You create a container by rotating the curve y = 3 ln(x − 3) for y = 0 to y = 8 around - the y-axis. You then fill the container to a height of 7 meters with a liquid that has density 800 kg/m³. The work required to pump the liquid out of this container (over its top edge) is: 11075866.704 X Joules (Recall that acceleration due to gravity is 9.81 m/sec².)

In this problem you will model the mixing energy of a mixture in a relatively simple way, in order to relate the existence of a solubility gap to molecular behavior. Consider a mixture of A and B molecules that is ideal in every way but one: The potential energy due to the interaction of neighboring molecules depends upon whether the molecules are like or unlike. Let n be the average number of nearest neighbors of any given molecule (perhaps 6 or 8 or 10). Let Uo be the average potential energy associated with the interaction between neighboring molecules that are the same (A-A or B-B), and let UAB be the potential energy associated with the interaction of a neighboring unlike pair (A-B). There are no interactions beyond the range of the nearest neighbors; the values of Uo and UAB are independent of the amounts of A and B; and the entropy of mixing is the same as for an ideal solution. Find a formula for the total potential energy when the system is mixed, in terms of x, the fraction…

Please don't provide hand writtin solution....