ericuh
24.08.2020 •
Mathematics
A small ball floats on the surface of the water in a wave pool. As a wave moves past the ball, the ball's
height above the bottom of the pool varies from 22 inches to 34 inches. The waves occur every
6 seconds. Which function 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?
d(t) = 12 cos(3At) + 28
d (t) = 6 cos(3mt) + 28
34 in.
d(t) = 6 cos (+) +
+ 28
22 in
d(t) = 12 cos( 5 ) + 28
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Ответ:
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
The standard wave equation is expressed as;
where:
A is the amplitude
Get the amplitude:
If the wave occurs every 3 seconds, then:
Get the midline D
Substitute the given parameters into the equation above to have;
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
Learn more here: link
Ответ:
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
Ответ:
153 miles
Step-by-step explanation:
36 * 4.25 = 153