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yKpoI14uk [10]
2 years ago
15

Maritza is baking cookies to bring to school and share with her friends on her birthday. The recipe requires 3 eggs for every 2

cups of sugar. To have enough cookies for all her friends, Maritza determined she would need 12 eggs. If her mom got 6 cups of sugar, does Marissa have enough sugar to make the cookies? Why or why not?Enter your question
Mathematics
1 answer:
Crazy boy [7]2 years ago
3 0
No, because if you work with fraction and do \frac{3}{2} (3 eggs for every 2 cups) then you would be multiplying 3x4 and now you have tot do that to the demominator so she would need 8 cups of sugar
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LUCKY_DIMON [66]
Make a change of coordinates:

u(x,y)=xy
v(x,y)=\dfrac xy

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}

and has a determinant of

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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)}

but we need the Jacobian determinant for the reverse transformation (from (x,y) to (u,v). To do this, notice that

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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
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Answer:

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Step-by-step explanation:

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