Answer:
160
Step-by-step explanation:
13² - 3² = 13 × 13 - 3 × 3 = 169 - 9 = 160
Answer:
4,600
Step-by-step explanation:
92,000/8= 11500
11500 x 4= 46000 to his wife
11500 for the son
92000-57500= 34500
34500/5= 6,900 each charity
11500-6900= 4600 is how more he is getting than each charity
Answer:
How far does Clare travel in one hour?
A: 36
How far does Clare travel in three hours?
A: 108
How far does Clare travel in 3.5 hours?
A: 126
Step-by-step explanation:
Find the Unit Value
72/2 = 36
Clare travels 36 miles per hour
Therefore, you must multiply the hours by the Unit travel time for the answers.
1 X 36 = 36
3 X 36 = 108
3.5 X 36 = 126
A.
Because in mathematics, a geometric progression, also known as a geometric sequence, is a sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.
Looks like we're given
![\vec F(x,y)=\langle-x,-y\rangle](https://tex.z-dn.net/?f=%5Cvec%20F%28x%2Cy%29%3D%5Clangle-x%2C-y%5Crangle)
which in three dimensions could be expressed as
![\vec F(x,y)=\langle-x,-y,0\rangle](https://tex.z-dn.net/?f=%5Cvec%20F%28x%2Cy%29%3D%5Clangle-x%2C-y%2C0%5Crangle)
and this has curl
![\mathrm{curl}\vec F=\langle0_y-(-y)_z,-(0_x-(-x)_z),(-y)_x-(-x)_y\rangle=\langle0,0,0\rangle](https://tex.z-dn.net/?f=%5Cmathrm%7Bcurl%7D%5Cvec%20F%3D%5Clangle0_y-%28-y%29_z%2C-%280_x-%28-x%29_z%29%2C%28-y%29_x-%28-x%29_y%5Crangle%3D%5Clangle0%2C0%2C0%5Crangle)
which confirms the two-dimensional curl is 0.
It also looks like the region
is the disk
. Green's theorem says the integral of
along the boundary of
is equal to the integral of the two-dimensional curl of
over the interior of
:
![\displaystyle\int_{\partial R}\vec F\cdot\mathrm d\vec r=\iint_R\mathrm{curl}\vec F\,\mathrm dA](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cint_%7B%5Cpartial%20R%7D%5Cvec%20F%5Ccdot%5Cmathrm%20d%5Cvec%20r%3D%5Ciint_R%5Cmathrm%7Bcurl%7D%5Cvec%20F%5C%2C%5Cmathrm%20dA)
which we know to be 0, since the curl itself is 0. To verify this, we can parameterize the boundary of
by
![\vec r(t)=\langle\sqrt5\cos t,\sqrt5\sin t\rangle\implies\vec r'(t)=\langle-\sqrt5\sin t,\sqrt5\cos t\rangle](https://tex.z-dn.net/?f=%5Cvec%20r%28t%29%3D%5Clangle%5Csqrt5%5Ccos%20t%2C%5Csqrt5%5Csin%20t%5Crangle%5Cimplies%5Cvec%20r%27%28t%29%3D%5Clangle-%5Csqrt5%5Csin%20t%2C%5Csqrt5%5Ccos%20t%5Crangle)
![\implies\mathrm d\vec r=\vec r'(t)\,\mathrm dt=\sqrt5\langle-\sin t,\cos t\rangle\,\mathrm dt](https://tex.z-dn.net/?f=%5Cimplies%5Cmathrm%20d%5Cvec%20r%3D%5Cvec%20r%27%28t%29%5C%2C%5Cmathrm%20dt%3D%5Csqrt5%5Clangle-%5Csin%20t%2C%5Ccos%20t%5Crangle%5C%2C%5Cmathrm%20dt)
with
. Then
![\displaystyle\int_{\partial R}\vec F\cdot\mathrm d\vec r=\int_0^{2\pi}\langle-\sqrt5\cos t,-\sqrt5\sin t\rangle\cdot\langle-\sqrt5\sin t,\sqrt5\cos t\rangle\,\mathrm dt](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cint_%7B%5Cpartial%20R%7D%5Cvec%20F%5Ccdot%5Cmathrm%20d%5Cvec%20r%3D%5Cint_0%5E%7B2%5Cpi%7D%5Clangle-%5Csqrt5%5Ccos%20t%2C-%5Csqrt5%5Csin%20t%5Crangle%5Ccdot%5Clangle-%5Csqrt5%5Csin%20t%2C%5Csqrt5%5Ccos%20t%5Crangle%5C%2C%5Cmathrm%20dt)
![=\displaystyle5\int_0^{2\pi}(\sin t\cos t-\sin t\cos t)\,\mathrm dt=0](https://tex.z-dn.net/?f=%3D%5Cdisplaystyle5%5Cint_0%5E%7B2%5Cpi%7D%28%5Csin%20t%5Ccos%20t-%5Csin%20t%5Ccos%20t%29%5C%2C%5Cmathrm%20dt%3D0)