Math Problem Statement
The depth of water in a harbor is modeled by the function d(t) = 5 * cos(πt/6) + 7, where d(t) is the depth in meters and t is the time in hours since midnight. If a boat requires at least 6 meters of water to dock, by what time must it leave the harbor? When can it return? Give the answers in HH:MM to the nearest minute.
Solution
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Math Problem Analysis
Mathematical Concepts
Trigonometry
Cosine Function
Time Calculation
Formulas
d(t) = 5 * cos(πt/6) + 7
Solve d(t) = 6 for t
Theorems
Cosine function properties
Inverse cosine for solving time
Suitable Grade Level
Grades 10-12
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