Answer:
Step-by-step explanation:
The rate of change of temperature of the coffee with respect to time is expressed by the differential equation
dT/dt=k(T−A) when k = -1 and A = 23. The equation will become:
dT/dt = -(T-23)
If the coffee cools at the rate of 1°C per minute, then dT/dt = -1 and T = 70
Substituting into the equation:
-1 = k(70-23)
-1 = 47k
k = -1/47
k = -0.0213
Substituting k = -0.0213 into the original equation, the differential equation will be:
dT/dt=k(T−A)
dT/dt = -0.0213(T-23)
dT/dt = -0.0213T+0.489
To get the value of T, we will use variable separable method
dt = dT/-0.0213T+0.489
Integrate both sides
t = -0.0213ln(-0.0213T+0.489)
At t = 1 minute
1 = -0.0213ln(-0.0213T+0.489)
1/-0.0213 = ln(-0.0213T+0.489)
-46.95 = ln(-0.0213T+0.489)
Apply exp to both sides
e^-46.95 = e^ln(-0.0213T+0.489)
4.073×10^-21= -0.0213T+0.489
-0.0213T = 4.073×10^-21-0.489
-0.0213T = -0.489
T = 0.489/0.0213
T = 22.96°C
Answer:
0 chance because there is no black ones but you would probably pick a yellow one bigger chance for yellow jelly bean.
Step-by-step explanation:
Answer: B
Number on the left: x-value
Number on the right: y-value
If there are 2 y-values for one x-value it is NOT considered a function.
For instance in the answer:
(2,3), (2,4), (3,3), (3,4)
You can clearly see that the x-values (2 & 3) repeat more than once; therefore, it is NOT a function.
On the other hand if you have 2 DIFFERENT x-values for the same y-value it IS A FUNCTION.
For ex D: (2,4), (3,4), (5,4), (6,4)
As you can see there are 4 DIFFERENT x-values with same y-value; therefore it is A FUNCTION
To make it easier:
If x-values appear more than once = NOT A FUNCTION
If x-values appear only ONCE = FUNCTION
Remember: y-values are ALLOWED to repeat
I hope this helps. If you have any questions please let me know in the comments.
Answer:
150 minutes
Step-by-step explanation:
First we have to express all these fractions of an hour in minutes, then add them and get the total of minutes.
To pass these numbers in hours to minutes, we only have to multiply by 60 because one hour has 60 minutes.
3/4 h =
3/4 * 60 = 45m
5/6 h =
5/6 * 60 = 50m
11/12 h =
11/12 * 60 = 55m
to calculate the total number of minutes we have to add the 3 values that we have
45m + 50m + 55m = 150m
Answer:
−7
Step-by-step explanation:
