A city averages 14 hours of daylight in June (the longest days) and 10 in December (the shortest days). Assume that the number of hours of daylight varies sinusoidal over a period of twelve months. Sketch the graph then use this data to find the following:

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okpalawalter8 okpalawalter8 · Answer 1 · 2022-02-23T10:02:10+01:00

We have that the graph will have a solution that is mathematically given as

y=12sin(6t-\pi)+2

Question Parameters:

A city averages 14 hours of daylight in June (the longest days) and 10 in December (the shortest days).

Generally the equation for the Amplitude and vertical shift is mathematically given as

[tex]A=\frac{Max+min}{2}\\\\A=\frac{10+14}{2}[/tex]

A=2

vertical shift =[tex]\frac{Max-min}{2}[/tex]

vertical shift =[tex]\frac{14-10}{2}[/tex]

vertical shift =1

Therefore, the time is given as

[tex]t=\frac{2\pi}{b}[/tex]

Where

[tex]b=\pi/6\\\\t=\frac{2\pi}{\pi/6}[/tex]

Hence,The graph will have a solution

y=12sin(6t-\pi)+2

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