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)
3520*5=17600. You could just use a calculator if you're going to cheat, you know.
We can see that the 33 degrees corresponds to angle A (parallel lines) meaning they’re equal.
This means that 33 + 2x = 5x (5x is the exterior angle, so the other two interior angles’ sum must equal to it)
3x = 33
x = 11
Answer: Rounded it would be 0, unrounded it would be 0.0144927536231884
Step-by-step explanation: Basic Division
Answer:
Step-by-step explanation:
<u>Let the number be x</u>
- 380% of x is 99
- x*3.8 = 99
- x = 99/3.8
- x = 26 rounded to the nearest whole number