Question 83815
An professor finds that the number of students enrolling in his class is approximated by s(t) = -tsquared + 20t + 80 where t is the number of tests given in one semester.
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Maximum:
You have a quadratic with a=-1,b=20,c=80
Max is at t=-b/2a = -20/-2 =10 
# of students will be maximum if he gives 10 tests.
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No students means s = 0
-t^2+20t+80=0
t = [-20+-sqrt(400-4*-1*80]/(-2)
t = [-20+-sqrt(720)]/-2
t = [-20+-12sqrt5]/(-2)
Positive solution:
t = 23.42 
Rounding down: No students if he gives 23 tests.
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Cheers,
Stan H.