Primary U. S. interstate highways are numbered 1-99. Odd numbers (like the 5 or 95) go north/south, and evens (like the 10 or 90) go east/west. Auxiliary highways are numbered 100-999, and service the primary highway indicated by the rightmost two digits. Thus, the 405 services the 5, and the 290 services the 90 Given a highway number, indicate whether it is a primary or auxiliary highway. If auxiliary, indicate what primary highway it serves. Also indicate if the (primary) highway runs north/south or east/west. Ex: If the input is: 90 the output is: The 90 is primary, going east/west.

For each of the following claims, determine whether they are true or false. justify your determination (show your work). if the claim is false, state the correct asymptotic relationship as o, θ, or ω. unless otherwise specified, lg is log2.(a) (b) (c) (d) (e) (f) (g) (h) (i) (j)n+1 =22n =2n =1 =ln2 n =n2 +2n−4 =33n = 2n+1 =√n = 10100 =o(n4) o(2n)θ(2n+7 ) o(1/n)θ(lg2 n) ω(n2 )θ(9n ) θ(2n lg n )o(lg n) θ(1)

Write code using c . (take input from user) calculate the size of a given file in kbs. in this task you will complete the function with the following prototype: float get_file_size(char * filename); the function takes the file name (address to the start of a null terminated character array) as input. the function should then open the file and find the number of bytes it contains till eof. the number of bytes divided by 1024 will give the size in kbs. if the file cannot be opened the function should return -1.

Write a program that begins by reading in a series of positive integers on a single line of input and then computes and prints the product of those integers. integers are accepted and multiplied until the user enters an integer less than 1. this final number is not part of the product. then, the program prints the product. if the first entered number is negative or 0, the program must print “bad input.” and terminate immediately. next, the program determines and prints the prime factorization of the product, listing the factors in increasing order. if a prime number is not a factor of the product, then it must not appear in the factorization. sample runs are given below. note that if the power of a prime is 1, then that 1 must appear in t