Using the phase plane program described in the introduction, plot the phase plane for the Lotka-Volterra model Here represents the population of a prey species, say mice, and is the population of a predator species, for example owls. If there are no owls, then the population of of mice grows exponentially, and if there are no mice, then the owls die off. However if the initial populations are both positive, then interesting stuff happens. Plot the phase plane including a number of solutions of this system with . You decide what is are good limits for your axes. Describe the solutions in a few words. Do you think that this model gives realistic behavior

Write a program that uses a random number generator to generate a two digit positive integer and allows the user to perform one or more of the following operations: a. double the number. b. reverse the digits of the number. c. raise the number to the power of 2, 3, or 4. d. sum the digits of the number. e. if the number is a two-digit number, then raise the first digit to the power of the second digit. f. if the number is a three-digit number and the last digit is less than or equal to 4, then raise the first two digits to the power of the last digit. after performing an operation if the number is less than 10, add 10 to the number. also, after each operation determine if the number is prime. each successive operation should be performed on the number generated by the last operation. your program should not contain any global variables and each of these operations must be implemented by a separate function. also, your program should be menu driven. 7. (fraction calculator) write a program that