f(x) = 7 sin (4πx) + 3. The function f(x) = 7 sin (4πx) + 3 describe a sinusoidal function whose period is 1/2, maximum value 10, minimum value -4, and it has a y-intercept of 3.
A sinudoidal function whose period is 1/2, maximum value is 10, minimum value is -4, and it has a y-intercept of 3. Let's write to the form f(x) = A sin (ωx +φ) + k, where A is the amplitude, ω is the angular velocity with ω=2πf, (ωx+φ) is the oscillation phase, φ the initial phase (horizontal shift), and k is y-intercept (vertical shift).
Calculating the amplitude:
A = |max - min/2|
A = |10 - (-4)/2| = 14/2
A = 7
calculating the ω:
The period of a sinusoidal is T = 1/f --------> f = 1 / T
ω = 2πf -------> ω = 2π ( 1/T) with T = 1/2
ω = 2π (1/(1/2) = 2π (2)
ω = 4π
The y-intercept k = 3
Writing the equation function with A = 7, ω = 4π, k = 3, φ = 0.
f(x) = A f(x) = A sin (ωx +φ) + k ----------> f(x) = 7 sin (4πx) + 3.
We expand first (cos x +cos y)^2+(sin x-sin y)^2:
= cos^2 x + 2 cos x cos y + cos^2 y+ sin ^2 x + sin ^2 y - 2 sin x sin y
= (cos^2 x + sin ^2 x) + (cos^2 y + sin ^2 y) + 2 (cos x cos y - sin x sin y)
then, apply the trigonometric identities of addition and summation of angles
= 1 + 1 + 2 cos (x+y)
we add the following identities above that results to
2 + 2 cos (x+y)
Answer:
Power analysis
Step-by-step explanation:
Power analysis is a significant part of test structure. It permits us to decide the example size required to recognize an impact of a given size with a given level of certainty. On the other hand, it permits us to decide the likelihood of recognizing an impact of a given size with a given degree of certainty, under example size requirements. On the off chance that the likelihood is unsuitably low, we would be shrewd to adjust or forsake the analysis.
The principle reason underlying power analysis is to assist the analyst with determining the littlest example size that is appropriate to recognize the impact of a given test at the ideal degree of hugeness.
9514 1404 393
Answer:
y +2 = 4/5(x -2)
Step-by-step explanation:
The two marked points differ vertically by 4 (rise = 4) and horizontally by 5 (run = 5). The slope is ...
m = rise/run = 4/5
The point-slope form of the equation for a line is ...
y -k = m(x -h) . . . . . . line with slope m through point (h, k)
For slope 4/5 and point (2, -2), the equation is ...
y +2 = 4/5(x -2)
2 x 2 x 2 = 8
so 222 would be an even number