Use a parametrization to find the flux SSF Fondo of F=2zk across the portion of the...
Use a parameterization to find the flux SSF 6./x2 + y2. Oszs6. Fondo of F-5xy i- 6z k outward (normal away from the z-axis) through the cone 264 The flux is a (Type an exact answer, using * as needed.)
section 16.6 Use a parametrization to find the flux SSFor Fón do across the surface in the given direction. F= - xi – yj + 3z?k outward (normal away from the z-axis) through the portion of the cone z = Vx² + y2 between the planes z = 3 and z = 4. The flux is (Type an exact answer, using a as needed.)
Use a parametrization to find the flux\(\iint_{S} \mathbf{F} \cdot \mathbf{n} \mathrm{d} \sigma\)of the field \(\mathbf{F}=\frac{9 x \mathbf{i}+9 y \mathbf{j}+9 z \mathbf{k}}{\sqrt{x^{2}+y^{2}+z^{2}}}\) across the portion of the sphere \(x^{2}+y^{2}+z^{2}=25\) in the first octant in the direction away from the origin.The flux is _______
S SSF. ds, where F = ci + yj + 2zk and S is the portion of the surface z = 1 - 22 - y2 above the xy-plane, with upward orientation.
In Exercises 31-36, find the flux of the field F across the portion of the sphere x2y z2= a2 in the first octant in the direction away from the origin 33. F(x, y, z) yi - xj k
Use the divergence theorem to find the outward flux of F across the boundary of the region D. F=3./x2 + y2 + 2? (xi + yj + zk) D: The region 35x2 + y2 +z+s4 The outward flux is- (Type an exact answer, using a as needed.)
Find a parametrization of the surface. The portion of the sphere x² + y2 + z = 2 between the planes z = and z= - 2 2 What is the correct parameterization? Select the correct choice below and fill in the answer boxes within your choice. (Type exact answers.) O A. r(0,0) = i+ k, sos sos sps sos OB. r(0,0) = O C. rq,0) = sos sos OD. r(0,0) =i+j+ k sos 1.ses
Use the Divergence Theorem to compute the net outward flux of the field F = (3x.y. -22) across the surface S, where is the sphere {x,y,z) x+yz? = 15) The net outward flux across the sphere is (Type an exact answer, using x as needed)
Use a parametrization to set up an integral to find the flux || F.Nds of F(x,y,z)= xyi - zk outward (normal away from z-axis) through the surface of the cone == /r’+y?, 05:51.
Use the surface integral in Stokes' Theorem to calculate the flux of the curl of the field F across the surface in the direction away from the origin. F-3y + (5 - 5x)j + (z? - 2K S: 7,0) = (v10 sin 6 cos 0) (V10 sin sine))+ ( 10 cos •)*, 05058/2,050 2x The flux of the curl of the field F across the surface S in the direction of the outward unit normal nis I (Type an exact...