[Solution] Compute the (outward) flux of the field F(x, y, z)=[c10 x+2 z , z , 2 x+y] through the sphere S implicitly defined by
Question: Compute the (outward) flux of the field \(\vec{F}(x, y, z)=\left[\begin{array}{c}10 x+2 z \\ z \\ 2 x+y\end{array}\right]\) through the sphere \(S\) implicitly defined by \(x^{2}+y^{2}+z^{2}=25\).
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![[Solved] Let F(x, y, z)=[c9 x+2 z](/images/solutions/MC-solution-library-46352.jpg "[Solved] Let F(x, y, z)=[c9 x+2 z , y-3 x , x^2 tan ^-1(y z)],")
[Solved] Let F(x, y, z)=[c9 x+2 z , y-3 x , x^2 tan ^-1(y z)],
![[See Solution] Let F(x, y, z)=[cy e^2](/images/solutions/MC-solution-library-46353.jpg "[See Solution] Let F(x, y, z)=[cy e^2 z , x e^2 z , 2 x y e^2")
[See Solution] Let F(x, y, z)=[cy e^2 z , x e^2 z , 2 x y e^2
![[All Steps] Let S be the surface](/images/solutions/MC-solution-library-46354.jpg "[All Steps] Let S be the surface of the cylinder defined by x^2+y^2")
[All Steps] Let S be the surface of the cylinder defined by x^2+y^2
(Step-by-Step) Let F(x, y, z)=[l2 x-y z-x^2 , 3 y+x z+y^3 , 4
![[Steps Shown] Let S be the surface](/images/solutions/MC-solution-library-46356.jpg "[Steps Shown] Let S be the surface defined implicitly by x^2+y^2+z^2=π^2.")
[Steps Shown] Let S be the surface defined implicitly by x^2+y^2+z^2=π^2.
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