A floating ball is represented by the equation: Z^3 - 3Z^2 + 4p = 0 where z = h / R and p is specific density.

a) Develop your Matlab script for solving the above problem using the Newton-Raphson method.

b) Develop your Matlab script for solving the above problem using the Regula Falsi method.

c) Compare the convergence characteristics (number of iterations) of the Bisection, Regula Falsi, and Newton-Raphson Matlab scripts for the values of specific density

p = 0, 0.2, 0.4, 0.5, 0.6, 0.8, 1.0, 1.2

Use a tolerance of = 0.00001 and maximum iteration number = 50 Present the convergence results in a Table format and comment on the results (which method converge in fewer steps and why). If a method fails to converge for a value of the specific density explain why this is the case.

Try to show all steps because I am really confused.