One third.
pam put two thirds into the bowl.
so...
cole put one third into the bowl.
one third was put into the bowl by cole.
Hope that helps = )
Answer:
6
Step-by-step explanation:
im just gonna name these couples by numbers 1 , 2 and 3 and each couple will take up 2 seats together.
1 2 3
3 2 1
2 3 1
1 3 2
2 1 3
3 1 2
To do this let's put 129 where X is, like this: -12(129)+14(129)-6(129)
Now we multiply -12 by 129, which is equal to -1548.
Now we multiply 14 by 129, which is equal to 1806.
Now we multiply -6 by 129, which is equal to -774.
Now, let's put these numbers into an equation, like this: -1548+1806-(-774).
The answer to this equation is 1032.
I hope this helps.
Notice that <em>C</em> has a clockwise orientation. By Green's theorem, we have
![\displaystyle\int_C\mathbf F(x,y)\cdot\mathrm d\mathbf r=-\iint_D\left(\frac{\partial(xy+x\cos x)}{\partial x}-\frac{\partial(y\cos x-xy)}{\partial y}\right)\,\mathrm dx\,\mathrm dy](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cint_C%5Cmathbf%20F%28x%2Cy%29%5Ccdot%5Cmathrm%20d%5Cmathbf%20r%3D-%5Ciint_D%5Cleft%28%5Cfrac%7B%5Cpartial%28xy%2Bx%5Ccos%20x%29%7D%7B%5Cpartial%20x%7D-%5Cfrac%7B%5Cpartial%28y%5Ccos%20x-xy%29%7D%7B%5Cpartial%20y%7D%5Cright%29%5C%2C%5Cmathrm%20dx%5C%2C%5Cmathrm%20dy)
where <em>D</em> is the triangule region with <em>C</em> as its boundary, given by the set
![D=\{(x,y)\mid0\le x\le2\land0\le y\le8-4x\}](https://tex.z-dn.net/?f=D%3D%5C%7B%28x%2Cy%29%5Cmid0%5Cle%20x%5Cle2%5Cland0%5Cle%20y%5Cle8-4x%5C%7D)
So we have
![\displaystyle\int_C\mathbf F(x,y)\cdot\mathrm d\mathbf r=-\int_0^2\int_0^{8-4x}((y+\cos x-x\sin x)-(\cos x-x\sin x))\,\mathrm dy\,\mathrm dx](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cint_C%5Cmathbf%20F%28x%2Cy%29%5Ccdot%5Cmathrm%20d%5Cmathbf%20r%3D-%5Cint_0%5E2%5Cint_0%5E%7B8-4x%7D%28%28y%2B%5Ccos%20x-x%5Csin%20x%29-%28%5Ccos%20x-x%5Csin%20x%29%29%5C%2C%5Cmathrm%20dy%5C%2C%5Cmathrm%20dx)
![\displaystyle\int_C\mathbf F(x,y)\cdot\mathrm d\mathbf r=-\int_0^2\int_0^{8-4x}y\,\mathrm dy\,\mathrm dx=\boxed{-\dfrac{64}3}](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cint_C%5Cmathbf%20F%28x%2Cy%29%5Ccdot%5Cmathrm%20d%5Cmathbf%20r%3D-%5Cint_0%5E2%5Cint_0%5E%7B8-4x%7Dy%5C%2C%5Cmathrm%20dy%5C%2C%5Cmathrm%20dx%3D%5Cboxed%7B-%5Cdfrac%7B64%7D3%7D)