Yes of course! Lol. You are funny young one.
Answer: 400 videos
Step-by-step explanation:
1000/1 x 1/2.5 = 400
Answer:
10% of the students ski and do not wake board
Step-by-step explanation:
The total number of students is 120. 28 students ski while 52 students wake board. 16 of the students ski and wake board.
Let S represent students who ski and W represent those who wake board also W' represent those who do not wake board.
Therefore:
S = 28
W = 52
n = total number of student = 120
S ∩ W = those who ski and wake board = 16
Those who ski and do not wake board = S ∩ W' = S - (S ∩ W) = 28 - 16 = 12
Probability of those who ski and do not wake board = (S ∩ W') / n = 12 / 120 = 0.1 = 10%
10% of the students ski and do not wake board
Parameterize the hemisphere
by
![\mathbf s(u,v)=\langle3\cos u\sin v,3\sin u\sin v,3\cos v\rangle](https://tex.z-dn.net/?f=%5Cmathbf%20s%28u%2Cv%29%3D%5Clangle3%5Ccos%20u%5Csin%20v%2C3%5Csin%20u%5Csin%20v%2C3%5Ccos%20v%5Crangle)
with
and
. Then the surface integral becomes
![\displaystyle\iint_{\mathcal S}(x^2+y^2)z\,\mathrm dS=27\int_{u=0}^{u=2\pi}\int_{v=0}^{v=\pi/2}\cos v\sin^2v\|\mathbf s_u\times\mathbf s_v\|\,\mathrm dv\,\mathrm du](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Ciint_%7B%5Cmathcal%20S%7D%28x%5E2%2By%5E2%29z%5C%2C%5Cmathrm%20dS%3D27%5Cint_%7Bu%3D0%7D%5E%7Bu%3D2%5Cpi%7D%5Cint_%7Bv%3D0%7D%5E%7Bv%3D%5Cpi%2F2%7D%5Ccos%20v%5Csin%5E2v%5C%7C%5Cmathbf%20s_u%5Ctimes%5Cmathbf%20s_v%5C%7C%5C%2C%5Cmathrm%20dv%5C%2C%5Cmathrm%20du)
We have
![\mathbf s_u\times\mathbf s_v=\langle-9\cos u\sin^2v,-9\sin u\sin^2v,-9\cos v\sin v\rangle](https://tex.z-dn.net/?f=%5Cmathbf%20s_u%5Ctimes%5Cmathbf%20s_v%3D%5Clangle-9%5Ccos%20u%5Csin%5E2v%2C-9%5Csin%20u%5Csin%5E2v%2C-9%5Ccos%20v%5Csin%20v%5Crangle)
![\implies\|\mathbf s_u\times\mathbf s_v\|=9\sin v](https://tex.z-dn.net/?f=%5Cimplies%5C%7C%5Cmathbf%20s_u%5Ctimes%5Cmathbf%20s_v%5C%7C%3D9%5Csin%20v)
The integral reduces to
![\displaystyle243\int_{u=0}^{u=2\pi}\int_{v=0}^{v=\pi/2}\cos v\sin^3v\,\mathrm dv\,\mathrm du](https://tex.z-dn.net/?f=%5Cdisplaystyle243%5Cint_%7Bu%3D0%7D%5E%7Bu%3D2%5Cpi%7D%5Cint_%7Bv%3D0%7D%5E%7Bv%3D%5Cpi%2F2%7D%5Ccos%20v%5Csin%5E3v%5C%2C%5Cmathrm%20dv%5C%2C%5Cmathrm%20du)
Substitute
,
:
![\displaystyle486\pi\int_{t=0}^{t=1}t^3\,\mathrm dt=\frac{243\pi}2](https://tex.z-dn.net/?f=%5Cdisplaystyle486%5Cpi%5Cint_%7Bt%3D0%7D%5E%7Bt%3D1%7Dt%5E3%5C%2C%5Cmathrm%20dt%3D%5Cfrac%7B243%5Cpi%7D2)