The answer is Strong Positive
Answer:
10.4 × 32.90 = 342.16
so yeah she should take the deal
459 water flows... not sure if this is right but it’s what calculated so good luck
Make a change of coordinates:
![u(x,y)=xy](https://tex.z-dn.net/?f=u%28x%2Cy%29%3Dxy)
![v(x,y)=\dfrac xy](https://tex.z-dn.net/?f=v%28x%2Cy%29%3D%5Cdfrac%20xy)
The Jacobian for this transformation is
![\mathbf J=\begin{bmatrix}\dfrac{\partial u}{\partial x}&\dfrac{\partial v}{\partial x}\\\\\dfrac{\partial u}{\partial y}&\dfrac{\partial v}{\partial y}\end{bmatrix}=\begin{bmatrix}y&x\\\\\dfrac1y&-\dfrac x{y^2}\end{bmatrix}](https://tex.z-dn.net/?f=%5Cmathbf%20J%3D%5Cbegin%7Bbmatrix%7D%5Cdfrac%7B%5Cpartial%20u%7D%7B%5Cpartial%20x%7D%26%5Cdfrac%7B%5Cpartial%20v%7D%7B%5Cpartial%20x%7D%5C%5C%5C%5C%5Cdfrac%7B%5Cpartial%20u%7D%7B%5Cpartial%20y%7D%26%5Cdfrac%7B%5Cpartial%20v%7D%7B%5Cpartial%20y%7D%5Cend%7Bbmatrix%7D%3D%5Cbegin%7Bbmatrix%7Dy%26x%5C%5C%5C%5C%5Cdfrac1y%26-%5Cdfrac%20x%7By%5E2%7D%5Cend%7Bbmatrix%7D)
and has a determinant of
![\det\mathbf J=-\dfrac{2x}y](https://tex.z-dn.net/?f=%5Cdet%5Cmathbf%20J%3D-%5Cdfrac%7B2x%7Dy)
Note that we need to use the Jacobian in the other direction; that is, we've computed
![\mathbf J=\dfrac{\partial(u,v)}{\partial(x,y)}](https://tex.z-dn.net/?f=%5Cmathbf%20J%3D%5Cdfrac%7B%5Cpartial%28u%2Cv%29%7D%7B%5Cpartial%28x%2Cy%29%7D)
but we need the Jacobian determinant for the reverse transformation (from
![(x,y)](https://tex.z-dn.net/?f=%28x%2Cy%29)
to
![(u,v)](https://tex.z-dn.net/?f=%28u%2Cv%29)
. To do this, notice that
![\dfrac{\partial(x,y)}{\partial(u,v)}=\dfrac1{\dfrac{\partial(u,v)}{\partial(x,y)}}=\dfrac1{\mathbf J}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cpartial%28x%2Cy%29%7D%7B%5Cpartial%28u%2Cv%29%7D%3D%5Cdfrac1%7B%5Cdfrac%7B%5Cpartial%28u%2Cv%29%7D%7B%5Cpartial%28x%2Cy%29%7D%7D%3D%5Cdfrac1%7B%5Cmathbf%20J%7D)
we need to take the reciprocal of the Jacobian above.
The integral then changes to
![\displaystyle\iint_{\mathcal W_{(x,y)}}e^{xy}\,\mathrm dx\,\mathrm dy=\iint_{\mathcal W_{(u,v)}}\dfrac{e^u}{|\det\mathbf J|}\,\mathrm du\,\mathrm dv](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Ciint_%7B%5Cmathcal%20W_%7B%28x%2Cy%29%7D%7De%5E%7Bxy%7D%5C%2C%5Cmathrm%20dx%5C%2C%5Cmathrm%20dy%3D%5Ciint_%7B%5Cmathcal%20W_%7B%28u%2Cv%29%7D%7D%5Cdfrac%7Be%5Eu%7D%7B%7C%5Cdet%5Cmathbf%20J%7C%7D%5C%2C%5Cmathrm%20du%5C%2C%5Cmathrm%20dv)
Answer:
40
Step-by-step explanation:
15x3 = 45
45-5 =40