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