that f(x, y) is not equal to the C, (579)
Math 2177 4) For vector field f(x, y) = (xy, 2-y): i set up the line integral along the following paranie trized curves. G: gradient of any function f(x, y). Horizontal E vertical - Ellipse (9,14) (7,11) (13,7) ii) show that f(x, y) is not equal to the C, (579)
. B4· [2+5 marks! Show that the vector feld F(r,hi)-(2i3 + 6y) İ + (6x-Zy») + (3r2:2-r) k is conservative and find a scalar function ,(z,y,z)such that Vf Fand r0.1, 1)-0. . B4· [2+5 marks! Show that the vector feld F(r,hi)-(2i3 + 6y) İ + (6x-Zy») + (3r2:2-r) k is conservative and find a scalar function ,(z,y,z)such that Vf Fand r0.1, 1)-0.
Exercise 2: Diagonal multiplication. Given a matrix X and a vector d, compute Y = diag(d)*X. #Code in Jupyter notebook [python] X = np.random.rand(5,3) d = np.random.rand(5) # Y = ... [ Continue...]
please read the description, and please explain the qnswer For each exercise, set up and evaluate an integral to find the total vector gravitational force due to the given solid on a unit mass located at the origin. The mass density, in kilograms per cubic meter, of each solid is (x,y,z)-(x2 + y2+2)v2 21. The rectangular solid such that 0sxsa, 0sysb, and Oszsc For each exercise, set up and evaluate an integral to find the total vector gravitational force due...
8, (5 points) Set up, but do not integrate, the line integral of the vector field G (z-y,3 the curve ya from(-1,-1) to (2,8). Simplify your integrand as much as possible. (5 points) Set up, but do not integrate, the line integral of the vector field GJ, 3 the curve y = x3 from (-1,-1) to (2,8). . Simplify your integrand as much as possible 8. (5 points) Set up, but do not integrate, the line integral of the vector...
Just question 5 Only question 5 In a bathtub, the velocity of water near2 the drain is given by the vector field (22 +1)2222 + 1 where r, y, and z are measured in centimeters and (0, 0,0) is at the center of the drain. 1. Rewriting F as follows, describe in words how the water is moving: Consider each of the three terms in equation (4). (Look at some plots.) For fixed z, what is the flow like? How...
Just question 6![ Just question 6! In a bathtub, the velocity of water near2 the drain is given by the vector field (22 +1)2222 + 1 where r, y, and z are measured in centimeters and (0, 0,0) is at the center of the drain. 1. Rewriting F as follows, describe in words how the water is moving: Consider each of the three terms in equation (4). (Look at some plots.) For fixed z, what is the flow like? How...