The answer is
. Reason is becasue you simplify it, making it
. How do we get this? Add similar elements of the numerator equation (the numerator on your question), making it
. Then x^2 - 4 would be the step, "apply difference of two squares formula," giving us (x+2)(x-2). Now we cancel the common factor, which is x + 2, giving us the answer that I gave you in the first sentence,
.
Hope this helped!
Nate
Hundredths: 8.98
Tenths: 9 whole
ones: 9 whole
tens: there is none
Parameterize the triangle
![\mathcal S](https://tex.z-dn.net/?f=%5Cmathcal%20S)
by the vector-valued function
![\mathbf s(u,v)](https://tex.z-dn.net/?f=%5Cmathbf%20s%28u%2Cv%29)
with
![\mathbf s(u,v)=(1-u)((1-v)(1,0,0)+v(0,1,0))+u(0,1,1)](https://tex.z-dn.net/?f=%5Cmathbf%20s%28u%2Cv%29%3D%281-u%29%28%281-v%29%281%2C0%2C0%29%2Bv%280%2C1%2C0%29%29%2Bu%280%2C1%2C1%29)
![\implies\mathbf s(u,v)=(\underbrace{(1-u)(1-v)}_{x(u,v)},\underbrace{v(1-u)+u}_{y(u,v)},\underbrace{u}_{z(u,v)})](https://tex.z-dn.net/?f=%5Cimplies%5Cmathbf%20s%28u%2Cv%29%3D%28%5Cunderbrace%7B%281-u%29%281-v%29%7D_%7Bx%28u%2Cv%29%7D%2C%5Cunderbrace%7Bv%281-u%29%2Bu%7D_%7By%28u%2Cv%29%7D%2C%5Cunderbrace%7Bu%7D_%7Bz%28u%2Cv%29%7D%29)
where
![0\le u\le1](https://tex.z-dn.net/?f=0%5Cle%20u%5Cle1)
and
![0\le v\le1](https://tex.z-dn.net/?f=0%5Cle%20v%5Cle1)
. Then the integral becomes
![\displaystyle\iint_{\mathcal S}xz\,\mathrm dS=\int_{v=0}^{v=1}\int_{u=0}^{u=1}x(u,v)z(u,v)\left\|\frac{\partial\mathbf s}{\partial u}\times\frac{\partial\mathbf s}{\partial v}\right\|\,\mathrm du\,\mathrm dv](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Ciint_%7B%5Cmathcal%20S%7Dxz%5C%2C%5Cmathrm%20dS%3D%5Cint_%7Bv%3D0%7D%5E%7Bv%3D1%7D%5Cint_%7Bu%3D0%7D%5E%7Bu%3D1%7Dx%28u%2Cv%29z%28u%2Cv%29%5Cleft%5C%7C%5Cfrac%7B%5Cpartial%5Cmathbf%20s%7D%7B%5Cpartial%20u%7D%5Ctimes%5Cfrac%7B%5Cpartial%5Cmathbf%20s%7D%7B%5Cpartial%20v%7D%5Cright%5C%7C%5C%2C%5Cmathrm%20du%5C%2C%5Cmathrm%20dv)
Answer:
2,799,360
Step-by-step explanation:
12x18x20x9x8x9=2,799,360