Pretty sure it's C ~~~~~~~~~~~~~~
T(t)=e−kt(∫ekt[KM(t)+H(t)+U(t)]dt+C)
M is the outside temperature, H is other things that affect temperature
in the tank(0 in this case), and U is the solar panel. K comes from the
time constant, and should be the inverse of the time constant I believe.
T is temperature, t is time.
T(t)=e−164t(∫e164t[164(80)+4t]dt
After integrating I keep getting
−16304+256t+Ce−164t
I calculate C to be 16414 setting t equal to 0 and using the initial conditions
Recall that 2sin(x) cos(x) is actually equal to sin(2x).
We can prove this by expanding sin(2x) to sin(x + x).
sin(x + x) = sin(x) cos(x) + cos(x) sin(x) = 2sinxcosx
Thus, 2sin(x/2)cos(x/2) can be rewritten in the form:
sin(2x/2), and this simplifies down to sinx.
