question 13 (1 point)\n(09.03 mc)\nthe height of a certain playground swing in motion can vary from 2 feet…

question 13 (1 point)\n(09.03 mc)\nthe height of a certain playground swing in motion can vary from 2 feet to 10 feet off the ground. the swing reaches its lowest height when time (t) is 0 and completes a full cycle in 5 seconds. what is the amplitude, period, and midline of a function that would model this periodic phenomenon?\no a amplitude = 4 feet; period = 5 seconds; midline: y = 12\no b amplitude = 4 feet; period = 5 seconds; midline: y = 6\no c amplitude = 8 feet; period = 5 seconds; midline: y = 12\no d amplitude = 8 feet; period = 5 seconds; midline: y = 6

question 13 (1 point)\n(09.03 mc)\nthe height of a certain playground swing in motion can vary from 2 feet to 10 feet off the ground. the swing reaches its lowest height when time (t) is 0 and completes a full cycle in 5 seconds. what is the amplitude, period, and midline of a function that would model this periodic phenomenon?\no a amplitude = 4 feet; period = 5 seconds; midline: y = 12\no b amplitude = 4 feet; period = 5 seconds; midline: y = 6\no c amplitude = 8 feet; period = 5 seconds; midline: y = 12\no d amplitude = 8 feet; period = 5 seconds; midline: y = 6

Answer

Explanation:

Step1: Calculate the mid - line

The mid - line of a periodic function for a height range from $h_{min}$ to $h_{max}$ is given by $y=\frac{h_{min} + h_{max}}{2}$. Here, $h_{min}=2$ feet and $h_{max}=10$ feet. So, $y=\frac{2 + 10}{2}=\frac{12}{2}=6$.

Step2: Calculate the amplitude

The amplitude $A$ of a periodic function for a height range from $h_{min}$ to $h_{max}$ is given by $A=\frac{h_{max}-h_{min}}{2}$. So, $A=\frac{10 - 2}{2}=\frac{8}{2}=4$ feet.

Step3: Identify the period

The problem states that the swing completes a full cycle in 5 seconds. So the period $T = 5$ seconds.

Answer:

B. Amplitude = 4 feet; period = 5 seconds; midline: y = 6