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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