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Question

The average monthly temperatures for the city of Seattle, Washington, are given below.

JanFebMarAprMayJunJulAugSepOctNovDec 41 44 47 50 56 61 65 66 61 54 46 42\begin{matrix} \text{Jan} & \text{Feb} & \text{Mar} & \text{Apr} & \text{May} & \text{Jun} & \text{Jul} & \text{Aug} & \text{Sep} & \text{Oct} & \text{Nov} & \text{Dec}\\ \ {41^{\circ}} & \ {44^{\circ}} & \ {47^{\circ}} & \ {50^{\circ}} & \ {56^{\circ}} & \ {61^{\circ}} & \ {65^{\circ}} & \ {66^{\circ}} & \ {61^{\circ}} & \ {54^{\circ}} & \ {46^{\circ}} & \ {42^{\circ}}\\ \end{matrix}

According to your model, what is the average monthly temperature in February? How does this compare to the actual average?

Solution

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The goal of this task is to determine the average temperature in February, according to model y=12.5sin16πt+53.5y=12.5\sin\dfrac{1}{6}\pi t+53.5 and compare it to the actual average temperature.

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