Ocean Word Problem: Find Equation

In summary: Please try again later when you have more information.In summary, the water depth in a harbour is 21m at high tide and 11m at low tide. One cycle is completed approximately every 12 hrs. Find an equation for y = 5sin(30t) + 16 when t = high tide, low tide, and period (12 hrs). The graph of y = 5sin(30t) + 16 would be shifted 3 units to the right from y = 5sin(30(t - 3)) + 16 when t = low tide.
  • #1
Veronica_Oles
142
3

Homework Statement



The water depth in a harbour is 21m at high tide and 11m at low tide. One cycle is completed approximately every 12 hrs.

Find an equation.

Homework Equations

The Attempt at a Solution



The answer to this problem is y = 5sin 30 (t-3) + 16

A = (M - m) / 2
= (21-11) / 2
= 5

C = (M+m) / 2
= (21+11)/2
=16

Period is 12 hrs.
K value would be 30 because 360 / 12.

But I don't know why it is (t-3) I'm not sure where that came from.
 
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  • #2
Veronica_Oles said:

Homework Statement



The water depth in a harbour is 21m at high tide and 11m at low tide. One cycle is completed approximately every 12 hrs.

Find an equation.

Homework Equations

The Attempt at a Solution



The answer to this problem is y = 5sin 30 (t-3) + 16

A = (M - m) / 2
= (21-11) / 2
= 5

C = (M+m) / 2
= (21+11)/2
=16

Period is 12 hrs.
K value would be 30 because 360 / 12.

But I don't know why it is (t-3) I'm not sure where that came from.
Is there a little bit more to the problem statement? What times are high tide and low tide? You need to know those times in order to get the time part of your equation correct... :smile:
 
  • #3
Veronica_Oles said:

Homework Statement



The water depth in a harbour is 21m at high tide and 11m at low tide. One cycle is completed approximately every 12 hrs.

Find an equation.

Homework Equations

The Attempt at a Solution



The answer to this problem is y = 5sin 30 (t-3) + 16

A = (M - m) / 2
= (21-11) / 2
= 5

C = (M+m) / 2
= (21+11)/2
=16

Period is 12 hrs.
K value would be 30 because 360 / 12.

But I don't know why it is (t-3) I'm not sure where that came from.
How would the graph of ##y = 5\sin(30t) + 16## look in comparison to ##y = 5\sin(30(t - 3)) + 16##?
 
  • #4
Mark44 said:
How would the graph of ##y = 5\sin(30t) + 16## look in comparison to ##y = 5\sin(30(t - 3)) + 16##?
Wouldn't the second graph be shifted 3 units to the right?
 
  • #5
Veronica_Oles said:
Wouldn't the second graph be shifted 3 units to the right?
Yes. So the point (0, 16) on the first graph is shifted to the right by 3 (hours?) is now at (3, 16).
 
  • #6
Veronica_Oles said:
Wouldn't the second graph be shifted 3 units to the right?
Why is it shifted? What in the original problem statement helps you to figure out when low tide is? You cannot answer this schoolwork problem without that information. And our help is limited by the accuracy of what you post about the Problem Statement.

EDIT -- Apologies, but this is a very straightforward problem if you post all of the question information.
 

1. What is the equation for finding the volume of an ocean?

The equation for finding the volume of an ocean is V = l*w*h, where V represents the volume, l is the length, w is the width, and h is the depth of the ocean.

2. How do you calculate the depth of an ocean using the equation?

To calculate the depth of an ocean, you will need the volume and the length and width of the ocean. You can rearrange the equation V = l*w*h to solve for h, which represents the depth. So, h = V/(l*w).

3. Can this equation be used to calculate the volume of any ocean?

Yes, this equation can be used to calculate the volume of any ocean as long as you have the necessary measurements of length, width, and depth.

4. How accurate is this equation in finding the volume of an ocean?

This equation is quite accurate in finding the volume of an ocean, as long as the measurements of length, width, and depth are precise. However, there may be other factors that can affect the accuracy, such as changes in the ocean's depth due to tides.

5. Are there any other equations or factors that should be considered when calculating the volume of an ocean?

Yes, there are other equations and factors that can affect the accuracy of calculating the volume of an ocean. For example, the shape of the ocean floor, currents, and temperature can also impact the volume. It is important to gather as much data as possible and use multiple equations to get a more accurate measurement.

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