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Answer :
To model the tides in the Hudson Bay, we need to find the amplitude, period, and midline of a function that describes this tidal variation.
1. Amplitude: The amplitude is the height from the midline to the maximum (or minimum) point of the wave. It is calculated as half the difference between the maximum and minimum tide levels.
- Minimum tide level = 3 feet
- Maximum tide level = 9 feet
The amplitude is calculated as:
[tex]\[
\text{Amplitude} = \frac{\text{Maximum} - \text{Minimum}}{2} = \frac{9 - 3}{2} = 3 \text{ feet}
\][/tex]
2. Period: The period is the time it takes to complete one full cycle of the wave. According to the problem, this is given as 14 hours.
- Period = 14 hours
3. Midline: The midline is the average level of the tide, essentially the middle value between the maximum and minimum tides. It is calculated as the average of these two values.
[tex]\[
\text{Midline} = \frac{\text{Maximum} + \text{Minimum}}{2} = \frac{9 + 3}{2} = 6 \text{ feet}
\][/tex]
Based on these calculations, the amplitude is 3 feet, the period is 14 hours, and the midline is at 6 feet. Therefore, the correct option is:
Amplitude = 3 feet; period = 14 hours; midline = 6
1. Amplitude: The amplitude is the height from the midline to the maximum (or minimum) point of the wave. It is calculated as half the difference between the maximum and minimum tide levels.
- Minimum tide level = 3 feet
- Maximum tide level = 9 feet
The amplitude is calculated as:
[tex]\[
\text{Amplitude} = \frac{\text{Maximum} - \text{Minimum}}{2} = \frac{9 - 3}{2} = 3 \text{ feet}
\][/tex]
2. Period: The period is the time it takes to complete one full cycle of the wave. According to the problem, this is given as 14 hours.
- Period = 14 hours
3. Midline: The midline is the average level of the tide, essentially the middle value between the maximum and minimum tides. It is calculated as the average of these two values.
[tex]\[
\text{Midline} = \frac{\text{Maximum} + \text{Minimum}}{2} = \frac{9 + 3}{2} = 6 \text{ feet}
\][/tex]
Based on these calculations, the amplitude is 3 feet, the period is 14 hours, and the midline is at 6 feet. Therefore, the correct option is:
Amplitude = 3 feet; period = 14 hours; midline = 6
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