The temperature T (in units of 100 F) of a university classroom on a cold winter day varies with time t (in hours) as
Suppose at 9:00 a.m., the heating unit is ON from 9-10 a.m., OFF from 10-11 a.m., ON again from 11 a.m.–noon, and so on for the rest of the day. How warm will the classroom be at noon? At 5:00 p.m.?
The temperature is 71.8-degree Fahrenheit at 12 noon and 26.9-degree Fahrenheit at 5pm and so on.
Here heat is on at time 9 a.m, 11a.m and 1 p.m. is the temperature at room.
The differential equation when heat is on.
The integrating factor is .then
Apply the initial conditions then
The differential equation when heat is off at time 10 a.m 12 noon and so on.
The integrating factor is . And apply the initial conditions then
Let now corresponding to 9 a.m. The temperature is 0 degree. And the heat is turned off.
Now at 10 a.m , then
Now at 11 a.m, then
Proceeding like this for heat is on then .
And proceeding for heat Is off then
At noon then
Thus, the temperature at this time is 71.8-degree Fahrenheit.
Similarly at 5pm then
Thus, the temperature at this time is 26.9-degree Fahrenheit.
Therefore the temperature is 71.8-degree Fahrenheit at 12 noon and 26.9-degree Fahrenheit at 5pm and so on.
A model for the velocity v at time t of a certain object falling under the influence of gravity in a viscous medium is given by the equation . From the direction field shown in Figure 1.14, sketch the solutions with the initial conditions v(0) = 5, 8, and 15. Why is the value v = 8 called the “terminal velocity”?
94% of StudySmarter users get better grades.Sign up for free