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](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cint_%7Bx%5E2%2By%5E2%3D9%7D%5Cvec%20F%28x%2Cy%29%5Ccdot%5Cmathrm%20d%5Cvec%20r%3D%5Ciint_D%5Cleft%28%5Cfrac%7B%5Cpartial%28xy%29%7D%7B%5Cpartial%20x%7D-%5Cfrac%7B%5Cpartial%28x%5E2%29%7D%7B%5Cpartial%20y%7D%5Cright%29%5C%2C%5Cmathrm%20dx%5C%2C%5Cmathrm%20dy%3D%5Ciint_Dy%5C%2C%5Cmathrm%20dx%5C%2C%5Cmathrm%20dy)
where
is the circle
and
is the interior of
, or the disk
.
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](https://tex.z-dn.net/?f=%5Cbegin%7Bcases%7Dx%3Dr%5Ccos%5Ctheta%5C%5Cy%3Dr%5Csin%5Ctheta%5Cend%7Bcases%7D%5Cimplies%5Cmathrm%20dx%5C%2C%5Cmathrm%20dy%3Dr%5C%2C%5Cmathrm%20dr%5C%2C%5Cmathrm%20d%5Ctheta)
Then the work done by
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](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Ciint_Dy%5C%2C%5Cmathrm%20dx%5C%2C%5Cmathrm%20dy%3D%5Cint_0%5E%7B2%5Cpi%7D%5Cint_0%5E3%28r%5Csin%5Ctheta%29r%5C%2C%5Cmathrm%20dr%5C%2C%5Cmathrm%20d%5Ctheta%3D%5Cleft%28%5Cint_0%5E%7B2%5Cpi%7D%5Csin%5Ctheta%5C%2C%5Cmathrm%20d%5Ctheta%5Cright%29%5Cleft%28%5Cint_0%5E3r%5E2%5C%2C%5Cmathrm%20dr%5Cright%29%3D%5Cboxed0)
Answer:
x7-3 as number is multiplied by 7 then subtracted by 3
Answer:
1 cm = 100 mi
28.9/1=28.9
28.9 x 100 = 2890 miles distance
2890 / 65 miles per hour = 44.4615 hours to drive
44.461/24 hours in a day = 1.85 rounded up is 2 days
About two days
If you have any questions you can ask
Step-by-step explanation:
Explanation:
A function is a relationship where any one x-value/input only has <u>one </u>corresponding y-value/output. (note: a y-value can have multiple x-values).
> This can be called "assigning one y-value to every x element".
The vertical line test places a line that would connect all y-values of an x-value (that is, if it were to have multiple y-values). If multiple points can be found along the vertical line, it is, therefore, by the definition of a function, not a function. (Because an x-value will have more than one y-value).
So, a graph that fails the vertical-line test does not represent a function because an x-value will correspond with more than one y-value.
hope this helps!!
Answer:
A true
Step-by-step explanation:
It is the correct answer i have read this