[Solution Library] Let F(x, y, z)=[c9 x+2 z , y-3 x , x^2 tan ^-1(y z)], and let S be that part of the ellipsoid x^2+fracy^29+fracz^216=1 that lies above the xy -plane.
Question: Let \(\vec{F}(x, y, z)=\left[\begin{array}{c}9 x+2 z \\ y-3 x \\ x^{2} \tan ^{-1}(y z)\end{array}\right]\), and let \(S\) be that part of the ellipsoid \(x^{2}+\frac{y^{2}}{9}+\frac{z^{2}}{16}=1\)
that lies above the xy -plane. Then \(\iint_{S}(\nabla \times \vec{F}) \cdot \hat{n} d \sigma=\) ?
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![[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.
(Steps Shown) What is the probability of drawing 3 clubs in a
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