Metals composed of small crystals are stronger than metals composed of fewer large crystals. the metal yield strength (the amount of stress at which the metal starts to permanently deform) is related to the average grain diameter by the hall–petch equation: s = s0 + k/d^0.5 where the symbols s0 and k represent constants that are different for every metal. reducing the grain size will cause the material to become stronger. grain size reduction is also a means to increase the toughness of a metal. create a function called hallpetch that requires three inputs— s0, k, and d—and calculates the value of yield strength. call this function from a script that supplies values of s0 and k (user entry), and diameter (generate a vector of diameter values from 0.1 to 10 mm in steps of 0.1) ask the user if he/she wants to plot the value of yield strength for values of d. you must create a function to plot named plotxy. this function must be able to be reused by any other program that needs to generate an x-y plot. validate all char inputs.