Visible light ultraviolet rays radio waves infrared waves
Answer:
![2cos^2(\theta) - 1 = cos(2\theta)](https://tex.z-dn.net/?f=2cos%5E2%28%5Ctheta%29%20-%201%20%3D%20cos%282%5Ctheta%29)
Explanation:
Given
![2cos^2(\theta) - 1](https://tex.z-dn.net/?f=2cos%5E2%28%5Ctheta%29%20-%201)
Required
Simplify
In trigonometry:
![sin^2(\theta) + cos^2(\theta) = 1](https://tex.z-dn.net/?f=sin%5E2%28%5Ctheta%29%20%2B%20cos%5E2%28%5Ctheta%29%20%3D%201)
So; the given expression becomes
![2cos^2(\theta) - (sin^2(\theta) + cos^2(\theta))](https://tex.z-dn.net/?f=2cos%5E2%28%5Ctheta%29%20-%20%28sin%5E2%28%5Ctheta%29%20%2B%20cos%5E2%28%5Ctheta%29%29)
Open Bracket
![2cos^2(\theta) - sin^2(\theta) - cos^2(\theta)](https://tex.z-dn.net/?f=2cos%5E2%28%5Ctheta%29%20-%20sin%5E2%28%5Ctheta%29%20-%20cos%5E2%28%5Ctheta%29)
Collect Like Terms
![2cos^2(\theta) - cos^2(\theta)- sin^2(\theta)](https://tex.z-dn.net/?f=2cos%5E2%28%5Ctheta%29%20-%20cos%5E2%28%5Ctheta%29-%20sin%5E2%28%5Ctheta%29)
![cos^2(\theta)- sin^2(\theta)](https://tex.z-dn.net/?f=cos%5E2%28%5Ctheta%29-%20sin%5E2%28%5Ctheta%29)
In trigonometry:
![cos(\theta + \theta) = cos^2(\theta)- sin^2(\theta)](https://tex.z-dn.net/?f=cos%28%5Ctheta%20%2B%20%5Ctheta%29%20%3D%20cos%5E2%28%5Ctheta%29-%20sin%5E2%28%5Ctheta%29)
This implies that:
![cos^2(\theta)- sin^2(\theta) = cos(\theta + \theta)](https://tex.z-dn.net/?f=cos%5E2%28%5Ctheta%29-%20sin%5E2%28%5Ctheta%29%20%3D%20cos%28%5Ctheta%20%2B%20%5Ctheta%29)
=
![cos(\theta + \theta)](https://tex.z-dn.net/?f=cos%28%5Ctheta%20%2B%20%5Ctheta%29)
![cos(2\theta)](https://tex.z-dn.net/?f=cos%282%5Ctheta%29)
Hence:
When you say full valence shell, are you talking about a valence electron shell?
I am learning about atoms and i know a little bit
Answer:
Explanation:
Let the luminosity of the star be I and luminosity of the sun be Isun.
2.4 billion light years = 2.4 x 10⁹ light years .
brightness = luminosity / (distance)²
Given Sun would have to be viewed from a distance of 1300 light-years to have the same apparent magnitude as 3C 273 so
For the sun
brightness = Isun / (1300 light years )²
For star
brightness = I / (2.4 x 10⁹ light years )²
Both these brightness are same
Isun / (1300 light years )² = I / (2.4 x 10⁹ light years )²
I = Isun x (2.4 x 10⁹ light years )² / (1300 light years )²
= Isun x 3.4 x 10¹² .