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algol [13]
3 years ago
15

140words in 4min in unit rate

Mathematics
2 answers:
gregori [183]3 years ago
8 0
140 words divided by 4 minutes = 35 words per minute
shutvik [7]3 years ago
5 0
140:4
divide both sides by 4
35:1
35 words per minute

Hope this helps :)
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Evaluate the integral e^xy w region d xy=1, xy=4, x/y=1, x/y=2
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

\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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3 years ago
Is the relationship linear, exponential, or neither?
irga5000 [103]
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2 years ago
Estimate the sum of 299 and 388
Svetllana [295]

For this case we have the following numbers:

299

388

Let's round up each of the numbers to the nearest hundred,

We have then:

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388 = 400

We note that now we have two numbers whose approximation is easier to add.

We have then:

300 + 400 = 700

Answer:

The sum of 299 + 388 is approximately:

700

7 0
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