Question

sea levels follow a periodic pattern of rise and fall called the tides. the graph below shows the sea level at a certain beach, in feet, over one day, where time t is measured in hours after 12:00 a.m. (midnight) on the first day. what is the midline and what does it represent in this context?

Explanation:

Step1: Identify maximum and minimum values

The maximum sea - level value is 26 feet (from points (0, 26) and (12, 26)) and the minimum sea - level value is 0 feet (from points (6, 0) and (18, 0)).

Step2: Calculate the midline

The formula for the midline of a periodic function \(y = f(x)\) with maximum value \(M\) and minimum value \(m\) is \(y=\frac{M + m}{2}\). Here, \(M = 26\) and \(m = 0\), so \(y=\frac{26+0}{2}=13\).

Step3: Interpret the midline

In the context of tides, the midline represents the average sea - level over the given time period. It is the sea - level around which the tides oscillate.

Answer:

The midline is \(y = 13\) feet. It represents the average sea - level over the one - day period for which the tides are being measured.