+885 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?
+9481 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 .
+9481 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 .
I understand it better now...
