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

b

step-by-step explanation:

(a) {a₁, a₁r, a₁r², … a₁rⁿ⁻¹, …}

(b) $59 398

step-by-step explanation:

(a) the annual sequence of profits

aₙ = a₁rⁿ⁻¹

the model for the sequence of profits is {a₁, a₁r, a₁r², … a₁rⁿ⁻¹, …} .

(b) profit after 15 yr

  a₁ = $ 30 000

  r = 1.05

a₁₅ = 30 000 × 1.05¹⁴

a₁₅ = 30 000 × 1.979 93

a₁₅ = $59 398

the profit in year 15 will be $59 398.