Solution
- The lowest value of the sinusoidal function is usually gotten using the formula:
[tex]\begin{gathered} L=M-A \\ where, \\ M=\text{ The value of the midline} \\ A=\text{ The Amplitude or highest value} \end{gathered}[/tex]
- The question says that the sea falls 6ft below sea level and rises 6ft above sea level.
- The midline M represents the sea level and the rise of 6ft represents the amplitude.
- Thus, the above equation can be rewritten as:
[tex]L=M-6[/tex]
- The formula for finding the peak of the sinusoidal is:
[tex]\begin{gathered} U=M+A \\ where, \\ U=\text{ The Peak or height of the water} \end{gathered}[/tex]
- We can similarly rewrite the equation as:
[tex]U=M+6[/tex]
- We have been given the peak height of the water to be 16. Thus, U = 16. Thus, we can find the midline (M) as follows:
[tex]\begin{gathered} U=M+6 \\ put\text{ }U=16 \\ 16=M+6 \\ \text{ Subtract 6 from both sides} \\ M=16-6=10 \end{gathered}[/tex]
- Thus, the midline (M) is at 10ft. This also implies that the sea level is at 10 ft.
- Thus, we can find the lowest value or low line as follows:
[tex]\begin{gathered} L=M-6 \\ \text{ We know that }M=10 \\ \\ \therefore L=10-6=4ft \end{gathered}[/tex]
Final Answer
The lowest value or Low line is at 4ft
