The function f(t) = 4 cos(pi over 3t) + 15 represents the tide in bright sea. it has a maximum of 19 feet when time (t) is 0 and a minimum of 11 feet. the sea repeats this cycle every 6 hours. after five hours, how high is the tide?

Answer with explanation:

The Cosine function which represents the tide in Bright Sea is represented as:

Where, k=0,1,2,3,...........

Cos function has a Period of .

Maximum , Cosine of an angle =1

Minimum, Cosine of an Angle = -1

At, t=0, →Maximum ,f(t)= 4 ×1 +15=19 feet

Minimum, f(t)= 4 × (-1) +15=15-4=11 feet

Tide repeats after ,every 6 hours.

After , 6 hours ,the tide function is represented in same way.That is

Here,k=6 n, where, n=0,1,2,3...

We have to find how tide function is represented after 5 hours.

→ 6 n=5

→

Height of tide after 5 hours = 17.68 feet

step-by-step explanation:

let

we know that

the y-intercept is the y-coordinate of the point when the value of x is equal to zero

so

the y-coordinate of the point a is the y-intercept

the answer part a) is

the value of y-intercept is

part b) find the slope m

we know that

the value of the slope is equal to

substitute the values

therefore

the answer part b) is

the value of the slope is equal to

the general answer is

the slope is

the value of y-intercept is

definitely a. the others have almost all data points on one side of the line.

step-by-step explanation: