We take a milk carton from the refrigerator and put it on the table at room temperature. we assume that the temperature of the carton, t, as a function of time follows newton's cooling law: dt / dt = k (t - a), where a is the temperature of the surroundings and k is a constant. we assume the temperature the surroundings are a = 20 (given in ◦c), and that t (0) = 4 (given in ◦c). a) show that t (t) = 20 - 16e ^ kt (given in ◦c). b) after 5 minutes the temperature of the carton is 8◦c. what is the temperature after 15 minutes?

step-by-step explanation:

12: 00 p.m. to 7: 00 p.m. is a total of 7 hours.

4: 00 p.m. to 7: 00 p.m. is a total of 3 hours.

this means that from 4: 00 p.m to 7: 00 p.m. this represents 3/7 of what was lost from 12: 00 p.m. to 7: 00 p.m.

after knowing this, after doing 11,600 - 6,800 = 4,800

4,800 represents 3/7 of what was lost for 7 hours.

we then divide 4,800 by 3 which gets 1,600.

because we know that 1,600 represents 1/7 of how much water was lost, we just have to multiply by 7, which gets 11,200.   after adding 11,200 to how much water was left at 7: 00 p.m. which was 6,800. 11,200 + 6,800 = 18,000

this means that the pool originally had 18,000 gallons in the pool.

you can also check your work by doing 18,000 - 4(1600), which becomes           1800 - 6400 which gets you 11,600.

2/3

step-by-step explanation:

the slope of a line is equal to the rise/run. in this case the line rises 2 units for every +3 units it moves