Math Problem Statement

There are two maize farms in the countryside. Farm one produces maize at a rate of 5 𝑡 t 5 ​ tons per year, where 𝑡 t is the number of years. Farm two produces maize at a rate of − 1.5 cos ⁡ 𝑡 cost −1.5 ​ tons per year, where 𝑡 t is the number of years. Question: What is the first time that the farms have the same production rate? Round your answer to the nearest hundredth.

Solution

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Math Problem Analysis

Mathematical Concepts

Trigonometry
Algebra
Numerical Methods

Formulas

5t = -1.5 cos(t)

Theorems

Cosine Function Behavior
Numerical Root Finding

Suitable Grade Level

Grades 10-12