Let the temperature (as a function of time) be T = a sin (nt + b) where t is the time in hours.
Set t = 0 as 4 AM and find the values of a, n and b.
Substitute the temperature values into the LHS of the equation and solve for t in each case.
In a particle accelerator, a fast moving particle (with v = 0.99c) decays into two photons, of total energy of 6.2 × 10−27 J. What is the rest mass of the fast moving particle?
there's a way to do it without using a substitution: use the fact that a = eln(a)
i.e. 2 = eln(2)
So 2ln(x) = eln(x)*ln(2)
then integrate the RHS to get the answer