Math  /  Trigonometry

Question3. At a seaport, the depth of the water, d , in meters, at time tt hours, during a certain day is given by: d=3.4sin(2π(t7.00)10.6)+2.8\mathrm{d}=3.4 \sin \left(2 \pi \frac{(\mathrm{t}-7.00)}{10.6}\right)+2.8 [4 marks] a) What is the depth of the water at 6:30pm6: 30 \mathrm{pm} ? (Answer to the nearest hundredths). b) How long will the depth be above 4 metres during one full day of 24 hours?

Studdy Solution
Calculate the duration for which the depth is above 4 meters by determining the length of the intervals found in Step 4.
Sum the lengths of these intervals to find the total duration.
The depth at 6:30 6:30 pm is approximately 5.89 \boxed{5.89} meters, and the depth is above 4 meters for approximately 7.2 \boxed{7.2} hours during one full day.

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