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Air flows steadily through a long pipe with a speed of u=50+.5x, where x is the distance along the pipe in feet, and u is in ft/s. Due to heat transfer into the pipe, the air temperature, T, within the pipe is T=300+10x degrees F. Determine the rate of change of the temperature of air particles as they flow past the section at x=5 ft.

Air flows steadily through a long pipe with a speed of u=50+.5x, where x is the distance along the pipe in feet, and u is in ft/s. Due to heat transfer into the pipe, the air temperature, T, within the pipe is T=300+10x degrees F. Determine the rate of change of the temperature of air particles as they flow past the section at x=5 ft.