In a certain chemical process, a lab technician supplies 292 J of heat to a system. At the same time, 68.0 J of work are done on the system by its surroundings. What is the increase in the internal energy of the system?

(a) assume the equation x = at^3 + bt describes the motion of a particular object, with x having the dimension of length and t having the dimension of time. determine the dimensions of the constants a and b. (use the following as necessary: l and t, where l is the unit of length and t is the unit of time.) (b) determine the dimensions of the derivative dx/dt = 3at^2 + b. (use the following as necessary: l and t, where l is the unit of length and t is the unit of time.)