A positive integer N is a power if it is of the form qk , where q, k are positive integers and k > 1.

(a) Give an efficient algorithm that takes as input a number N and determines whether it is a square, that is, whether it can be written as q2 for some positive integer q. What is the running time of your algorithm?

(b) Show that if N = qk (with N, q, and k all positive integers), then either k ? log N or N = 1.

(c) Give an efficient algorithm for determining whether a positive integer N is a power. Analyze its running time.

For all machines-not just hammers- the user applies force force to the machine to the machine over a certain distance. a. input b. output c. duo d. none of the above

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

What is the power dissipated by a resistor with a current of 0.02 a and a resistance of 1,000 ? a. 200 w b. 20 w c. 0.4 w d. 4 w