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elena-14-01-66 [18.8K]
3 years ago
5

Let C be the closed, piecewise smooth curve formed by traveling in straight lines between the points (-2,1), (-2,-3), (1,-1) , (

1,5), and back to (-2,1), in that order. Use Green's theorem to evaluate the integral:
Integral(C) (2xy) dx +(xy^2) dy
Mathematics
1 answer:
Greeley [361]3 years ago
6 0

The given points are the vertices of the quadrilateral

Q=\left\{(x,y)\mid-2\le x\le1,\dfrac{2x-5}3\le y\le\dfrac{4x+11}3\right\}

By Green's theorem, the line integral is

\displaystyle\int_C2xy\,\mathrm dx+xy^2\,\mathrm dy=\iint_Q\frac{\partial(xy^2)}{\partial x}-\frac{\partial(2xy)}{\partial y}\,\mathrm dA

=\displaystyle\int_{-2}^1\int_{(2x-5)/3}^{(4x+11)/3}y^2-2x\,\mathrm dy\,\mathrm dx=\boxed{61}

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Find the tenth term of the geometric sequence, given the first term and common ratio.
Natalija [7]

Answer:

a_{10}=\dfrac{1}{128}

Step-by-step explanation:

In the geometric series:

a_1=4\\ \\r=\dfrac{1}{2}

The nth term of the geometric sequence can be calculated using formula

a_n=a_1\cdot r^{n-1}

In your case, n = 10, then

a_{10}\\ \\=4\cdot \left(\dfrac{1}{2}\right)^{10-1}\\ \\=4\cdot \left(\dfrac{1}{2}\right)^9\\ \\=2^2\cdot \dfrac{1}{2^9}\\ \\=\dfrac{1}{2^{9-2}}\\ \\=\dfrac{1}{2^7}\\ \\=\dfrac{1}{128}

8 0
3 years ago
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zzz [600]

<u><em>The answer:</em></u> 6x^3+18x

<u><em>The Explanation:</em></u> You need to uses distributive property to 6x to x^2+3 which will be 6x^3+18x

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3 years ago
2x-y=10 y=-4x+2 substitution method
AlladinOne [14]

Answer:

the solution is (2, -6)

Step-by-step explanation:

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Simplifying, we get:

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Substituting 2 for x in the second equation yields y = -4(2) + 2 = 0, or y = -6

Then the solution is (2, -6).

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