the depth of water at the end of a boat dock can be modeled by a senusoidal function Y=Asin [B(r+C) ]+D where y represents the depth in feet of the water, hours after midnight on a certain day, the depth is 10 feet at low tide at 6 am and 18 feet at high tide at noon find the amplitude and midline for the general sine function that can be used to model the water’s depth.
Question
Answer:
A=4 ft
Midline: y=14
Step-by-step explanation:
When talking about sinusoidal waves, we know the amplitude will be the distance between the midline and the highest or lowest point of the graph. This can be found by first, finding the distance between the lowest point and the highest point:
d= 18ft – 10ft = 8ft
and divide this distance into 2:
[tex]A=\frac{8}{2}[/tex]
A= 4 ft
in order to find the midline, we need to figure the midpoint between the highest and lowest value. We can do so by using the following formula:
[tex]Midpoint=\frac{high+low}{2}[/tex]
so:
[tex]Midpoint=\frac{18+10}{2}[/tex]
Midpoint = 14
so the midline is located at the line:
y=14