Answer:
-196π
Step-by-step explanation:
F can be rewritten as
if S is the upper hemisphere
oriented upward, then the border of S is the circle C
traversed counterclockwise
By Stoke's theorem
where C is the circle of center (0,0,0) and radius 7 on the XY-plane traveled counterclockwise.
This circle can be parametrized as
<em>r(t) = (7cos(t), 7sin(t),0) with 0 ≤t ≤ 2π </em>
Computing the curve integral
![\bf \displaystyle\int_{C}F.dC=\displaystyle\int_{0}^{2\pi}F(r(t))\bullet r'(t)dt=\displaystyle\int_{0}^{2\pi}F(7cos(t),7sin(t),0)\bullet (-7sin(t),7cos(t),0)dt=\\\\=\displaystyle\int_{0}^{2\pi} (28sin(t),0,7cos(t)e^{7sin(t)})\bullet(-7sin(t),7cos(t),0)dt=\\\\-196\displaystyle\int_{0}^{2\pi}sin^2(t)dt=\boxed{-196\pi}](https://tex.z-dn.net/?f=%5Cbf%20%5Cdisplaystyle%5Cint_%7BC%7DF.dC%3D%5Cdisplaystyle%5Cint_%7B0%7D%5E%7B2%5Cpi%7DF%28r%28t%29%29%5Cbullet%20r%27%28t%29dt%3D%5Cdisplaystyle%5Cint_%7B0%7D%5E%7B2%5Cpi%7DF%287cos%28t%29%2C7sin%28t%29%2C0%29%5Cbullet%20%28-7sin%28t%29%2C7cos%28t%29%2C0%29dt%3D%5C%5C%5C%5C%3D%5Cdisplaystyle%5Cint_%7B0%7D%5E%7B2%5Cpi%7D%20%2828sin%28t%29%2C0%2C7cos%28t%29e%5E%7B7sin%28t%29%7D%29%5Cbullet%28-7sin%28t%29%2C7cos%28t%29%2C0%29dt%3D%5C%5C%5C%5C-196%5Cdisplaystyle%5Cint_%7B0%7D%5E%7B2%5Cpi%7Dsin%5E2%28t%29dt%3D%5Cboxed%7B-196%5Cpi%7D)
Answer: $2.50
Step-by-step explanation: I don't really know if I'm right let me know if I am but what I came up with is half of 20 is 10 half of 10 is 5 and half of 5 is two and a half so $2.50
C(n) = 20n + 15
<span>y = 20n + 15 </span>
<span>20n = y - 15</span>
<span>n = (y - 15)/20 </span>
B.)
<span>N(c) = (c-15)/20
(:
</span>
Answer:
4 minutes and then 0.25 or 1/4
Step-by-step explanation:
Answer:
{HH,CC,HC,CH}
Step-by-step explanation:
We are given that
H denotes hot and cloudy denotes C.
We have to find the total possible outcomes for the weather on two consecutive days.
The possible cases in two consecutive days
Both days are hot=HH
Both days are cloud=CC
First day is hot other day cloudy=HC
First day is cloudy other day is hot=CH
Total possible cases=HH,CC,HC,CH
Therefor, the total outcomes for the weather on two consecutive days={HH,CC,HC,CH}