5. Atmospheric temperature depends on position and time. If we denote position by three spatial coordinates x, y, and z (measured in kilometres) and time by t (measured in hours), then the temperature (in degree Celsius) is a function of four variables, T(x, y, z, t). Suppose that T(x, y, z, t) = (1 + t) and a thermometer is attached to a weather balloon moving along the curve r = t, y = 2t, z = t -+2. (a) What physical rates of change are represented by the expressions aT at and di? (b) Give a formula for " in terms of t. of aT aT aT ar ' dy ' dz ' at . (c) Find the rate of change in the temperature being recorded by the weather balloon at time t = 1