(5) (20 points total) The region W lies between the spheres x2y z2 1 and x2y2 + z2 9 and within t...
22 + y2 with (1 point) The region W lies between the spheres x2 + y2 + z2 = 1 and 22 + y2 + x2 = 4 and within the cone z = z > 0; its boundary is the closed surface, S, oriented outward. Find the flux of F=ri+y +z3k Out of S. flux =
x2 + y2 with z 2 0; its (1 point) The region W lies between the spheres x² + y2 + z2 = 4 and x² + y2 + z = 16 and within the cone z = boundary is the closed surface, S, oriented outward. Find the flux of Ě = x; i+y?1+z2k out of S. flux = 5952pi/20(1-1/sqrt2)
Previous Problem Problem List Next Problem x2 + y2 with 2 2 0; its boundary (1 point) The region W lies between the spheres x2 + y2 + z = 9 and x2 + y2 + z = 25 and within the cone z = Is the closed surface, S., oriented outward. Find the flux of F = x +y +z'k out of S. flux
ohpolar0 124) The Silk Road...Villa Gabriela lugar... Math 392 Lecture 4.. ork MATHEMATICAL ASSOCIATION OF AMERICA webwork /19sp392 j/13.9/4 13.9: Problem 4 (1 point) The region W lies between the spheres z2 + y2 + z2 1 and z2 + y2 + z2 9 and within the cone z , z4y2 with z > 0; its boundary is the closed surface, S, oriented outward. Find the flux of Fiyj+kout of S ms flux= ((729(2-sqrt(2))pi))/5 You have attempted this problem 2...
2. Follow the steps to verify the Divergence Theorem forF(x, y, z)-(z2, 2y, 49) and the solid cylinder E : r2 + y2 < 4, 0 2. (a) 9 pts] Evaluate F dS directly where S is the closed cylinder S which bounds E oriented outward. Note that S consists of three surfaces: S1 the surface of the cylinder x2 + y-4 for 0 z 2, the disc Di : x2 +92-4 which lies in the plane z 0 and...
please help with Q1 and 3 1. Let V be the solid region in R3 that lies within the sphere 2+y+z2-4, above the zy-plane, and below the cone z -Vx2 + y2 (a) Sketch the region V (b) Calculate the volume of V by using spherical coordinates. (c) Find the surface area of the part of V that lies on the sphere z2 y 24, by calculatinga surface integral. (d) Verify your solution to (c) by calculating the surface integral...
Q1. Evaluate the line integral f (x2 + y2)dx + 2xydy by two methods a) directly, b) using Green's Theorem, where C consists of the arc of the parabola y = x2 from (0,0) to (2,4) and the line segments from (2,4) to (0,4) and from (0,4) to (0,0). [Answer: 0] Q2. Use Green's Theorem to evaluate the line integral $. F. dr or the work done by the force field F(x, y) = (3y - 4x)i +(4x - y)j...
This is for an advanced calculus/advanced math course. Please be as detailed as possible in your answer. Thank you so much in advance. PLEASE DO NOT USE CALCULATORS OR SOFTWARE TO SOLVE THESE PROBLEMS. PLEASE DO EVERYTHING BY HAND. THANK YOU!! You can use the theorem below to solve the problem: 16. Apply the Divergence Theorem to compute I = SS. F.dS, where F(x, y, z) = (xz2 + cos(y + 2), šv* +e”,z²z+y+ 2) 1 and S is the...
Help Entering Answers (1 point) Use the Divergence Theorem to evaluate F . dS where F =くz2xHFz, y + 2 tan(2), X22-1 and S is the top half of the sphere x2 +y2 25 Hint: S is not a closed surface. First compute integrals over S and S2, where Si is the disk x2 +y s 25, z 0 oriented downward and s,-sus, F-ds, = 滋 dy dx F.dS2 = S2 where X1 = 리= Z2 = IE F-ds, =...
7. Use Green's Theorem to find Jc F.nds, where C is the boundary of the region bounded by y = 4-x2 and y = 0, oriented counter-clockwise and F(x,y) = (y,-3z). what about if F(r, y) (2,3)? x2 + y2 that lies inside x2 + y2-1. Find the surface area of this 8. Consider the part of z surface. 9. Use Green's Theorem to find Find J F Tds, where F(x, y) (ry,e"), and C consists of the line segment...