Based on the information given the average speed for his trip is 64 miles.
<h3>
Average speed:</h3>
Using this formula
d=rt
r=d/t
Where:
r=rate=?
d=distance=512 miles
t=time=8 hours
Let plug in the formula
r=512/8
r=64 miles
Inconclusion the average speed for his trip is 64 miles.
Learn more about average speed here:brainly.com/question/6504879
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
A = √(18+b)(18-b), -√(18+b)(18-b)
b= √(18+a)(18-a), -√(18+a)(18-a)
take the root of both sides and solve I hope this helps
Answer:
y = x^2 +2
Step-by-step explanation:
x^2 is parabolic not linear
I would say pick the second diagram. And 25 hours.