All that's going on here is to align the first model (d = 12 sin(30(t - 5)) + 14) so that a high point on the graph comes at 5am.Veronica_Oles said:Homework Statement
Modify the model d = 12 sin (30(t-5)) + 14 to match the new data which is as follows; maximum water depth is 22 m minimum is 6 m, and the first high tide occurs at 5:00am.
Homework Equations
The Attempt at a Solution
The answer is y= 8 sin (30(t-2)) + 14
Ik it's 8 b/c (22-6) / 2 = 8 but the (t-2) not sure where it comes from.
I assume t is measured in hours, and the 30(t-5) is in degrees.Veronica_Oles said:Homework Statement
Modify the model d = 12 sin (30(t-5)) + 14 to match the new data which is as follows; maximum water depth is 22 m minimum is 6 m, and the first high tide occurs at 5:00am.
Homework Equations
The Attempt at a Solution
The answer is y= 8 sin (30(t-2)) + 14
Ik it's 8 b/c (22-6) / 2 = 8 but the (t-2) not sure where it comes from.
I'm not quite sure what to do?haruspex said:I assume t is measured in hours, and the 30(t-5) is in degrees.
What value of t, between 0 and 12, maximises sin(30(t-5))?
What value of x between 0 and 360 degrees maximises sin(x)?Veronica_Oles said:I'm not quite sure what to do?
The variable "d" represents the distance of an object from its starting point, which is determined by the given equation.
The number "12" is the amplitude of the sine function, which determines the maximum distance the object will travel from its starting point. The number "14" is the vertical shift, which determines the starting point of the object.
"sin" is a mathematical function called sine, which represents the ratio of the length of the side opposite to an angle in a right triangle to the length of the hypotenuse.
The number "30" is the frequency of the sine function, which determines how many complete cycles the object will make in one unit of time. In this case, the object will complete 30 cycles in one unit of time.
"(t-5)" is the horizontal shift, which determines the starting point of time for the object. In this case, the object will start moving at time t=5.