Consider two concentric spheres whose radii differ by t = 1 nm, the "thickness" of the interface. at what radius (in nm) of sphere does the volume of a shell equal that of the interior sphere? assume the shell thickness to be t = 1 nm.
consider two concentric spheres whose radii differ by t = 1 nm, the "thickness" of the interface. on log-log axes, plot the ratio of the shell volume to the interior sphere volume for an interior sphere radius of 10 microns to 1 nm. assume the shell thickness to be t = 1 nm.

Aparticle's position is given by x = 3.00 - 9.00t + 3t2, in which x is in meters and t is in seconds. (a) what is its velocity at t = 1 s? (b) is it moving in the positive or negative direction of x just then? (c) what is its speed just then? (d) is the speed increasing or decreasing just then? (try answering the next two questions without further calculation.) (e) is there ever an instant when the velocity is zero? if so, give the time t; if not, answer "0". (f) is there a time after t = 3 s when the particle is moving in the negative direction of x? if so, give the time t; if not, answer "0".