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A cake is removed from an oven with an initial, uniform temperature Ti and left to cool in a room with a constant temperature To (-1)n sin(nar/ R) (nar / R) exp [-D ( "17 ) 21 7 n= Deduce that the temperature at the centre of the cake, To(t) = T(0, t), even- tually decreases at a rate that is proportional to Te(t) - To, dTc To - To dt T and express the timescale 7 in terms of D and R