Over a 24-hour period, the tide in a harbor can be modeled by one period of a sinusoidal function. the tide measures 7ft at midnight, rises to a high of 12ft, falls to a low of 2ft, and then rises to 7ft by the next midnight. what is the equation for the sone function f(x), where x represents time in hours since the beginning of the 24-hour period

Step-by-step explanation:

The general equation of a sinusoidal function is:

Where:

A = amplitude

w = angular velocity =

T = period =

c = phase angle

s = vertical displacement.

So, the equation is:

The given function will be f(x) = 5 sin(πx/12) + 7

Step-by-step explanation:

Let the sin function be f(x) = a sin( bx+c) + d

In the given question tide measured at midnight was = 7 ft which rose to a high of 12 ft and fell to a low of 2 ft.

Therefore amplitude a = (12-2)÷2 = 10÷2 = 5

Period b = 2π÷24 = π/12

Horizontal displacement c = 0

Vertical shift d = 7

Now by putting these values in the assumed function.

f(x) = 5 sin(πx/12) + 7

So the right answer is f(x) = 5 sin(πx/12) +7

a 4/6 = 9/12   not proportional

step-by-step explanation:

to find which are not proportional, we can use cross products

if it is true, they are proportional.   if it is not true, they are not proportional.

a 4/6 = 9/12

4* 12 = 6*9

48 = 54

not this is not proportional  

b 2/3 = 12/18  

2* 18 = 3 * 12

36 = 36

this is proportional

c 5/4 = 10/8  

5*8 = 4*10

40 = 40

this is proportional

d 7/5 = 35/25

7*25 = 5 * 35

175 = 175

is proportional