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In Exercises 31-36, find the flux of the field F across the portion of the sphere...
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 _______
Use a parametrization to find the flux SSF Fondo of F=2zk across the portion of the sphere x² + y2 +22=awhere z is positive in the direction away from the origin. The flux is (Type an exact answer in terms of t.)
Evaluate the surface integral S F · dS for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation. F(x, y, z) = x i − z j + y k S is the part of the sphere x2 + y2 + z2 = 36 in the first octant, with orientation toward the origin
Evaluate the surface integral SSS F·ds for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation. F(x, y, z) = xi - zj + y k S is the part of the sphere x2 + y2 + z2 = 36 in the first octant, with orientation toward the origin.
8.) (12 pts.) Find the Flux of the Vector Field F(x, y, z) = (z)i + (x)} + (y)k through Surface S, which is that portion of the plane 2++2 = 3 is the 1st octant, and r is the unit normal vector pointing away from the origin.
Evaluate the surface integral | Fds for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation. JJS F(x, y, z) = xi - z j + y k S is the part of the sphere x2 + y2 + z2 = 49 in the first octant, with orientation toward the origin
Find the upward flux of F=−yi+xj+12kF=−yi+xj+12k across the part of the spherical surface GG determined by z=f(x,y)=12−x2−y2‾‾‾‾‾‾‾‾‾‾‾‾√,0≤x2+y2≤5 Find the upward flux of F =-yi + xj + 12k across the part of the spherical surface G determined by 30 pi Find the upward flux of F =-yi + xj + 12k across the part of the spherical surface G determined by 30 pi
Evaluate the surface integral ∫∫sF·ds for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation. F(x, y,z) = xi - zj +yk S is the part of the sphere x2 + y2 + z2 = 16 in the first octant, with orientation toward the origin.
5. Calculate the surface area of the portion of the sphere x2+y2+12-4 between the planes z-1 and z ะไ 6. Evaluate (xyz) dS, where S is the portion of the plane 2x+2y+z-2 that lies in the first octant. 7. Evaluate F. ds. a) F = yli + xzj-k through the cone z = VF+ア0s z 4 with normal pointing away from the z-axis. b) F-yi+xj+ek where S is the portion of the cylinder+y9, 0szs3, 0s r and O s y...
F(x,y,z)=8xi+8yj+8zk,S is the surface of the sphere x^2+y^2+z^2=4 in the first octant directed away from the origin,then find what is the flux of the vector field F across the surface S in the indicated direction.