I apologise.. this question may be a little convoluted
this problem is based on the temperature of a room....
the variable (t) is the time in hours after 4pm eg. at 5pm t=1 .... for the purpose of the question we are considering from 4pm until midnight t=0... till t=8
there are to differential equations to consider
1. dT/dt= -k(T-8) without heater And
2. dT/dt= -k(T-8)+H .... where H=2 with heater
where k is a constant relating to insulation k is approx= 0.1732867951
when t=0, T=16 and..... in d.e number 2. the H, which =2, is relating to the power of the heating system
the temperature in the room throughout the 8 hour period Cannot fall below T=15 if it does the heater automatically comes on until the temperature rises to T=16... then the heater goes off... if it goes below T=15 then the heater comes on again until T=16 and this cycle continues throughout the 8 hour period...
When the heater is ON, you use differ. equation 2
When the heater is OFF, you use D.E 1
I'm really sorry i hope this is clear!!!!!!
a. graph the fluctuation in Temperature against time for the 8 hour period and find the FIRST time, to the nearest minute, that the heater First turns OFF
b. As a percentage, find the proportion of time that the heater is ON during the 8 hour period
(i have a suspicion that the graph may have a zig zag shape ..??!!)
I am sorry if it is confusing... i have no idea how work this out because you have to use both differential equations.... someone PLEASE help me!!!!!
Thank you for your time... if you want to contact me to clarify what i have asked please fell free to email me Thanks again,