Answer:
θ = 
(60° )
Step-by-step explanation:
Using the identity
sin²x + cos²x = 1 ⇒ sin²x = 1 - cos²x
Given
cos²θ - sin²θ = 2 - 5cosθ
cos²θ - (1 - cos²θ) = 2 - 5cosθ
cos²θ - 1 + cos²θ = 2 - 5cosθ
2cos²θ - 1 = 2 - 5cosθ ( subtract 2 - 5cosθ from both sides )
2cos²θ + 5cosθ - 3 = 0 ← in standard form
(cosθ + 3)(2cosθ - 1) = 0 ← in factored form
Equate each factor to zero and solve for θ
cosθ + 3 = 0
cosθ = - 3 ← not possible as - 1 ≤ cosθ ≤ 1
2cosθ - 1 = 0
cosθ = 
, so
θ = 
( ) = ( or 60° )
0.06 x 0.5 = 0.03 (I think that is what you're asking)
Answer:
1. 1340
2. Variance = 47200, standard deviation = 217.25556
Step-by-step explanation:
1-
If X is the random variable that give the number of admissions, then the expected number of admissions<em> E[X]</em> for the fall semester is
1080*P(X=1080)+1380*P(X=1380)+1540*P(X=1540) =
1080*0.4+1380*0.1+1540*0.5 = 1340
2-
The <em>variance</em> is defined as
![\sigma^2=E[X^2]-(E[X])^2}](https://tex.z-dn.net/?f=%5Csigma%5E2%3DE%5BX%5E2%5D-%28E%5BX%5D%29%5E2%7D)
We have
![E[X^2]=(1080)^2*0.4+(1380)^2*0.1+(1540)^2*0.5=1842800](https://tex.z-dn.net/?f=E%5BX%5E2%5D%3D%281080%29%5E2%2A0.4%2B%281380%29%5E2%2A0.1%2B%281540%29%5E2%2A0.5%3D1842800)
whereas
![(E[X])^2=(1340)^2=1795600](https://tex.z-dn.net/?f=%28E%5BX%5D%29%5E2%3D%281340%29%5E2%3D1795600)
So the variance equals
The <em>standard deviation is just the square root of the variance</em>, so, the standard deviation is
Step-by-step explanation:
By using the Pythagoras' Theorem,
Height of Kite
= √[(50m)² - (35m)²]
= 35.71m.
