SOLUTION: an approximate model for the average temp. of a city is given by -3/2m^2+20m+17, where m is the month(january=1, february=2 and so on). 1. When is the temp the highest (a non inte

Question 973496: an approximate model for the average temp. of a city is given by -3/2m^2+20m+17, where m is the month(january=1, february=2 and so on).
1. When is the temp the highest (a non integer result means the corresponding part of the month e.g 1.5 equivalent to jan. 15),and what is the maximum value.
2.In this model the average temp. will cross 80 twice(on the way up and on the way down) and will stay above between these two dates. What are those dates?
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
-3/2m^2+20m+17
The vertex m value (date) is at -b/2a. That is -20/-3 = +6.67 (June 20)
At that time the temperature maximum is -1.5(400/9)+1200/9 +17= (600/9)+17=83.33 degrees.
-1.5 m^2 + 20 m -63 =0, moving 80 to the left
1.5^m^2 - 20 m +63=0
(1/3) * [20 +/- sqrt (400-378)] = (1/3) [20 +/- sqrt 22] sqrt 22=4.69
(1/3) 24.69=8.23 August 7
(1/3) 15.31=5.10 May 3

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