Answer:
Survey
Step-by-step explanation: A survey is a research method of collecting data from a particular target group through questions aimed at extracting specific information from them
Answer:
And the range is all real numbers except 0. The definition of range is the set of all possible values that the function will give when we give in the domain as input.
Step-by-step explanation :D give brainly
For the transformation
![\begin{cases}x=7u+v\\y=u+7v\end{cases}](https://tex.z-dn.net/?f=%5Cbegin%7Bcases%7Dx%3D7u%2Bv%5C%5Cy%3Du%2B7v%5Cend%7Bcases%7D)
the Jacobian is
![\dfrac{\partial(x,y)}{\partial(u,v)}=\begin{bmatrix}7&1\\1&7\end{bmatrix}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cpartial%28x%2Cy%29%7D%7B%5Cpartial%28u%2Cv%29%7D%3D%5Cbegin%7Bbmatrix%7D7%261%5C%5C1%267%5Cend%7Bbmatrix%7D)
with determinant
![\det\left(\begin{bmatrix}7&1\\1&7\end{bmatrix}\right)=48](https://tex.z-dn.net/?f=%5Cdet%5Cleft%28%5Cbegin%7Bbmatrix%7D7%261%5C%5C1%267%5Cend%7Bbmatrix%7D%5Cright%29%3D48)
The vertices of the triangle in the
-plane are
![(x,y)=(0,0)\implies(u,v)=(0,0)](https://tex.z-dn.net/?f=%28x%2Cy%29%3D%280%2C0%29%5Cimplies%28u%2Cv%29%3D%280%2C0%29)
![(x,y)=(7,1)\implies(u,v)=(1,0)](https://tex.z-dn.net/?f=%28x%2Cy%29%3D%287%2C1%29%5Cimplies%28u%2Cv%29%3D%281%2C0%29)
![(x,y)=(1,7)\implies(u,v)=(0,1)](https://tex.z-dn.net/?f=%28x%2Cy%29%3D%281%2C7%29%5Cimplies%28u%2Cv%29%3D%280%2C1%29)
Then the integral is
![\displaystyle\iint_R(x-8y)\,\mathrm dA=-48\int_0^1\int_0^{1-v}(u+55v)\,\mathrm du\,\mathrm dv=\boxed{-448}](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Ciint_R%28x-8y%29%5C%2C%5Cmathrm%20dA%3D-48%5Cint_0%5E1%5Cint_0%5E%7B1-v%7D%28u%2B55v%29%5C%2C%5Cmathrm%20du%5C%2C%5Cmathrm%20dv%3D%5Cboxed%7B-448%7D)