6. (12pts) Use the divergence theorem to find the flux F.ndS with outward pointing normal n with F(x, y, z) =< x2,-y, z >, where s is the surface of the hemisphere z = V 1-x2-y2 and its base in...
Let F(x,y,z) =( x3z)I+(y3z-yz3)j+z4k use the divergence theorem to calculate ∫∫cF•ds, that is , calculate flux of F across S, where S is the surface of the solid bounded by the hemisphere z = √ 2 - x2 - y2 and the xy - plane .
Use the Divergence Theorem to evaluate If /F. F.NDS and find the outward flux of F through the surface of the solid S bounded by the graphs of the equations. Use a computer algebra system to verify your results. F(x, y, z) = xeļi + ye?j + ek S: z = 9 - y, z = 0, x = 0, x = 6, y = 0
Let F(x, y, 2)-3xi -4yi+2zk and let S be hemisphere- V9-y2 together with diskx29 in the xy- plane. Use the divergence theorem to calculate the outward flux 90π Let F(x, y, 2)-3xi -4yi+2zk and let S be hemisphere- V9-y2 together with diskx29 in the xy- plane. Use the divergence theorem to calculate the outward flux 90π
Problem #4: F.ndS Use the divergence theorem find the outward flux of the field to vector e+7 cosxj +y? and x2 + y2 V 49 an (3y + 8z) i 2 2 k, where S is the surface of the region bounded by the F graphs of z Vx V + symbolically, Enter your answer (sqrt(2)-1)*(686/3*pi) as in these examples Problem #4 686 JT 3 Submit Problem # 4 for Grading Just Save Attempt #3 Problem #4 Attempt #1 Attempt...
Let E-xi vi + 2zk be an electrostatic field. Use Gauss's Law to find the total charge enclosed by the closed surface consisting of the hemisphere- V1-x2 - y2 and its circular base in the xy-plane. Use the Divergence Theorem to evaluate F.N dS and find the outward flux of F through the surface of the solid bounded by the graphs of the equations. Use a computer algebra system to verify your results F(x, y, z) =xyì + 7yj +xzk...
6. Use the Divergence Theorem to evaluate SSF. ds, where Ể(x, y, z) = (x/x2 + y2 + z2 , yvx2 + y2 + z2 , z7 x2 + y2 + z2 ) and S consists of the hemisphere z V1 – x2 - y2 and the disk x2 + y2 = 1 in the xy-plane.
5 Use the Divergence theorem to find the outward flux. a. F(a, y,z)-(6x2+ + 2xy, 2y + xz, 4x2y); G: The solid cut from the first octant by the cylinder x2+y - 4 and the plane 3. (In(x2+Уг),-2z arctan(y/x), z (x2 +y2); G:The solid between the b. F(r, y, z) Vx + y*); G: The solid between the cylinders x2 + y.2 1 and x2+ y2 2, -1szs4. c Fxy)-(2xy', 2x'y, -): G: The solid bounded by the cylinder x?1...
please help me solve the following question 8. Compute JJ f dS where f(x, y, 2)22+2 and S is the top hemisphere x2 + y2 + Z2, 220. 9. Compute JJ F-n dS where F-: (x, y, z) and s is the cone z2 x2 + y2, 0 S 2 1; with the outward pointing normal. 8. Compute JJ f dS where f(x, y, 2)22+2 and S is the top hemisphere x2 + y2 + Z2, 220. 9. Compute JJ...
#4 please 3. (12 pts). (a) (8 pts) Directly compute the flux Ф of the vector field F-(x + y)1+ yj + zk over the closed surface S given by z 36-x2-y2 and z - 0. Keep in mind that N is the outward normal to the surface. Do not use the Divergence Theorem. Hint: Don't forget the bottom! (b) (4 pts) Sketch the surface. ts). Use the Divergence Theorem to compute the flux Ф of Problem 3. Hint: The...
3. (5 points) Use the Divergence Theorem to find the outward flux of the vector field F(x, y, z) - 3ry? i + xe'j + 23k across the surface of the solid bounded by the cylinder y2 + z-1 and the planes z =-1 and x = 2. 3. (5 points) Use the Divergence Theorem to find the outward flux of the vector field F(x, y, z) - 3ry? i + xe'j + 23k across the surface of the solid...