Before a tidal wave the sea level usually drops first leaving the seabed exposed. (normally about 30 feet below sea level) then it rises an equal distance above sea level. Waves hitting a city with a maximum height of 38.9 meters. The cycle of rise and fall was 26-35 minutes with the waves following the sine curve (height Y of the tsunami wave varies sinusoidally with time t) make a model to describe the event.

1. Use A*sin(b*t) + k
2. How long did the water recede before the waves came crashing in at 35 minutes and at 26 minutes. Does this model have limitations
-H-shift I did (Max+min/2) with 30 feet converted to 9.144 meters. (38.9+(-9.144)/2)=14.878 meters=K
-for Amplitude I got 38.9-14.878= 24.022 =A
Frequency was 1wave every 35 minutes so I did( 2pi/35)=.17952=b and V-shift(26/2pi)=40.84= t
So for the equation I got 24.022 sin (.17952x-40.84) + 14.878
Someone please help me, I've been struggling with this to the max, I'll be grateful for any type of help at all.

Hmmm. It says "the waves came crashing in at 35 minutes and at 26 minutes". That sounds like a period of 9 minutes, so I'd make b=2pi/9 rather than 2pi/35.

so, for #2, I'd say the water receded for 4.5 minutes before crashing in.

Other than that, your work looks good.

ohh no i meant to write if it came at 35 and what if it came at 26, but that's great, thanks alot for looking over it!!!!

Your model equation looks correct. The equation is given by:

Y = A*sin(b*t) + k

Where:
- Y represents the height of the tsunami wave above or below sea level
- A is the amplitude of the wave, which is the difference between the maximum and minimum heights (in this case, 38.9 meters - 9.144 meters = 29.756 meters)
- b is the frequency of the wave, which is determined by the time it takes for one complete cycle (in this case, b = 2π/35 minutes ≈ 0.17952)
- t represents the time in minutes
- k is the vertical shift, which is the average of the maximum and minimum heights (in this case, (38.9 meters + (-9.144 meters))/2 ≈ 14.878 meters)

To use this model to find out how long the water receded before the waves came crashing in at 35 minutes and 26 minutes, you simply substitute these values into the equation.

At t = 35 minutes:
Y = 24.022*sin(0.17952*35 - 40.84) + 14.878

At t = 26 minutes:
Y = 24.022*sin(0.17952*26 - 40.84) + 14.878

After substituting these values and evaluating the equations, you will get the height of the tsunami wave at those specific times. If the height is negative, it means the water has receded below sea level. If the height is positive, it means the water has risen above sea level.

Regarding the limitations of this model, it is important to note that it assumes a sine wave pattern for the tsunami and does not take into account other factors that may affect the behavior and magnitude of a tsunami, such as the shape of the coastline, underwater topography, or the specific characteristics of the event causing the tsunami. Real-life tsunamis can be much more complex and unpredictable.