Over a 24-hour period, the tide in a harbor can be modeled by one period of a sinusoidal function. The tide measures 4.35 ft at midnight, rises to a high of 8.3 ft, falls to a low of 0.4 ft, and then rises to 4.35 ft by the next midnight.

What is the equation for the sine function f(x), where x represents time in hours since the beginning of the 24-hour period, that models the situation?

Enter your answer in the box.

answer:

3.95sin(pix/12)+4.35

Step-by-step explanation:

A = amplitude = (max-min)/2 = (8.3-0.4) / 2 = 3.95

Vertical displacement = (max+min)/2 = (8.3+0.4)/2 = 4.35

period = 2pi /b

b= 2pi /period = 2pi/24 = pi/12

phase shift = 12

y = 3.95 cos ( (pi/12)(x)) + 4.35

answer: evaluate the objective function at each vertex to determine which - and -values, if any, maximize or minimize the function. example: find the minimum value and maximum value of the objective function f ( x , y ) = 4 x + 5 y , subject to the following constraints