A one meter long bar is heated unevenly with temperature in C at a distance x meters from one end at time t given by H x t 120e

Question

A one meter long bar is heated unevenly with temperature in C at a distance x meters from one end at time t given by H x t 120e 0 15t sin x 0 x 1 On a sheet of paper sketch a graph of H against for t 0 and t 1 Think about why your graphs make sense a Calculate each of H 0 2 t H 0 8 t Be sure that you can say in words what the practical interpretation in terms of temperature of these two partial derivatives is and why each has the sign that it does b Calculate x t Again be sure that you understand why it has the sign that it does and what its interpretation in terms of temperature is

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