Assume a flux of a quantity given by the density u(x, t) on the real line is given by ф(x) = sin(2πx). determine the following 1. assume r(x) = 0. specify all regions on the real line where the density u is growing, shrinking, or staying the same. 2. assume the system is in equilibrium at every point on the real line. determine r(x). specify on what regions of the line is there a source and sink.

Two microscope slides are placed horizontally, one on top of the other, with a drop of a dishwashing liquid between them. the gap between the slides is 1 mm. a machine pulls the top slide to the right with a velocity of 0.15 millimeters per second while the bottom slide is held stationary. a stress gage indicates that a shearing stress of 0.5 pa is required to pull the top slide with this velocity. if the dishwashing liquid adheres to both slides during this process, what is the viscosity of the liquid? specify whether your answer is dynamic or kinematic viscosity, and use appropriate units.