Asecond order chemical reaction involves the interaction (collision) of one molecule of a substance p with one molecule of a substance q to produce one molecule of a new substance x; this is denoted by p + q → x. suppose that p and q, where p = q, are the initial concentrations of p and q, respectively, and let x(t) be the concentration of x at time t. then p − x(t) and q − x(t) are the concentrations of p and q at time t, and the rate at which the reaction occurs is given by the equation dx/dt = α(p − x)(q − x), (i) where α is a positive constant. (a) if x(0) = 0, determine the limiting value of x(t) as t → ∞ without solving the differential equation. then solve the initial value problem and find x(t) for any t.

You are a researcher for a golf club manufacturer. you are given two identical looking cubes of a metal alloy. you are informed that they are made of the exact same material, but one is crystalline, whereas the other is amorphous. it is your job to determine which one is amorphous this one is more stress-resistant and is useful in reinforcing golf clubs. which of the following is the best way to determine which is which? a. determine the density of each cube. the more dense one is the amorphous solid. b. melt both cubes and look for a broader range of melting temperatures. the one that melts over a broader range of temperatures is the amorphous solid. c. determine the density of each cube. the less dense cube is the amorphous solid. d. melt both cubes and measure the range of melting temperatures. the one that melts over a narrower range of temperatures is the amorphous solid.