In a certain power plant it was found necessary to store some water in a vertical tank 5 inches in diameter and 10 ft. long at a temperature of 200 degrees F. When the water temperature dropped to 125 degrees F it was necessary to replenish the tank with hot water. Observations showed that it cooled 10 degrees F in 1 hour 15 minutes at an outside temperature of 75 degrees F. How long will it take to cool to 125 degrees F when the 100 drop in 1.25 hours occurs with the initial water temperature of 2000 F.

It takes approximately 13.737 hours for the 200 degree water to cool down to 125 degrees.

Step-by-step explanation:

Recall Newton's Law of heating and cooling for an object of initial temperature , in an ambient temperature :

where t is the time elapsed.

We know the ambient temperature and the initial temperature of the object, but we don't know the value of the constant "k" that describes the cooling process. We can obtain such value (k) by using the information that the 200 degrees water cooled 10 degrees in 1.25 hours.

In such case we have:

Therefore, we have now the complete expression for the cooling process:

To find the time it takes to cool the 200 degree water down to 125 degrees, we use:

he used the algebra tiles correctly.

step-by-step explanation:

given : 3x(2x-1)

solution :

since he used algebra tiles .

armando's solution is the same in the solution shown in figure

as he distributed 2x into x and x and wrote them vertically

and also write   -1 vertically

and 3x into x and x and x and wrote it horizontally

performing the multiplication in the algebra tiles we get

and solving the given expression :

3x(2x-1)

since solving the expression using tiles   and solving the expression algebraically we get the same answer

thus   we can choose the first statement as the answer to this problem which is "he used the algebra tiles correctly".

f(x) = - 2/3x + 5; f(5/2)

substitute 5/2 in for x:

f(5/2) = -2/3(5/2) + 5

simplify the right side:

f(5/2) = -5/3 + 5

f(5/2) = 10/3

answer:

f(5/2) = 10/3

i hope this you!