Using master theorem, give the asymptotic bounds for T(n) defined by the following recurrences. Then use the recursion tree to show that the answer you have obtained using the master theorem is correct. Need to show your work clearly indicating required constants, recursion tree expansion and derivation of the running time:. a) T(a)=3T(2/3)+ n
b) T(n) = 27T(n/3) +n

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