is a closed surface with interior
, so you can use the divergence theorem.
![\vec F(x,y,z)=x\,\vec\imath+y\,\vec\jmath+9\,\vec k\implies\nabla\cdot\vec F(x,y,z)=\dfrac{\partial(x)}{\partial x}+\dfrac{\partial(y)}{\partial y}+\dfrac{\partial(9)}{\partial z}=2](https://tex.z-dn.net/?f=%5Cvec%20F%28x%2Cy%2Cz%29%3Dx%5C%2C%5Cvec%5Cimath%2By%5C%2C%5Cvec%5Cjmath%2B9%5C%2C%5Cvec%20k%5Cimplies%5Cnabla%5Ccdot%5Cvec%20F%28x%2Cy%2Cz%29%3D%5Cdfrac%7B%5Cpartial%28x%29%7D%7B%5Cpartial%20x%7D%2B%5Cdfrac%7B%5Cpartial%28y%29%7D%7B%5Cpartial%20y%7D%2B%5Cdfrac%7B%5Cpartial%289%29%7D%7B%5Cpartial%20z%7D%3D2)
By the divergence theorem, the flux of
across
is given by the integral of
over
:
![\displaystyle\iint_S\vec F\cdot\mathrm d\vec S=\iiint_R(\nabla\cdot\vec F)\,\mathrm dV](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Ciint_S%5Cvec%20F%5Ccdot%5Cmathrm%20d%5Cvec%20S%3D%5Ciiint_R%28%5Cnabla%5Ccdot%5Cvec%20F%29%5C%2C%5Cmathrm%20dV)
Convert to cylindrical coordinates, setting
![x=u\cos v](https://tex.z-dn.net/?f=x%3Du%5Ccos%20v)
![y=y](https://tex.z-dn.net/?f=y%3Dy)
![z=u\sin v](https://tex.z-dn.net/?f=z%3Du%5Csin%20v)
The integral is then
![\displaystyle2\int_{v=0}^{v=2\pi}\int_{u=0}^{u=1}\int_{y=0}^{y=8-u\cos v}u\,\mathrm dy\,\mathrm du\,\mathrm dv=\boxed{16\pi}](https://tex.z-dn.net/?f=%5Cdisplaystyle2%5Cint_%7Bv%3D0%7D%5E%7Bv%3D2%5Cpi%7D%5Cint_%7Bu%3D0%7D%5E%7Bu%3D1%7D%5Cint_%7By%3D0%7D%5E%7By%3D8-u%5Ccos%20v%7Du%5C%2C%5Cmathrm%20dy%5C%2C%5Cmathrm%20du%5C%2C%5Cmathrm%20dv%3D%5Cboxed%7B16%5Cpi%7D)
Answer:
The claim that less than 50% of internet users get their health questions answered online is correct, given that according to the survey, 45.98% of people do.
Step-by-step explanation:
Since an online health and medicine company claims that about 50% of Internet users would go to an online sight first for information regarding health and medicine, and a random sample of 1318 Internet users was asked where they will go for information the next time they need information about health or medicine; 606 said that they would use the Internet, to test the claim that less than 50% of Internet users get their health questions answered online, the following calculation must be performed:
1318 = 100
606 = X
606 x 100/1318 = X
60600/1318 = X
45.978 = X
Therefore, the claim that less than 50% of internet users get their health questions answered online is correct, given that according to the survey, 45.98% of people do.
Answer:
Ours is today. Feels weird how we came a long way with the pandemic presiding our academic studies.
Step-by-step explanation:
Answer:
305
Step-by-step explanation:
sorry if im not right
The point (-11,34) has the coordinates x = -11 and y = 34
The point (47,0) has the coordinates x = 47 and y = 0
Let's focus on just the x coordinates of each point for now. Those values are -11 and 47. Add them up to get -11+47 = 36. Then divide by two to end up with 36/2 = 18
The x coordinate of the midpoint is x = 18
Repeat those steps for the y coordinates. First add them up: 34+0 = 34. Then divide by two: 34/2 = 17
The y coordinate of the midpoint is y = 17
<h3>Therefore the midpoint is located at (x,y) = (18,17)</h3>
--------------------------
side note:
If you want, you can use the formulas
xm = (x1+x2)/2
ym = (y1+y2)/2
where (x1,y1) and (x2,y1) are the two endpoints and (xm, ym) is the midpoint. Though this method may be a bit confusing.