The answer of 799/4 is equal 1
![z=f(x(u,v),y(u,v)),\begin{cases}x(u,v)=2u+v^2\\y(u,v)=3u-v\end{cases}](https://tex.z-dn.net/?f=z%3Df%28x%28u%2Cv%29%2Cy%28u%2Cv%29%29%2C%5Cbegin%7Bcases%7Dx%28u%2Cv%29%3D2u%2Bv%5E2%5C%5Cy%28u%2Cv%29%3D3u-v%5Cend%7Bcases%7D)
We're given that
and
, and want to find
.
By the chain rule, we have
![\dfrac{\partial z}{\partial v}=\dfrac{\partial z}{\partial x}\dfrac{\partial x}{\partial v}+\dfrac{\partial z}{\partial y}\dfrac{\partial y}{\partial v}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cpartial%20z%7D%7B%5Cpartial%20v%7D%3D%5Cdfrac%7B%5Cpartial%20z%7D%7B%5Cpartial%20x%7D%5Cdfrac%7B%5Cpartial%20x%7D%7B%5Cpartial%20v%7D%2B%5Cdfrac%7B%5Cpartial%20z%7D%7B%5Cpartial%20y%7D%5Cdfrac%7B%5Cpartial%20y%7D%7B%5Cpartial%20v%7D)
and
![\dfrac{\partial x}{\partial v}=2v](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cpartial%20x%7D%7B%5Cpartial%20v%7D%3D2v)
![\dfrac{\partial y}{\partial v}=-1](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cpartial%20y%7D%7B%5Cpartial%20v%7D%3D-1)
Then
![\dfrac{\partial z}{\partial v}(1,2)=\dfrac{\partial z}{\partial x}(6,1)\dfrac{\partial x}{\partial v}(1,2)+\dfrac{\partial z}{\partial y}(6,1)\dfrac{\partial y}{\partial v}(1,2)](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cpartial%20z%7D%7B%5Cpartial%20v%7D%281%2C2%29%3D%5Cdfrac%7B%5Cpartial%20z%7D%7B%5Cpartial%20x%7D%286%2C1%29%5Cdfrac%7B%5Cpartial%20x%7D%7B%5Cpartial%20v%7D%281%2C2%29%2B%5Cdfrac%7B%5Cpartial%20z%7D%7B%5Cpartial%20y%7D%286%2C1%29%5Cdfrac%7B%5Cpartial%20y%7D%7B%5Cpartial%20v%7D%281%2C2%29)
(because the point
corresponds to
)
![\implies\dfrac{\partial z}{\partial v}(1,2)=3\cdot2\cdot2+(-1)\cdot(-1)=\boxed{13}](https://tex.z-dn.net/?f=%5Cimplies%5Cdfrac%7B%5Cpartial%20z%7D%7B%5Cpartial%20v%7D%281%2C2%29%3D3%5Ccdot2%5Ccdot2%2B%28-1%29%5Ccdot%28-1%29%3D%5Cboxed%7B13%7D)
Answer:
3 players
Step-by-step explanation:
15 times 20% = 3.
You can check yourself if you'd like.
HOPE THIS HELPS :)
87.35 squared would be 7,630.02.(87.35)^2 = 7,630.02Rounded off further, it will be 7,630.On a number line numbered in tenths, 7,630.02 could be plotted on 7,630, as rounding off the number to the nearest integer, the answer will be 7,630.
Answer:
8+6n
Step-by-step explanation:
First, distribute the 2 into the parenthesis.
2(6)+2(3n)-4
Then, multiply the numbers.
12+6n-4
Now add(subtract in this case) the common multiples.
12-4= 8
8+6n
Since you can no longer simplify the equation, this is the answer..
8+6n