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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?

 Dec 30, 2017

Best Answer 

 #1
avatar+8961 
+1

temperature  =  -t2 + 12t + 50

 

And we want to know what  t  is when the temperature is  77  .

 

77   =   -t2 + 12t + 50        Now we want to solve this equation for  t .

                                         Get one side of the equation equal to zero.

t2 - 12t + 27   =   0

                                         Now we can factor the left side like this..

(t - 9)(t - 3)   =   0

                                         Set each factor equal to zero.

 

t - 9  =  0          or          t - 3  =  0

t  =  9               or          t  =  3

 

The largest value of  t  that causes the expression    -t2 + 12t + 50   to be  77  is   9   .

 Dec 30, 2017
 #1
avatar+8961 
+1
Best Answer

temperature  =  -t2 + 12t + 50

 

And we want to know what  t  is when the temperature is  77  .

 

77   =   -t2 + 12t + 50        Now we want to solve this equation for  t .

                                         Get one side of the equation equal to zero.

t2 - 12t + 27   =   0

                                         Now we can factor the left side like this..

(t - 9)(t - 3)   =   0

                                         Set each factor equal to zero.

 

t - 9  =  0          or          t - 3  =  0

t  =  9               or          t  =  3

 

The largest value of  t  that causes the expression    -t2 + 12t + 50   to be  77  is   9   .

hectictar Dec 30, 2017
 #2
avatar+878 
+3

Boom! You rock, hectictar! It's correct!smiley I understand it better now...

 Dec 30, 2017
 #3
avatar+8961 
+1

Thanks!! Glad to be of some help!! laugh

hectictar  Dec 30, 2017

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