Answer:
- Option B. <em><u>The height of the waves are at least 8 feet between 12:00 am and 8:00 am.</u></em>
Explanation:
The correct function H(x) that approximate the height of the waves is:
Now, understand what each term and factor mean:
<u>1. Coefficient 6:</u>
- 6 is the amplitude of the wave. It means that the crest of the wave is 6 feet above the rest point, and the trough is 6 feet below the rest point.
<u>2. Constant term 8:</u>
- 8 is the height of the rest point of the wave. That means that the crest of the wave will b 6 feet + 8 feet = 14 feet; and the trough will be - 6 feet + 8 feet = 2 feet.
This is the wave will be oscilating between 2 and 14 feet.
<u>3. Sine part of the function:</u>
The period of the sine function is given by:
That means that the pattern of the wave will repeat every 16 hours (period = 16 hours).
<u>4. Calculate the height of the wave at midnight, i.e x = 0</u>
Then, then the waves will be 8 feet the first time at midnight.
<u>5. Find the time when the wave reaches the maximumm height first time:</u>
- H(max) = 6 feet + 8 feet = 14
Hence, the wave will be at its maximum height (14 feet) at 4 am.
<u>6. Use symmetry.</u>
The wave tool 4 hours to go from 8 feet to 16 feet; given the symmetry of the function it will take other 4 hours to fall from 16 feet to 8 feet.
Hence, the wave will be 8 feet again at 4am + 4 = 8 am.
<u>7 Conclusion:</u>
- The height of the waves will be at least 8 feet between 12:00 am (midnight) and 8:00 am. This is the option B.