is the circle with radius 4 centered at (0, 0, 0) lying in the plane
. We can parameterize it by
![\vec r(t)=\langle0,4\cos t,4\sin t\rangle](https://tex.z-dn.net/?f=%5Cvec%20r%28t%29%3D%5Clangle0%2C4%5Ccos%20t%2C4%5Csin%20t%5Crangle)
with
. By Stokes' theorem,
![\displaystyle\iint_M(\nabla\times\vec F)\cdot\mathrm d\vec S=\int_{\partial M}\vec F\cdot\mathrm d\vec r](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Ciint_M%28%5Cnabla%5Ctimes%5Cvec%20F%29%5Ccdot%5Cmathrm%20d%5Cvec%20S%3D%5Cint_%7B%5Cpartial%20M%7D%5Cvec%20F%5Ccdot%5Cmathrm%20d%5Cvec%20r)
![=\displaystyle\int_0^{2\pi}\langle0^2,0,16\cos^2t\rangle\cdot\langle0,-4\sin t,4\cos t\rangle\,\mathrm dt](https://tex.z-dn.net/?f=%3D%5Cdisplaystyle%5Cint_0%5E%7B2%5Cpi%7D%5Clangle0%5E2%2C0%2C16%5Ccos%5E2t%5Crangle%5Ccdot%5Clangle0%2C-4%5Csin%20t%2C4%5Ccos%20t%5Crangle%5C%2C%5Cmathrm%20dt)
![=\displaystyle\int_0^{2\pi}64\cos^3t\,\mathrm dt=\boxed0](https://tex.z-dn.net/?f=%3D%5Cdisplaystyle%5Cint_0%5E%7B2%5Cpi%7D64%5Ccos%5E3t%5C%2C%5Cmathrm%20dt%3D%5Cboxed0)
The correct answer is 28.27 <span />
Answer:
5/7
decimal form : 0.714285-
Step-by-step explanation:
Answer:
y= -2/3x + 5
Step-by-step explanation:
Slope-intercept form is y=mx+b
The m is the slope (followed by an x), the b is the y-intercept.
The line intercepts (or crosses) the line x=0 at y=5, so the y-intercept is 5.
The slope can be found with rise over run.
Beginning point is (0,5), end point is (3,3) which equals -2/3