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Minchanka [31]
3 years ago
14

Help me please because I don’t get it

Mathematics
1 answer:
oksian1 [2.3K]3 years ago
5 0
For #3 - #6, everything is simply just dividing.

#3 3 strikes per inning

#4 9 points per minute

#5 30 beats per 20 seconds = 1.5 beats per second
      90 beats per 60 seconds =  1.5 beats per second
      The rates are equivalent.

#6 15 pages in 20 minutes = 0.75 pages per minute
      10 pages in 15 minutes = <span>0.666666666667
      The rates are NOT equivalent.

For #7, all you have to do is multiply.

#7 40,000 gallons per second
     1 minute = 60 seconds
     40,000 * 60 = 2,400,000
     The dam releases 2,400,000 gallons per minute.</span>
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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}

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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

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