Answer:
y = In | cos(2x + c ) | + c
Step-by-step explanation:
y" + (y')^2 + 4 = 0
substituting u = y'
u' + u^2 + 4 = 0
hence : u' = - (u^2 + 4 )
= 1 ------- (1)
integrating both sides of the equation 1
x + c =
hence u = -2 tan(2x + c )
remember u = y'
y' = -2 tan(2x + c) ------ (2)
integrating both sides of the equation 2
y = ∫ ![\frac{-sin u}{cos u } du](https://tex.z-dn.net/?f=%5Cfrac%7B-sin%20u%7D%7Bcos%20u%20%7D%20du)
therefore Y = In | cosu | + c
y = In | cos(2x + c ) | + c
Answer:
You are expected to lose $0.05 (or win -$0.05)
Step-by-step explanation:
Since the roulette wheel has the numbers 1 through 36, 0, and 00, there are 38 possible outcomes.
In this bet, you are allowed to pick 3 out of the 38 numbers. Thus, your chances of winning (P(W)) and losing (P(L)) are:
![P(W)=\frac{3}{38}\\P(L) = 1 - P(W)\\P(L) = \frac{35}{38}\\](https://tex.z-dn.net/?f=P%28W%29%3D%5Cfrac%7B3%7D%7B38%7D%5C%5CP%28L%29%20%3D%201%20-%20P%28W%29%5C%5CP%28L%29%20%3D%20%5Cfrac%7B35%7D%7B38%7D%5C%5C)
The expected value of the bet is given by the sum of the product of each outcome pay by its probability. Winning the bet means winning $11 while losing the bet means losing $1. The expected value is:
![EV = (11*\frac{3}{38}) -(1*\frac{35}{38})\\EV = -\$0.0525](https://tex.z-dn.net/?f=EV%20%3D%20%2811%2A%5Cfrac%7B3%7D%7B38%7D%29%20-%281%2A%5Cfrac%7B35%7D%7B38%7D%29%5C%5CEV%20%3D%20-%5C%240.0525)
Therefore, with a $1 bet, you are expected to lose roughly $0.05
Answer:
x = π/12 and x = π/4.
Step-by-step explanation:
2sin^2(2x) + 1 = 3sin(2x)
2sin^2(2x) - 3sin(2x) + 1 = 0
(2sin(2x) - 1)(sin(2x) - 1) = 0
2sin(2x) - 1 = 0
2sin(2x) = 1
sin(2x) = 1/2
When there is a variable n = π/6, sin(π/6) = 1/2 [refer to the unit circle].
2x = π/6
x = π/12
sin(2x) - 1 = 0
sin(2x) = 1
When there is a variable n = π/2, sin(π/2) = 1 [refer to the unit circle].
2x = π/2
x = π/4
Hope this helps!
Answer:
the answer its d
Step-by-step explanation:
I hope this helps