Trigonometric word problem PLEASE HELP :)

[aikastarri]

The depth, D, (in metres) of water at the entrance to a harbour at t hours after midnight on a givenday is represented byD(t)=10+3 sin(πt/6+π/3) for t∈[0, 24]

A boat is permitted to enter the harbour only if the depth of water at the entrance is at least dmetres for a continuous interval of three hours. Algebraically approximate the largest value ofd which satisfies this condition.

 

[Deleted member 4993]

The depth, D, (in metres) of water at the entrance to a harbour at t hours after midnight on a givenday is represented byD(t)=10+3 sin(πt/6+π/3) for t∈[0, 24]

A boat is permitted to enter the harbour only if the depth of water at the entrance is at least d metres for a continuous interval of three hours. Algebraically approximate the largest value of d which satisfies this condition.

What is the maximum water depth in the harbor?

What is the minimum water depth in the harbor? These are limits on "d".

Although the problem said calculate algebraically, I would graph the function and draw a horizontal line - say at d = 12 and see where does it intersect the graph. What can I deduce from it (pertinent to the problem)?

What are your thoughts?

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