Question

what phenomenon can be represented by the graph? (1 point) \bigcirc high tide occurs at 15 feet; low tide occurs at 0 feet 12 seconds later. \bigcirc a 30-inch-diameter tire takes 12 seconds to rotate all the way around. \bigcirc a 15-inch-diameter tire takes 12 seconds to rotate all the way around. \bigcirc a 30-foot wheel takes 9 seconds to rotate all the way around.

Explanation:

Step1: Analyze the amplitude

The amplitude of the graph is the distance from the mid - line to the maximum or minimum. The mid - line is at \(y = 15\) (since the range is from \(y = 0\) to \(y = 30\) approximately, and \(\frac{0 + 30}{2}=15\)). The amplitude \(A=\frac{30 - 0}{2}=15\). For a circular motion (like a tire rotating), the diameter \(d = 2A\). So \(d=30\) (if \(A = 15\)).

Step2: Analyze the period

The period \(T\) of a periodic function is the horizontal length of one full cycle. Looking at the graph, from \(x = 4\) to \(x = 16\) (one full cycle of the repeating pattern), \(T=16 - 4=12\). The period of a rotating tire represents the time it takes to complete one full rotation.

Answer:

A 30 - inch - diameter tire takes 12 seconds to rotate all the way around.