<h3>
Answer: Choice H) 2</h3>
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Explanation:
Recall that the pythagorean trig identity is ![\sin^2 x + \cos^2x = 1](https://tex.z-dn.net/?f=%5Csin%5E2%20x%20%2B%20%5Ccos%5E2x%20%3D%201)
If we were to isolate sine, then,
![\sin^2 x + \cos^2x = 1\\\\\sin^2 x = 1-\cos^2x\\\\\sin x = \sqrt{1-\cos^2x}\\\\](https://tex.z-dn.net/?f=%5Csin%5E2%20x%20%2B%20%5Ccos%5E2x%20%3D%201%5C%5C%5C%5C%5Csin%5E2%20x%20%3D%201-%5Ccos%5E2x%5C%5C%5C%5C%5Csin%20x%20%3D%20%5Csqrt%7B1-%5Ccos%5E2x%7D%5C%5C%5C%5C)
We don't have to worry about the plus minus because sine is positive when 0 < x < pi/2.
Through similar calculations,
Cosine is also positive in this quadrant.
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So,
![\frac{\sqrt{1-\cos^2x}}{\sin x}+\frac{\sqrt{1-\sin^2x}}{\cos x}\\\\\frac{\sin x}{\sin x}+\frac{\cos x}{\cos x}\\\\1+1\\\\2](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%7B1-%5Ccos%5E2x%7D%7D%7B%5Csin%20x%7D%2B%5Cfrac%7B%5Csqrt%7B1-%5Csin%5E2x%7D%7D%7B%5Ccos%20x%7D%5C%5C%5C%5C%5Cfrac%7B%5Csin%20x%7D%7B%5Csin%20x%7D%2B%5Cfrac%7B%5Ccos%20x%7D%7B%5Ccos%20x%7D%5C%5C%5C%5C1%2B1%5C%5C%5C%5C2)
Therefore,
![\frac{\sqrt{1-\cos^2x}}{\sin x}+\frac{\sqrt{1-\sin^2x}}{\cos x}=2](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%7B1-%5Ccos%5E2x%7D%7D%7B%5Csin%20x%7D%2B%5Cfrac%7B%5Csqrt%7B1-%5Csin%5E2x%7D%7D%7B%5Ccos%20x%7D%3D2)
is an identity as long as 0 < x < pi/2
Answer:
56 ways
Step-by-step explanation:
Number of ways is given by n combination r (n!/(n - r)!r!)
n = total number of students = 8, r = the number of summer courses = 3
Number of ways = 8 combination 3 = 8!/(8-3)!3! = 8!/5!3! = 8×7×6×5!/5!×6 = 8×7 = 56 ways
Answer:
D
Step-by-step explanation:
F(x) = -9 + 10.3x probably.
It's definitely not the first or last option as they have negative gradients (i.e. negative x-coefficient) and so represent a negative correlation. The data given tells us there is a positive gradient and so a positive correlation.
It could be the second option as the second and third are not so vastly different but I would go for the third because it appears to most closely fit the data pattern.
The last statement is true