Question

bonus:using the formula tn = t0 + (n × 52.7), * estimate when high tide will be on sunday if high tide on thursday is at 10 a.m. 12:40 p.m 11:55 a.m 11:55 pm 8:15 a.m.

Explanation:

Step1: Calculate the number of days between Thursday and Sunday

From Thursday to Sunday, there are \(N = 3\) days.

Step2: Substitute values into the formula

We know \(T0=10\) (10 A.M. on Thursday) and \(N = 3\). Using the formula \(TN=T0+(N\times52.7)\). First, calculate \(N\times52.7=3\times52.7 = 158.1\) minutes.

Step3: Convert minutes to hours and minutes

\(158.1\) minutes \(= 2\) hours and \(38.1\) minutes (since \(158.1\div60 = 2\) hours and \(38.1\) minutes).

Step4: Add to the initial time

Starting from 10 A.M. on Thursday, adding \(2\) hours and \(38.1\) minutes for \(3\) days. \(10\) A.M. \(+ 2\) hours \(38.1\) minutes\(\times3\). \(2\times3 = 6\) hours and \(38.1\times3=114.3\) minutes. \(114.3\) minutes \(= 1\) hour and \(54.3\) minutes. So total time added is \(6 + 1=7\) hours and \(54.3\) minutes. \(10\) A.M. \(+7\) hours \(54.3\) minutes \(= 5:54.3\) P.M. on Thursday? No, wait, wrong approach. Wait, actually, the formula is cumulative. Wait, no, another way:
The time between Thursday 10 A.M. and Sunday 10 A.M. is \(3\times24 = 72\) hours. But the formula \(TN=T0+(N\times52.7)\) (assuming \(N\) is the number of intervals). Wait, perhaps the formula is for each day, the high - tide is \(52.7\) minutes later.
From Thursday 10 A.M. to Sunday (3 days later). \(52.7\times3=158.1\) minutes \(= 2\) hours \(38.1\) minutes. \(10\) A.M. \(+ 2\) hours \(38.1\) minutes \(= 12:38.1\) P.M. (approx \(12:40\) P.M.)

Answer:

12:40 P.M.