Jamey says she only has 30% of her book to go before she finishes it. she has read 147 pages so far

1 answer:

4 0

Let's just change your problem to 147 of 30%

"Of" is always equaling to multiplication (×)

Now, it would be easier to simplify

30% (147)
30% ÷ 100 = 0.3
0.3(147)
Now, we get to your answer which might be 44.1

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Evaluate the integral e^xy w region d xy=1, xy=4, x/y=1, x/y=2

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Make a change of coordinates:

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

The Jacobian for this transformation is

$\mathbf J=\begin{bmatrix}\dfrac{\partial u}{\partial x}&\dfrac{\partial v}{\partial x}\\\\\dfrac{\partial u}{\partial y}&\dfrac{\partial v}{\partial y}\end{bmatrix}=\begin{bmatrix}y&x\\\\\dfrac1y&-\dfrac x{y^2}\end{bmatrix}$

and has a determinant of

$\det\mathbf J=-\dfrac{2x}y$

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

$\dfrac{\partial(x,y)}{\partial(u,v)}=\dfrac1{\dfrac{\partial(u,v)}{\partial(x,y)}}=\dfrac1{\mathbf J}$

we need to take the reciprocal of the Jacobian above.

The integral then changes to

$\displaystyle\iint_{\mathcal W_{(x,y)}}e^{xy}\,\mathrm dx\,\mathrm dy=\iint_{\mathcal W_{(u,v)}}\dfrac{e^u}{|\det\mathbf J|}\,\mathrm du\,\mathrm dv$
$=\displaystyle\frac12\int_{v=}^{v=}\int_{u=}^{u=}\frac{e^u}v\,\mathrm du\,\mathrm dv=\frac{(e^4-e)\ln2}2$

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Plz tell me how u got it and hurry please

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Because the shape is a cube, we know that all sides must be 5cm. To find the area of a side, you do base × height, so 5 × 5 = 25. If you look at the net, you'll notice that there are 6 faces, which means you have to do 25 × 6 = 150cm^2. I hope this helps!

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