4. (15 points) In a study of frost penetration it was found that the temperature T (in degrees) of the ground at time t (measured in days of a year) at a depth x (measured in feet) can be modeled by the function T(x, t) = To+ Tie- sin(wt - Xx), where w = 27/365 and A, To and Ti are positive constants. Note: One of the best ways to begin to make sense of a new model is to examine a few specific values and try to interpret their meaning. (a) Consider T(6, 0). What is its physical significance? What are the units? (b) Find . What is its physical significance? What are the units? (Note: your answer will be in terms of the constants of the model.) (c) Find or (12). What is its physical significance? What are the units? (Note: your answer will be in terms of the constants of the model.) (d) Find . What is its physical significance? What are the units? (e) Assume you're taking measurements at the surface (x = 0). At what t-value(s) during the year is the ground the coldest (the temperature the lowest)? Optional: Can you use that to make a guess as to what time of year t = 0 corresponds to? It might depend on where you live