Answer:
The correct option is;
d(t) = 6·cos(π/3·t) + 28
Step-by-step explanation:
The general form of a cosine function is given as follows;
y = A·cos(B·x - C) + D
Where;
A = The amplitude = The distance from the peak to the midline = 1/2×(Maximum - minimum)
The amplitude = 1/2 × (34 - 22) = 6 inches
B = 2·π/P = 2·π/6 = π/3
P = The period = 6 seconds
C/B = The phase shift
D = The midline = Minimum + Amplitude = 22 + 6 = 28 inches
x = The independent variable
Therefore, to model the function of the wave can be given as follows;
d(t) = 6·cos(π/3·t) + 28
A function that models the distance from the bottom of the pool to the ball, as it moves from wave crest to wave crest, as a function of t in seconds is [tex]d(t)= 6cos(\frac{\pi}{3} t) + 28[/tex]
The standard wave equation is expressed as;
[tex]y=Acos(Bx-C)+D[/tex] where:
A is the amplitude
Get the amplitude:
[tex]A=\frac{1}{2}(34-22)\\A=\frac{1}{2}(12)\\A= 6\\[/tex]
If the wave occurs every 3 seconds, then:
[tex]B=\frac{2 \pi}{k} \\B=\frac{2\pi }{6}\\B=\frac{\pi}{3}[/tex]
Get the midline D
[tex]D=minimum + amplitude\\D=22+6\\D = 28[/tex]
Substitute the given parameters into the equation above to have;
[tex]y= 6cos(\frac{\pi}{3} t) + 28[/tex]
Hence a function that models the distance from the bottom of the pool to the ball, as it moves from wave crest to wave crest, as a function of t in seconds is [tex]d(t)= 6cos(\frac{\pi}{3} t) + 28[/tex]
Learn more here: https://brainly.com/question/25524388
