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a_sh-v [17]
2 years ago
14

Help pls pls Polk brain if correct

Mathematics
1 answer:
Sidana [21]2 years ago
5 0

Answer:

https://youtu.be/AWGqoCNbsvM

Step-by-step explanation:

okay?

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Use the given transformation x=4u, y=3v to evaluate the integral. ∬r4x2 da, where r is the region bounded by the ellipse x216 y2
exis [7]

The Jacobian for this transformation is

J = \begin{bmatrix} x_u & x_v \\ y_u & y_v \end{bmatrix} = \begin{bmatrix} 4 & 0 \\ 0 & 3 \end{bmatrix}

with determinant |J| = 12, hence the area element becomes

dA = dx\,dy = 12 \, du\,dv

Then the integral becomes

\displaystyle \iint_{R'} 4x^2 \, dA = 768 \iint_R u^2 \, du \, dv

where R' is the unit circle,

\dfrac{x^2}{16} + \dfrac{y^2}9 = \dfrac{(4u^2)}{16} + \dfrac{(3v)^2}9 = u^2 + v^2 = 1

so that

\displaystyle 768 \iint_R u^2 \, du \, dv = 768 \int_{-1}^1 \int_{-\sqrt{1-v^2}}^{\sqrt{1-v^2}} u^2 \, du \, dv

Now you could evaluate the integral as-is, but it's really much easier to do if we convert to polar coordinates.

\begin{cases} u = r\cos(\theta) \\ v = r\sin(\theta) \\ u^2+v^2 = r^2\\ du\,dv = r\,dr\,d\theta\end{cases}

Then

\displaystyle 768 \int_{-1}^1 \int_{-\sqrt{1-v^2}}^{\sqrt{1-v^2}} u^2\,du\,dv = 768 \int_0^{2\pi} \int_0^1 (r\cos(\theta))^2 r\,dr\,d\theta \\\\ ~~~~~~~~~~~~ = 768 \left(\int_0^{2\pi} \cos^2(\theta)\,d\theta\right) \left(\int_0^1 r^3\,dr\right) = \boxed{192\pi}

3 0
2 years ago
Evaluate 0.1m+8-12n0.1m+8−12n0, point, 1, m, plus, 8, minus, 12, n when m=30m=30m, equals, 30 and n=\dfrac14n= 4 1 ​ n, equals,
Rom4ik [11]

Answer:

8

Step-by-step explanation:

We are required to evaluate:

0.1m+8-12n

When m=30, n=\frac{1}{4}

Substituting these values into the expression, we have:

0.1m+8-12n=0.1(30)+8-12(\frac{1}{4})\\=3+8-\frac{12}{4}\\=3+8-3\\=8

8 0
3 years ago
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What is the solution to the equation below?
Alekssandra [29.7K]

Answer :

It is D because you have to subtract 4.73 from both sides in order to isolate the y by itself and get the answer which is 3.27

Step-by-step explanation:

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1 year ago
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What is the slope of the line?
mr Goodwill [35]

Answer:

infant/0

Step-by-step explanation:

it goes up forever

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2 years ago
What is 5.756565x 344
qaws [65]
1980.25836 is the answer
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3 years ago
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