Question

A scientist adds ice to water to cool it down for an experiment. The temperature of the water as a function

of time since the ice is added is f(x) = 0.2x² - 6x +79. The experiment needs to be conducted when
the temperature of the water is 60 degrees or cooler.

The two times the water will be 60 degrees are at (9.9, or 3.6, or 2.9) and (32.9, or 39.9, or 26.4)
This means that the scientist has about (22.8, or 30)
minutes to conduct her experiment.

Answer 1

Explanation:

To find the times when the temperature of the water is 60 degrees or cooler, we need to solve the equation:

0.2x² - 6x + 79 = 60

Subtracting 60 from both sides, we get:

0.2x² - 6x + 19 = 0

We can solve this quadratic equation using the quadratic formula:

x = (-b ± sqrt(b² - 4ac)) / 2a

where a = 0.2, b = -6, and c = 19.

Plugging in these values, we get:

x = (-(-6) ± sqrt((-6)² - 4(0.2)(19))) / 2(0.2)

x = (6 ± sqrt(16.4)) / 0.4

Simplifying, we get:

x = 9.9 or 3.6

or

x = 32.9 or 26.4

or

x = 39.9

These are the four times when the temperature of the water is 60 degrees or cooler. To find the time the scientist has to conduct her experiment, we need to take the difference between the two smallest times or the two largest times:

30 - 2.9 = 27.1

or

39.9 - 32.9 = 7

Therefore, the scientist has about 7 to 27.1 minutes to conduct her experiment, depending on which two times she chooses to use.