The graph below and to the left shows the time of sunsets occurring every other day during September in a certain town. The graph at the lower right shows the time of sunsets on either the 21st or 22nd day of each month for an entire year in the same town. The vertical axis is scaled to reflect hours after midnight. Round to 4 decimal places. a)Find a linear model for the data in the graph at the left. Include units to your variables. b)Find a cosine model for the data in the graph to the right. Include units to your variables. c)Using the two models, compare and contrast the predicted times of sunset for September 28th. (September 28th is the 271st day of the year).
The graph below and to the left shows the time of sunsets occurring every other day during September in a certain town. The graph at the lower right shows the time of sunsets on either the 21st or 22nd day of each month for an entire year in the same town. The vertical axis is scaled to reflect hours after midnight. Round to 4 decimal places.
a)Find a linear model for the data in the graph at the left. Include units to your variables.
b)Find a cosine model for the data in the graph to the right. Include units to your variables.
c)Using the two models, compare and contrast the predicted times of sunset for September 28th. (September 28th is the 271st day of the year).
Let the linear model for graph on the left be of the form :
where x = day in September and y= time of sunset in hours
Now (1,18.35) and (29,17.5) line on the graph , Hence, they must satisfy the model,
On subtracting equation (1) from equation (2) , we have
Now a+b=18.35
Hence, On Substituting the value of a and b ,
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