Siree wants to go surfing for one hour tomorrow. the height of the waves on a local beach can be approximated by the function h(x)=6sin(xπ8)+8, where x is time in hours.

assume x=0 is midnight, x=1 is 1 a.m., x=2 is 2 a.m., etc.

when will the waves be at least 8 feet in the next 12 hours?

a.the height of the waves are at least 8 feet between at 4: 00 a.m. and 12: 00 p.m.

b. the height of the waves are at least 8 feet between at 12: 00 a.m. and 8: 00 a.m.

c.the height of the waves are at least 8 feet between at 4: 00 p.m. and 8: 00 p.m.

d.the height of the waves are at least 8 feet between at 8: 00 a.m. and 4: 00 p.m.

, i don't know where to start! can i get the brainliest person?

Option B. The height of the waves are at least 8 feet between 12:00 am and 8:00 am.

Explanation:

The correct function H(x) that approximate the height of the waves is:

Now, understand what each term and factor mean:

1. Coefficient 6:

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.

2. Constant term 8:

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.

3. Sine part of the function:

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).

4. Calculate the height of the wave at midnight, i.e x = 0

Then, then the waves will be 8 feet the first time at midnight.

5. Find the time when the wave reaches the maximumm height first time:

H(max) = 6 feet + 8 feet = 14

Hence, the wave will be at its maximum height (14 feet) at 4 am.

6. Use symmetry.

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.

7 Conclusion:

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.

a

Step-by-step explanation: