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Ierofanga [76]
3 years ago
13

Parallelogram 15 in 18 in Area:

Mathematics
1 answer:
olga_2 [115]3 years ago
3 0

Answer:

270

Step-by-step explanation:

brianliest?

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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
8 0
3 years ago
6. Solve this inequality: j/4 -8 < 4.
Vaselesa [24]

Answer:

D

Step-by-step explanation:

Given

\frac{j}{4} - 8 < 4 ( add 8 to both sides )

\frac{j}{4} < 12

Multiply both sides by 4 to clear the fraction

j < 48 → D

6 0
3 years ago
Find the area of the parallelogram in square units.
uysha [10]
I think it’s 40
The width is 8
And the length is 5
8 x 5 is 40
3 0
3 years ago
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One bag contains 3/5 kg of corn. A farmer feeds his chickens 4 bags of corn each week. How many kilograms of corn do they eat ea
Andrews [41]
4 x 3/5
4/1 x 3/5
4x3/5x1
12/5kg of corn a week
(12/5)/7
12/5(1/7)
12/5x7
12/35kg per day

4 0
3 years ago
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Which of the following numbers are greater than or equal to 4/7<br> A. 2/5<br> B. 0.57<br> C. 2/3
Bumek [7]

Answer:

B.

Step-by-step explanation:

If you were to divide 4 by 7, you would get a decimal that would be rounded up to that value. 2/3 is roughly .66 and 2/5 is .4.

6 0
3 years ago
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