Achemistry student mixes two solutions to study the properties of the resulting mixture. the temperature of the new solution is given by the function t = 24t − 2t2 + 5, where t is the temperature in degrees celsius and t is the time elapsed in seconds after the solutions are mixed. what is the time interval that the temperature of the solution will be at least 69°c? [2, 6] [3, 8] [5, 8] [4, 8]

  [4, 8]

Step-by-step explanation:

You want to find t such that ...

  T ≥ 69

  24t − 2t^2 + 5 ≥ 69

  t^2 -12t +32 ≤ 0 . . . . . subtract the left side, divide by 2

  (t -4)(t -8) ≤ 0 . . . . . . . factor

The factors will have different signs, so their product will be negative, for values of t between 4 and 8. Of course, the equality holds at t=4 and t=8, so the solution interval is ...

  t ∈ [4, 8]

what do u need to know

step-by-step explanation:

27 + 13x + 15 = (x + 5)( =

step-by-step explanation:

27 + 13x + 15 = (x + 5)( = 27 + 13x + 15 = (x + 5)( = 27 + 13x + 15 = (x + 5)( =