Question

The water level in a harbor is described by the function y = 7 cosine (pix/6) + 25, where y represents the water level measured in feet, and x represents the number of hours since high tide. The period of time between high tides is 12 hours. After approximately how many hours is the water expected to reach a depth of 28 feet the second time? Round to the nearest hour.?

Answer 1

To find the approximate number of hours it takes for the water to reach a depth of 28 feet the second time, we need to determine the values of x that satisfy the equation y = 28.

Step-by-step explanation:

To find the approximate number of hours it takes for the water to reach a depth of 28 feet the second time, we need to determine the values of x that satisfy the equation y = 28. The equation of the water level is given by y = 7 cos(pi*x/6) + 25. Setting y to 28, we get:

28 = 7 cos(pi*x/6) + 25

Subtracting 25 from both sides:

3 = 7 cos(pi*x/6)

Dividing both sides by 7:

3/7 = cos(pi*x/6)

Taking the inverse cosine of both sides:

pi*x/6 = arccos(3/7)

Multiplying both sides by 6/pi:

x = (6/pi) * arccos(3/7)

After evaluating the right side of the equation, we can approximate x to the nearest hour.