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

256π units²   (answer b)

step-by-step explanation:

the formula for the surface area of a sphere of radius r

is             a = 4πr²

and so, if r = 8 units, then the surface area is:

a = 4π(8 units)² = 256π units²   (answer b)

add an image !

step-by-step explanation: