I am in math urgent care. Please help.

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

1 hour
2 hours
10 hours
12 hours

Answer:

10 hours

Step-by-step explanation:

The total number of hours the water is expected to reach a depth of 28 feet the second time is 2 hours and this can be determined by using the given data.

Given :

Substitute the value of y = 28 in the given function in order to determine the total number of hours water expected to reach a depth of 28 feet the second time.

[tex]\rm 28 = 7cos\dfrac{\pi x}{6}+25[/tex]

Subtract 25 on both sides in the above function.

[tex]\rm 3= 7cos\dfrac{\pi x}{6}[/tex]

Divide on both sides by 7 in the above expression.

[tex]\rm \dfrac{3}{7}= cos\dfrac{\pi x}{6}[/tex]

Further, simplify the above expression.

[tex]\rm 64.62= \dfrac{\pi x}{6}[/tex]

Cross multiply in the above expression.

[tex]\rm x = \dfrac{64.62\times 6 }{\pi}[/tex]

To convert into radian multiply the above expression by [tex]\pi/180[/tex].

[tex]\rm x = \dfrac{64.62\times 6 }{\pi}\times \dfrac{\pi}{180}[/tex]

x = 2.42 hours

x [tex]\approx[/tex] 2 hours (round off to the nearest hour)

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