The second option. A is 36 and B is 20. FD is half of AC, so 18*2 is 36. FB is half of EC, so it’s 20.
Answer:
10
Step-by-step explanation:
Each pie was cut into 6 pieces. 6 x 10= 60.
(4,3) Down 3 from 6 on y-axis and left 2 on x-axis.
Your answer is 30 bags, if you do 18/3=6 then 5*6=30
I'll go ahead and assume you meant to say that <em>S</em> is the surface given by
![S = \left\{(x,y,z) \mid z = \cos(y)\text{ with } 0\le y\le \pi\text{ and }0\le x\le4\right\}](https://tex.z-dn.net/?f=S%20%3D%20%5Cleft%5C%7B%28x%2Cy%2Cz%29%20%5Cmid%20z%20%3D%20%5Ccos%28y%29%5Ctext%7B%20with%20%7D%200%5Cle%20y%5Cle%20%5Cpi%5Ctext%7B%20and%20%7D0%5Cle%20x%5Cle4%5Cright%5C%7D)
This immediately gives us a parameterization for the surface,
![\vec r(x, y) = \left\langle x, y, \cos(y)\right \rangle](https://tex.z-dn.net/?f=%5Cvec%20r%28x%2C%20y%29%20%3D%20%5Cleft%5Clangle%20x%2C%20y%2C%20%5Ccos%28y%29%5Cright%20%5Crangle)
The upward-pointing normal vector to this surface is then
![\vec n = \dfrac{\partial\vec r}{\partial x} \times \dfrac{\partial\vec r}{\partial y} = \left\langle0,\sin(y),1\right\rangle](https://tex.z-dn.net/?f=%5Cvec%20n%20%3D%20%5Cdfrac%7B%5Cpartial%5Cvec%20r%7D%7B%5Cpartial%20x%7D%20%5Ctimes%20%5Cdfrac%7B%5Cpartial%5Cvec%20r%7D%7B%5Cpartial%20y%7D%20%3D%20%5Cleft%5Clangle0%2C%5Csin%28y%29%2C1%5Cright%5Crangle)
Then the flux of
across <em>S</em> is
![\displaystyle \iint_S \vec F(x,y,z)\cdot\mathrm d\vec s = \int_0^4\int_0^\pi \vec F(x,y,\cos(y))\cdot\vec n\,\mathrm dy\,\mathrm dx \\\\ = \int_0^4\int_0^\pi \left\langle e^{-\cos(y)},4\cos(y),6xy\right\rangle \cdot \left\langle0,\sin(y),1\right\rangle \,\mathrm dy\,\mathrm dx \\\\ = \int_0^4\int_0^\pi (4\sin(y)\cos(y)+6xy)\,\mathrm dy\,\mathrm dx \\\\ = 2 \int_0^4\int_0^\pi (\sin(2y) + 3xy)\,\mathrm dy\,\mathrm dx = \boxed{24\pi^2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Ciint_S%20%5Cvec%20F%28x%2Cy%2Cz%29%5Ccdot%5Cmathrm%20d%5Cvec%20s%20%3D%20%5Cint_0%5E4%5Cint_0%5E%5Cpi%20%5Cvec%20F%28x%2Cy%2C%5Ccos%28y%29%29%5Ccdot%5Cvec%20n%5C%2C%5Cmathrm%20dy%5C%2C%5Cmathrm%20dx%20%5C%5C%5C%5C%20%3D%20%5Cint_0%5E4%5Cint_0%5E%5Cpi%20%5Cleft%5Clangle%20e%5E%7B-%5Ccos%28y%29%7D%2C4%5Ccos%28y%29%2C6xy%5Cright%5Crangle%20%5Ccdot%20%5Cleft%5Clangle0%2C%5Csin%28y%29%2C1%5Cright%5Crangle%20%5C%2C%5Cmathrm%20dy%5C%2C%5Cmathrm%20dx%20%5C%5C%5C%5C%20%3D%20%5Cint_0%5E4%5Cint_0%5E%5Cpi%20%284%5Csin%28y%29%5Ccos%28y%29%2B6xy%29%5C%2C%5Cmathrm%20dy%5C%2C%5Cmathrm%20dx%20%5C%5C%5C%5C%20%3D%202%20%5Cint_0%5E4%5Cint_0%5E%5Cpi%20%28%5Csin%282y%29%20%2B%203xy%29%5C%2C%5Cmathrm%20dy%5C%2C%5Cmathrm%20dx%20%3D%20%5Cboxed%7B24%5Cpi%5E2%7D)