✌HEYA!!!
HERE IS YOUR ANSWER=
THERE ARE ONLY TWO CASES WHEN COMPUTER PICKED A 1 AND A 2 OUT OF 25..
CASES= (1,2);(2,1)
P (E)=2/25
O.O8
WHICH IS OPTION D.
HOPE IT HELPS YOU '_'
Answer:
9/4 x 16/5
=36/5
Step-by-step explanation:
Parameterize
by
![\vec r(u,v)=\dfrac23u\cos v\,\vec\imath+\dfrac23u\sin v\,\vec\jmath+u\,\vec k](https://tex.z-dn.net/?f=%5Cvec%20r%28u%2Cv%29%3D%5Cdfrac23u%5Ccos%20v%5C%2C%5Cvec%5Cimath%2B%5Cdfrac23u%5Csin%20v%5C%2C%5Cvec%5Cjmath%2Bu%5C%2C%5Cvec%20k)
with
and
. Take the normal vector to
to be
![\vec r_u\times\vec r_v=-\dfrac23u\cos v\,\vec\imath-\dfrac23u\sin v\,\vec\jmath+\dfrac49u\,\vec k](https://tex.z-dn.net/?f=%5Cvec%20r_u%5Ctimes%5Cvec%20r_v%3D-%5Cdfrac23u%5Ccos%20v%5C%2C%5Cvec%5Cimath-%5Cdfrac23u%5Csin%20v%5C%2C%5Cvec%5Cjmath%2B%5Cdfrac49u%5C%2C%5Cvec%20k)
(orientation doesn't matter here)
Then the area of
is
![\displaystyle\iint_S\mathrm dA=\iint_S\|\vec r_u\times\vec r_v\|\,\mathrm du\,\mathrm dv](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Ciint_S%5Cmathrm%20dA%3D%5Ciint_S%5C%7C%5Cvec%20r_u%5Ctimes%5Cvec%20r_v%5C%7C%5C%2C%5Cmathrm%20du%5C%2C%5Cmathrm%20dv)
![=\displaystyle\frac{2\sqrt{13}}9\int_0^{2\pi}\int_4^5u\,\mathrm du\,\mathrm dv](https://tex.z-dn.net/?f=%3D%5Cdisplaystyle%5Cfrac%7B2%5Csqrt%7B13%7D%7D9%5Cint_0%5E%7B2%5Cpi%7D%5Cint_4%5E5u%5C%2C%5Cmathrm%20du%5C%2C%5Cmathrm%20dv)
![=\displaystyle\frac{4\sqrt{13}\,\pi}9\int_4^5u\,\mathrm du=\boxed{2\sqrt{13}\,\pi}](https://tex.z-dn.net/?f=%3D%5Cdisplaystyle%5Cfrac%7B4%5Csqrt%7B13%7D%5C%2C%5Cpi%7D9%5Cint_4%5E5u%5C%2C%5Cmathrm%20du%3D%5Cboxed%7B2%5Csqrt%7B13%7D%5C%2C%5Cpi%7D)
![a_n=a_1+d(n-1) \\ a_1=-6 \\ d=3 \\ a_n=-6+3(n-1)=-6+3n-3=3n-9](https://tex.z-dn.net/?f=a_n%3Da_1%2Bd%28n-1%29%20%5C%5C%0Aa_1%3D-6%20%5C%5C%20d%3D3%20%5C%5C%0Aa_n%3D-6%2B3%28n-1%29%3D-6%2B3n-3%3D3n-9)
The nth term of the sequence is 3n-9.
Now replace n with 22.
![a_{22}=3 \times22-9=66-9=57](https://tex.z-dn.net/?f=a_%7B22%7D%3D3%20%5Ctimes22-9%3D66-9%3D57)
57 is the 22nd term of this sequence.