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Over [174]
3 years ago
14

Consider the force field and circle defined below.

Mathematics
1 answer:
grin007 [14]3 years ago
4 0

By Green's theorem,

\displaystyle\int_{x^2+y^2=9}\vec F(x,y)\cdot\mathrm d\vec r=\iint_D\left(\frac{\partial(xy)}{\partial x}-\frac{\partial(x^2)}{\partial y}\right)\,\mathrm dx\,\mathrm dy=\iint_Dy\,\mathrm dx\,\mathrm dy

where C is the circle x^2+y^2=9 and D is the interior of C, or the disk x^2+y^2\le1.

Convert to polar coordinates, taking

\begin{cases}x=r\cos\theta\\y=r\sin\theta\end{cases}\implies\mathrm dx\,\mathrm dy=r\,\mathrm dr\,\mathrm d\theta

Then the work done by \vec F on the particle is

\displaystyle\iint_Dy\,\mathrm dx\,\mathrm dy=\int_0^{2\pi}\int_0^3(r\sin\theta)r\,\mathrm dr\,\mathrm d\theta=\left(\int_0^{2\pi}\sin\theta\,\mathrm d\theta\right)\left(\int_0^3r^2\,\mathrm dr\right)=\boxed0

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puteri [66]

Answer:

Line M would also have a slope of 2/3.

Step-by-step explanation:

When two line are parallel that means that they will never intersect.

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Since lines K and line M are parallel to each other they have to have the same slope.

6 0
3 years ago
1 + 2 + (-5) + 4 <br><br> A . -6<br> B . -5 <br> C . 0<br> D . 2<br> E . 4<br> F . 12
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Answer:

Option D. 2

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A ticket broker is selling seats to a rock concert. If the broker's commission is a $5.00 base fee and $0.50 extra for every tic
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3 0
3 years ago
|2x+1|-14=9 solve the absolute equation
sergey [27]
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