At an ocean depth of 10 meters, a buoy bobs up and then down 6 meters from the ocean's depth. Ten seconds pass from the time the
buoy is at its highest point to when it is at its lowest point. Assume at x = 0 the buoy is at normal ocean depth. Use the sine tool to graph the function. The first point must be on the midline and the second point must be a maximum or minimum value on the graph closest to the first point.
1 answer:
The sine function that corresponds to the scenario is y = 6sin((π / 10) x) - 10.
Step-by-step explanation:
The general equation for a sine function is Asin(Bx)+C.
A buoy rises and drops 6 meters, indicating a vertical and horizontal movement of 6 meters—this is the amplitude.
Thus, the amplitude A is 6.
The period is defined as the horizontal distance for one complete wave cycle.
The buoy takes 10 seconds to go from its peak to its lowest point (half a cycle).
Hence, the total period for a complete cycle is 20 seconds.
Additionally, Period = 2π divided by B.
Thus, 20 (B) = 2π.
This results in B being equal to 2π / 20.
= π / 10.
Since the buoy operates at a depth of 10 meters, C equals -10.
<pinserting all="" values="" into="" the="" formula="" yields:="">⇒y = 6sin((π/10)x) - 10.
The first point marks the midline,
When x=0,
⇒y=6sin(0)-10.
y= -10.
∴ Thus, the line begins at y = -10.
The consecutive point will represent the maximum or minimum value.
Those are (5,-4) and (15, -16.)
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