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Nataly [62]
3 years ago
14

Giving brainliest!! easy*

Mathematics
2 answers:
DaniilM [7]3 years ago
8 0

Answer:

1584mm^2

Step-by-step explanation:

20 x20 = 400 and there are 3 of them

400+400+400 = 1200

1/2(16x24 ) =192 and there are 2 of them

192+192 = 384

1200+384

mixas84 [53]3 years ago
3 0

Answer:

1408

Step-by-step explanation:

20·16+24·16+20·16+12·﹣204+2·(20·24)2+2·(20·20)2﹣244+2·(24·20)2﹣204=1408

if i did something wrong please let me know

(i might have done it wrong, please use the answer above which would be 1584mm^2)

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Use the Divergence Theorem to evaluate S F · dS, where F(x, y, z) = z2xi + y3 3 + sin z j + (x2z + y2)k and S is the top half of
GenaCL600 [577]

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\displaystyle\iint_{S\cup D}\vec F(x,y,z)\cdot\mathrm d\vec S=\iiint_R\mathrm{div}\vec F(x,y,z)\,\mathrm dV

where R is the interior of the joined surfaces S\cup D.

Compute the divergence of \vec F:

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Compute the integral of the divergence over R. Easily done by converting to cylindrical or spherical coordinates. I'll do the latter:

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From this we need to subtract the contribution of

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that is, the integral of \vec F over the disk, oriented downward. Since z=0 in D, we have

\vec F(x,y,0)=\dfrac{y^3}3\,\vec\jmath+y^2\,\vec k

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\vec r(u,v)=u\cos v\,\vec\imath+u\sin v\,\vec\jmath

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\dfrac{\partial\vec r}{\partial v}\times\dfrac{\partial\vec r}{\partial u}=-u\,\vec k

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==>  486π/5 - (-81π/4) = 2349π/20

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