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3 years ago

how do I find the area of a shaded region and the non shaded region inside the non shaded region???????

Mathematics

1 answer:

mixer [17]3 years ago

7 0

There's no diagram here so I can't be specific, but I've attached an image.

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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

Please help me. Hurry, linear equations.

Lisa [10]

Answer:

Let's simplify step-by-step.

3−3/4x−1/4x−7

=3+ −3/4x+ −1/4x+ −7

Combine Like Terms:

=3+ −3/4x+ −1/4x+ −7

=(−3/4x+ −1/4x)+(3+ −7)

=−x+ −4

Answer:=−x−4

Step-by-step explanation:

answer:-4

8 0

3 years ago

There are white, blue, and red boats in a marina. Two-thirds of the boats in the marina are white, five-eighths of the remaining

sammy [17]

X = total boats
2/3x are white....so the remaining boats = 1/3x
5/8 of the remaining boats are blue.....5/8 * 1/3 = 5/24x are blue

2/3 + 5/24 = 16/24 + 5/24 = 21/24 are blue and white......so 3/24 are red
3/24x = 6
x = 6 * 24/3
x = 144/3
x = 48 total boats in the marina <==

2/3(48) = 32 white
5/24(48) = 10 blue
3/24(48) = 6 red

6 0

2 years ago

The surface area of a cube is 24 cm squared. What would the surface are of the prism be if each dimension were quadrupled?

kenny6666 [7]

CubeSA=6 squares
SA=6s^2
SA=24
24=6s^2
divide 6
4=s^2
2=s

quadrupled means times 4
2*4=8
8=new side
sub back
SA=6(8^2)
SA=6(64)
new SA=384 cm^2

6 0

3 years ago

What are the three angle measures in the triangle shown below

Zanzabum

Answer:

B. 31°, 106°, and 43°.

Step-by-step explanation:

the sum of the measures of the angles in a triangle add up to 180°, so:

3x+1+11x-4+5x-7=180

19x-10=180

19x=190

x=10

now that we know x is equal to 10, we can find the three angle measures:

3x+1 -> 3(10)+1 = 31°

11x-4 -> 11(10)-4 = 110-4 = 106°

5x-7 -> 5(10)-7 = 50-7 = 43°

so, the answer is B.

7 0

2 years ago