Find the mass of the lamina described by the inequalities x 20 and 7
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- = Let er be the unit radial vector field. Compute the outward flux of the vector field F er/r² through the ellipsoid 4x² + 6y² + 9z² = 36. [Hint: Because F is not defined at zero, you cannot use the divergence theorem on the bounded region inside of S. ]Calculate the flux of vector field F = (xy°, x²y) across the circle of radius 1 centered at coordinates (0, –1).Can you can explain the proof of "the equation of continuity", in an easy-to-understand manner? Attached images are the proof my professor gave. I really do not understand all the simple v's , capital v's and all? Can you kindly explain it in an easy-to-understand manner? Thank you!
- Find the flux of F = 3zi + 5y? j+ 3x k out of the closed cone y = Vx2 + z², with 0 < y <1. flux =Find the flux of F = xi - 2yj + zk across the portion of cylinder x² + z² = 9 in the first and forth octants. (3,-3,0) n X (0,0,3) (3,0,0) (0,3,0) yEvaluate the integral. dx (x – 4)(x – 3)(x + 5) | (Use symbolic notation and fractions where needed. Use C for the arbitrary constant.) dx %3D J (x – 4)(x – 3)(x + 5)
- Calculate the flux of the vector field F(x, y, z) = 5i + 5j + zk through the closed circular cylinder of radius 4 centered about the z-axis for -6 ≤ z < 6, oriented away from the z-axis. Note: a closed cylinder has a top and a bottom. Flux = SS F.dĀ=Evaluate the surface integral 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 - yj + z³k, S is the part of the cone z = √x² + y² between the planes z = 1 and z = 4 with downward orientation ZA z = √√x² + y² xx 0 z=4