The Hudson Bay tides vary between 3 feet and 9 feet. The tide is at its lowest point when time (t) is 0 and completes a full cycle in 14 hours. What is the amplitude, period, and midline of a function that would model this periodic phenomenon?

Step-by-step explanation:

The function that could model this periodic phenomenon will be of the form

The tide varies between 3ft and 9ft, which means its amplitude is

and its midline is

.

Furthermore, since at the tide is at its lowest ( 3 feet ), we know that the trigonometric function we must use is .

The period of the full cycle is 14 hours, which means

giving us

With all of the values of the variables in place, the function modeling the situation now becomes

mental cunning

explanation:

he is often referred to as a man of twists and turns

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below: