The percentage of the moons surface that is visible to a person standing on earth varies with the time since the moon was full. The moon passes through a full cycle in 28days, from full moon to full moon. The maximum percentage of the moons surface that is visible is 50%. Determine an equation, in the form “P=Acos(Bt)+C” for the percentage of the surcare that is visible, p, as function of the number of days,t, since the moon was full. Show the work that leads to the values of A, B and C. (Please help )

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lhabdulsamirahmed lhabdulsamirahmed · Answer 1 · 2022-05-12T12:29:20+02:00

To find the percentage of moon visible compared to the previous full moon, we have to solve the given equation which will give us the equation

[tex]P = 25cos(\frac{\pi }{14t} ) + 25[/tex]

To find the percentage of the full moon, we can write an equation in the form P = Acos(Bt) + C

After 14 days, the percentage of moon is zero

[tex]A = \frac{max- min}{2} = \frac{50}{2} = 25[/tex]

The period = 28 days

[tex]P = Acos(BT=t) + c\\B = \frac{2\pi }{period} = \frac{2\pi }{28} = \frac{\pi }{14} \\A = 25\\c = min + A = 0+25 = 25[/tex]

This implies that

[tex]P = 25cos (\frac{\pi }{14t} ) + 25[/tex]

Here, p is the percentage of the moon visible compared to the previous full moon.

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