By the divergence theorem,
![\displaystyle\iint_S\mathbf f\cdot\mathrm d\mathbf S=\iiint_R(\nabla\cdot\mathbf f)\,\mathrm dV](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Ciint_S%5Cmathbf%20f%5Ccdot%5Cmathrm%20d%5Cmathbf%20S%3D%5Ciiint_R%28%5Cnabla%5Ccdot%5Cmathbf%20f%29%5C%2C%5Cmathrm%20dV)
where
![R](https://tex.z-dn.net/?f=R)
is the solid whose boundary is
![S](https://tex.z-dn.net/?f=S)
. We have
![\nabla\cdot\mathbf f=\dfrac{\partial z}{\partial x}+\dfrac{\partial y}{\partial y}+\dfrac{\partial zx}{\partial z}=1+x](https://tex.z-dn.net/?f=%5Cnabla%5Ccdot%5Cmathbf%20f%3D%5Cdfrac%7B%5Cpartial%20z%7D%7B%5Cpartial%20x%7D%2B%5Cdfrac%7B%5Cpartial%20y%7D%7B%5Cpartial%20y%7D%2B%5Cdfrac%7B%5Cpartial%20zx%7D%7B%5Cpartial%20z%7D%3D1%2Bx)
so we set up the volume integral as
![\displaystyle\iiint_R(\nabla\cdot\mathbf f)\,\mathrm dV=\int_{x=0}^{x=1/a}\int_{y=0}^{y=(1-ax)/b}\int_{z=0}^{z=(1-ax-by)/c}(1+x)\,\mathrm dz\,\mathrm dy\,\mathrm dx](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Ciiint_R%28%5Cnabla%5Ccdot%5Cmathbf%20f%29%5C%2C%5Cmathrm%20dV%3D%5Cint_%7Bx%3D0%7D%5E%7Bx%3D1%2Fa%7D%5Cint_%7By%3D0%7D%5E%7By%3D%281-ax%29%2Fb%7D%5Cint_%7Bz%3D0%7D%5E%7Bz%3D%281-ax-by%29%2Fc%7D%281%2Bx%29%5C%2C%5Cmathrm%20dz%5C%2C%5Cmathrm%20dy%5C%2C%5Cmathrm%20dx)
Answer:
-39.7184
Step-by-step explanation:
(58.9 + 9.58)x = ?
x = -0.580
(58.9 + 9.58)-0.580 = ?
-34.162-5.5564
-39.7184
so (58.9 + 9.58)x = -39.7184
Answer:
61 ft
Step-by-step explanation:
2πr(X/360)
2(3.14)(13)(270/360) = 61.23
Answer:
200
Step-by-step explanation:
25 cars can be washed in a hour so we do 25×8=200