The function f(t) = 5 cos(pi over 6t) + 7 represents the tide in Stanley Sea. It has a maximum of 12 feet when time (t) is 0 and

Question

3 years ago

6

The function f(t) = 5 cos(pi over 6t) + 7 represents the tide in Stanley Sea. It has a maximum of 12 feet when time (t) is 0 and

a minimum of 2 feet. The sea repeats this cycle every 12 hours. After four hours, how high is the tide?
11.3 feet

9.5 feet

4.5 feet

2.6 feet

Mathematics

2 answers:

Aliun [14] · Answer 1 · 2022-03-31T22:18:52+03:00

Aliun [14]3 years ago

7 0

Answer:

the answer to this question would be 4.5

Juliette [100K] · Answer 2 · 2022-03-31T20:24:38+03:00

Juliette [100K]3 years ago

4 0

The function for the height is
$f(t) = 5cos( \frac{ \pi }{6} t)+7$

f(0) = 5 cos(0) + 7 = 5 + 7 = 12 (verified)
The period is T = 12 hours.

After 4 hours (t = 4), the height is
$f(4) = 5cos( \frac{ 4\pi }{6} )+7 = 5*(-0.5)+7=4.5$

A graph of f(t) confirms the answer.

Answer: 4.5 ft