<span>Y is directly proportional to x^2. It could be represented by the expression:
y </span>α x^2
We can make it into an equality by inserting the proportionality constant, k.
y = kx^2
k would be constant for any value of y with a corresponding value of x. We solve the problem by this concept as follows:
y1/(x1)^2 = y2/(x2)^2
10/(x1)^2 = y2/(x1/2)^2
10/4 = y2
Therefore, when the value of x is halved, y is equal to 10/4.
Perimeter of a rectangle is 2L+2W
let L=L
W= 2L-7
2L^2 - 7L = 100
Factor it at find that L= -5.53 or 9.03
Length can’t be a negative value si answer is 9.03 for length.
Plug this value in for W=2L-7
W=11.06
Answer:
See Explanation Below
Step-by-step explanation:
Given
![(sin x - cos x)^2 = sec^2x - tan^2x - 2sinx.cos x.](https://tex.z-dn.net/?f=%28sin%20x%20-%20cos%20x%29%5E2%20%3D%20sec%5E2x%20-%20tan%5E2x%20-%202sinx.cos%20x.)
Required
Prove
To start with; we open the bracket on the left hand side
![(sin x - cos x)^2 = (sin x - cos x)(sin x - cos x)](https://tex.z-dn.net/?f=%28sin%20x%20-%20cos%20x%29%5E2%20%3D%20%28sin%20x%20-%20cos%20x%29%28sin%20x%20-%20cos%20x%29)
![(sin x - cos x)^2 = (sin x )(sin x - cos x)- (cos x)(sin x - cos x)](https://tex.z-dn.net/?f=%28sin%20x%20-%20cos%20x%29%5E2%20%3D%20%28sin%20x%20%29%28sin%20x%20-%20cos%20x%29-%20%28cos%20x%29%28sin%20x%20-%20cos%20x%29)
![(sin x - cos x)^2 = sin^2 x -sinx cos x - sin xcos x + cos^2 x](https://tex.z-dn.net/?f=%28sin%20x%20-%20cos%20x%29%5E2%20%3D%20sin%5E2%20x%20-sinx%20cos%20x%20-%20sin%20xcos%20x%20%2B%20cos%5E2%20x)
![(sin x - cos x)^2 = sin^2 x -2sinx cos x + cos^2 x](https://tex.z-dn.net/?f=%28sin%20x%20-%20cos%20x%29%5E2%20%3D%20sin%5E2%20x%20-2sinx%20cos%20x%20%2B%20cos%5E2%20x)
Reorder
![(sin x - cos x)^2 = sin^2 x + cos^2 x - 2sinx cos x](https://tex.z-dn.net/?f=%28sin%20x%20-%20cos%20x%29%5E2%20%3D%20sin%5E2%20x%20%2B%20cos%5E2%20x%20-%202sinx%20cos%20x)
From trigonometry;
![sin^2x + cos^2x = 1](https://tex.z-dn.net/?f=sin%5E2x%20%2B%20cos%5E2x%20%3D%201)
So;
![(sin x - cos x)^2 = sin^2 x + cos^2 x - 2sinx cos x](https://tex.z-dn.net/?f=%28sin%20x%20-%20cos%20x%29%5E2%20%3D%20sin%5E2%20x%20%2B%20cos%5E2%20x%20-%202sinx%20cos%20x)
becomes
![(sin x - cos x)^2 = 1 - 2sinx cos x](https://tex.z-dn.net/?f=%28sin%20x%20-%20cos%20x%29%5E2%20%3D%201%20-%202sinx%20cos%20x)
Also from trigonometry;
![sec^2x - tan^2x = 1](https://tex.z-dn.net/?f=sec%5E2x%20-%20tan%5E2x%20%3D%201)
So,
![(sin x - cos x)^2 = 1 - 2sinx cos x](https://tex.z-dn.net/?f=%28sin%20x%20-%20cos%20x%29%5E2%20%3D%201%20-%202sinx%20cos%20x)
becomes
![(sin x - cos x)^2 = sec^2x - tan^2x - 2sinx cos x](https://tex.z-dn.net/?f=%28sin%20x%20-%20cos%20x%29%5E2%20%3D%20sec%5E2x%20-%20tan%5E2x%20%20-%202sinx%20cos%20x)
Proved
The third answer is correct 4^0
Because the equation equals to 1
And anything powered to 0 is qual to 1