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]

d. $180

step-by-step explanation:

if the dimensions of the room is 9ft by 12 ft, we have the area of the floor as,

so the area of the floor is 108 square feet, converting that into square yards we get,

the cost of carpet is $15 per square yard, therefore the cost of carpet for 12 square yards is,

hence, the cost of carpet is $180.

assuming the dimensions of the room be,

15 ft by 12 ft

so, the area of the floor of that room is,

we can convert 180 square feet into square yards, we know that,

1 sq ft = 0.111 sq yard

so, 180 square feet is,

so the area of floor is 20 square yards.

now, the cost of carpet is 15 dollars per square yard, therefore the cost of carpet for 20 square yards is,

so, it will cost $300.