In a certain city the temperature (in degrees Fahrenheit) t hours after 9am was approximated by the function T(t)= 80 + 16sin(((pi)(t))/(12)) Determine the temperature at 9 am, at 3 pm and find the  average temperature during the period from 9 am to 9 pm.

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T(t)= 80 + 16sin(((pi)(t))/(12))

At 9:00 am t=0

 

T(t)

= 80 + 16sin(((pi)(0))/(12))

= 80 + 16sin(0)

= 80+0

= 80F

 

At 3:00 pm t=6

T(t)

= 80 + 16sin(((pi)(6))/(12))

= 80 + 16sin(pi/2)

= 80+16

= 96F

 

At 9:00 pm t=12

T(t)

= 80 + 16sin(((pi)(12))/(12))

= 80+16sin(pi)

= 80+0

= 80F

 

Average temperature from 9am to 9pm = (80+96)/2 F =88F

 

 

 

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