question archive 1)A city averages 14 hours of daylight in June (the longest days) and 10 in December (the shortest days)

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

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1)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.  Write the sinusoidal function based on the information about and then sketch the graph. Then supply sine equation to model the hours of daylight.

2.Astronomers have noticed that the number of visible sunspots varies from a minimum of about 20 to a maximum of about 130 per year, with a sinusoidal pattern that has a repeating period every 11 years. Assume we started tracking the data in 2000 when the number of sunspots was at a maximum. Supply a cosine function n(t) which models this phenomenon in terms of the time t which represents the years since 2000.

3.A superhero trying to fight crime is swinging back and forth in front of the window. At t = 3s, he is at one end of his swing and 4m from the window. At t = 7s, he is at the other end of his swing and 20m from the window. Supply equation to model this situation.

4.A few construction workers finished up their work early and are playing skip rope. As the rope rotates it is observed that its maximum height is 2.75m after 1 second. The first minimum height of 0.25m occurs 2 seconds after the maximum height. Sketch a graph to model the situation. 

 

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