3 years ago

HELPPPPPP

Mathematics

1 answer:

dimaraw [331]3 years ago

5 0

32, i believe is the answer

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A foreign country uses the stellar as its currency. Before a trip to that country, Jon wants to exchange $1,500 to stellars. W

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Step-by-step example

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2 years ago

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2 years ago

Use Green's Theorem to calculate the circulation of F =2xyi around the rectangle 0≤x≤8, 0≤y≤3, oriented counterclockwise.

Tamiku [17]

Green's theorem says the circulation of $\vec F$ along the rectangle's border $C$ is equal to the integral of the curl of $\vec F$ over the rectangle's interior $D$ .

Given $\vec F(x,y)=2xy\,\vec\imath$ , its curl is the determinant

$\det\begin{bmatrix}\frac\partial{\partial x}&\frac\partial{\partial y}\\2xy&0\end{bmatrix}=\dfrac{\partial(0)}{\partial x}-\dfrac{\partial(2xy)}{\partial y}=-2x$

So we have

$\displaystyle\int_C\vec F\cdot\mathrm d\vec r=\iint_D-2x\,\mathrm dx\,\mathrm dy=-2\int_0^3\int_0^8x\,\mathrm dx\,\mathrm dy=\boxed{-192}$

6 0

3 years ago