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The average high temperature in Phoenix in January is 50o F. Choose a cosine function representing the temperature over a 1-day cycle that begins at the low temperature.Select one:a. y = 15 cos2πΘ +35b. y = - 15 cos2πΘ +35c. y = 30 cos2πΘ +15d. y = 30 cos2πΘ +35 Do you know how I can solve this?

User Ilaria
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1 Answer

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Hello! To answer this exercise, we'll have to solve the alternatives and find which one equals 50ºF. Let's solve:

a.


\begin{gathered} y=15.\cos (2\pi)+35 \\ y=15.\cos (2.180)+35 \\ y=15.\cos (360)+35 \\ y=(15.1)+35 \\ y=50 \end{gathered}

b.


\begin{gathered} y=-15.cos(2\pi)+35 \\ y=-15.cos(2.180)+35 \\ y=-15.cos(360)+35 \\ y=(-15.1)+35 \\ y=(-15)+35 \\ y=20 \end{gathered}

c.


\begin{gathered} y=30.cos(2\pi)+15 \\ y=30.cos(2.180)+15 \\ y=30.cos(360)+15 \\ y=(30.1)+15 \\ y=30+15 \\ y=45 \end{gathered}

d.


\begin{gathered} y=30.cos(2\pi)+35 \\ y=30.cos(2.180)+35 \\ y=30.cos(360)+35 \\ y=(30.1)+35 \\ y=30+35 \\ y=65 \end{gathered}

So, the answer will be the first alternative: a. y = 15 cos2π +35

User Andygjp
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