need 3 and 4 using the data above

The size of nanovoids in a material (such as those between neighboring atoms) can be measured using a technique called positron annihilation. A positron - an antimatter particle that resembles an electron but has a positive charge is emitted during radioactive decay of some atoms, such as 22Na. An experiment can be designed such that some positrons then extract an electron from the material of interest, forming a hydrogen atom-type complex called positronium. This pseudo-atom exists for a short time, 3 nanoseconds (1ns109s), before it collides with an electron of a neighboring atom and is annihilated in a photon of gamma radiation. With good electronics and appropriate data analysis, both the positron and subsequent gamma ray emissions can be measured in time and thus 3 can be determined. S. J. Tao, in the paper "Positronium Annihilation in Molecular Substances" (Journal of Chemical Physics, 1972, 56, 5499-5510), performed a quantum mechanical analysis and obtained an equation 3=[1R+1.656R+21sin(R+1.6562R)]1/2 that relates 3 (in ns) to the radius R (in ngstroms, 1A1010m=0.1nm ) of the cavity in which the positronium resides. (He assumed that the cavity is a sphere, so R is the radius of a sphere that is equivalent in some sense to the original volume.) It is not possible to solve for R analytically, given a measured value of 3. An experiment (Lind et al., J. Polym. Sci. A: Polymer Chemistry Edition, 1986, 24, 3033-3047) found the following positronium lifetimes in annealed isotactic polypropylene: An experiment (Lind et al., J. Polym. Sci. A: Polymer Chemistry Edition, 1986, 24, 3033-3047) found the following positronium lifetimes in annealed isotactic polypropylene: Use the secant method to determine the corresponding radii R to within a relative error of 103 for the first two of the 3 data points, using equation 2 . Use the fixed-point iteration method to determine the corresponding radii R to within a relative error of 103 for the last two of the 3 data points, using equation 2 . Comment: Some rearrangements of equation 2 will work for fixed point iteration. Others won't. If your first rearrangement doesn't work, then try another one