Allison is a beautiful young woman with a small home in Arkansas and she lives there with her husband Robert and daughter Lindsay who both like to go out fishing during the summer in Wisconsin where Robert's parents, Carrie and Mitch live near a sparkling, blue lake.
It seems that the boundary of
is the circle
in the plane
. 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)
Parameterize
by
![\vec r(t)=(7\cos t,7\sin t,0)](https://tex.z-dn.net/?f=%5Cvec%20r%28t%29%3D%287%5Ccos%20t%2C7%5Csin%20t%2C0%29)
with
. Then the line integral is
![\displaystyle\int_{\partial M}\vec f(x(t),y(t),z(t))\cdot\mathrm d\vec r=\int_0^{2\pi}(56\sin t,35\cos t,0)\cdot(-7\sin t,7\cos t,0)\,\mathrm dt](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cint_%7B%5Cpartial%20M%7D%5Cvec%20f%28x%28t%29%2Cy%28t%29%2Cz%28t%29%29%5Ccdot%5Cmathrm%20d%5Cvec%20r%3D%5Cint_0%5E%7B2%5Cpi%7D%2856%5Csin%20t%2C35%5Ccos%20t%2C0%29%5Ccdot%28-7%5Csin%20t%2C7%5Ccos%20t%2C0%29%5C%2C%5Cmathrm%20dt)
![=\displaystyle\int_0^{2\pi}(245\cos^2t-392\sin^2t)\,\mathrm dt=\boxed{-147\pi}](https://tex.z-dn.net/?f=%3D%5Cdisplaystyle%5Cint_0%5E%7B2%5Cpi%7D%28245%5Ccos%5E2t-392%5Csin%5E2t%29%5C%2C%5Cmathrm%20dt%3D%5Cboxed%7B-147%5Cpi%7D)
Answer: x3−3x2−6x+6
Step-by-step explanation:
Let's simplify step-by-step.
x3−2x+3−(3x2+4x−3)
Distribute the Negative Sign:
=x3−2x+3+−1(3x2+4x−3)
=x3+−2x+3+−1(3x2)+−1(4x)+(−1)(−3)
=x3+−2x+3+−3x2+−4x+3
Combine Like Terms:
=x3+−2x+3+−3x2+−4x+3
=(x3)+(−3x2)+(−2x+−4x)+(3+3)
=x3+−3x2+−6x+6
Answer: x3−3x2−6x+6
Answer:
July 2
Step-by-step explanation:
June has 30 days total.
2 weeks is 7(2) or 14 days
18 + 14 = 32
July 2nd would be the correct option because the 2 extra days that come from 32 would go into July. Hope this helps :)
Answer:
Two angles are called complementary if their measures add to 90 degrees, and called supplementary if their measures add to 180 degrees. ... For example, a 50-degree angle and a 40-degree angle are complementary; a 60-degree angle and a 120-degree angle are supplementary