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On a particular day in Salt Lake, UT, the temperature was given by $-t^2 +12t+50$ where $t$ is the time in hours past noon. What is the largest $t$ value at which the temperature was exactly 77 degrees?

 Jun 9, 2019
 #1
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+2

We need to solve this

 

-t^2 + 12t + 50  = 77     subtract 77 from both sides

-t^2 + 12t - 27 = 0        multiply through by -1

 

t^2 - 12t + 27  = 0

 

Factor

 

(t -9) ( t -3)  = 0

 

Set each factor to 0  and solve for t

 

t - 9  = 0           t - 3  = 0

t =9                     t = 3  

 

So....9 hours past noon  =  9 PM

 

cool cool cool

 Jun 9, 2019
 #2
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+1

Thank you so much! It makes sense how you did it!

 Jun 9, 2019

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