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Nadusha1986 [10]
2 years ago
5

I WILL GIVE BRAINLIEST TO WHOEVER IS CORRECT

Mathematics
1 answer:
tatiyna2 years ago
5 0
The first one is correct
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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
(4÷y+2) +(2÷y-3) =(6÷y+6)
Evgesh-ka [11]
<span>Simplifying 4(y + -3) = 6(y + 2) Reorder the terms: 4(-3 + y) = 6(y + 2) (-3 * 4 + y * 4) = 6(y + 2) (-12 + 4y) = 6(y + 2) Reorder the terms: -12 + 4y = 6(2 + y) -12 + 4y = (2 * 6 + y * 6) -12 + 4y = (12 + 6y) Solving -12 + 4y = 12 + 6y Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-6y' to each side of the equation. -12 + 4y + -6y = 12 + 6y + -6y Combine like terms: 4y + -6y = -2y -12 + -2y = 12 + 6y + -6y Combine like terms: 6y + -6y = 0 -12 + -2y = 12 + 0 -12 + -2y = 12 Add '12' to each side of the equation. -12 + 12 + -2y = 12 + 12 Combine like terms: -12 + 12 = 0 0 + -2y = 12 + 12 -2y = 12 + 12 Combine like terms: 12 + 12 = 24 -2y = 24 Divide each side by '-2'. y = -12 Simplifying y = -12</span>
3 0
3 years ago
WILL MARK BRAINLIEST!!!!<br> What is the equation of the line shown in this graph?
Eduardwww [97]
Y=1 because no matter the x value y will be 1
7 0
2 years ago
Read 2 more answers
Write each proof as a two column proof​
Karo-lina-s [1.5K]

Answer:

Step-by-step explanation:

What can be used as a statement in a two column proof?

A two-column proof consists of a list of statements, and the reasons why those statements are true. The statements are in the left column and the reasons are in the right column. The statements consists of steps toward solving the problem.

8 0
2 years ago
I NEED HELP PLEASEEEEEEEEEEEEEEEEEEEEEEEEE
ser-zykov [4K]

Answer:

58 square feet

Step-by-step explanation:

The room is already broken down into two smaller rectangles.

The smaller of the two measures 4 ft by 2 ft. A=lw, so substitute 4 for l and 2 for w.

A(smaller rectangle) =(4)(2), or (4*2).

A(smaller rectangle) =8

The larger measures 10 ft by 5 ft, so using the same method, multiply l times w.

A(larger rectangle) =(10)(5), or (10*5).

A(larger rectangle) =50

Add the two rectangles' areas together to find the total area of the room.

8 + 50 = 58

8 0
3 years ago
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