Answer:
ΔT = ΔT0 e^-K T
As I understand Newton's Law of Cooling
ΔT at any time is the difference between the temperature and the surroundings
Originally ΔT0 = 95 - 22 difference between 95 and room temperature
65 - 22 = 33 = 73 e^-KT where t is time to cool to 65 deg
ln (33/73) = -KT K = .794 / 5 = .159 where 5 is time to cool to 65 deg
40 - 22 = 73 e^-.159 T where t is time to cool to 40 deg
18 = 73 e^-.159 T
ln (18 / 73) = -.159 T
T = 8.8 min
It would take 8.8 min for the object to cool to 40 deg C
Suppose the object cooled from 95 to 90 deg, then
ln 68 / 73 = -.159 T and T = .45 min
Answer:
6 hours. ( I DID IT USING PROPORTIONS!)
Step-by-step explanation:
houses/hours
130/2.5= 312/x
(cross multiply)
130x = 780
130x/130 = 780/ 130 (divide each by 130)
6 = h
Answer:
Coordinate Q is (0.8, 0.7)
Step-by-step explanation:
We are told that the coordinates of point Pare (0.6,0.1).
This means that along the x-axis, x = 0.6 and along the y-axis, y = 0.1.
Now, by inspection of the graph, we can see that when we count boxes from the origin to the point P, we have 6 boxes. Thus, each box corresponds to 0.1. So, for point Q, from the origin to that point, on the x-axis, we have 8 boxes. Since one box = 0.1, then the x - value of Coordinate Q is 0.8.
On the y - axis, we see that we have one box from the origin up for the corresponding y-value of coordinate P.
This means that one box is 0.1.
For coordinate Q, we will count 7 boxes. Thus, y-value of coordinate Q is 0.7.
Thus,coordinate Q is (0.8, 0.7)
D A A C A C A B A D A C B B 1/1/3 B 43/1/5 A A
Answer:
The correct option is D) 
Step-by-step explanation:
Consider the provided information.
People are entering a building at a rate modeled by f (t) people per hour and exiting the building at a rate modeled by g (t) people per hour,
The change of number of people in building is:
Where f(t) is people entering in building and g(t) is exiting from the building.
It is given that "The functions f and g are non negative and differentiable for all times t."
We need to find the the rate of change of the number of people in the building.
Differentiate the above function with respect to time:
![h'(x)=\frac{d}{dt}[f(t)-g(t)]](https://tex.z-dn.net/?f=h%27%28x%29%3D%5Cfrac%7Bd%7D%7Bdt%7D%5Bf%28t%29-g%28t%29%5D)
It is given that the rate of change of the number of people in the building is increasing at time t.
That means 
Therefore, 
Hence, the correct option is D)
