The following sentence could be added to the loop invariant for the Euclidean algorithm: There exist integers u, v, s, and t such that a = u A + vB and b = s A + t B. 5.5.12 a. Show that this sentence is a loop invariant for while (b = 0) r := a mod b a := b b := r end while b. Show that if initially a = A and b = B, then sentence (5.5.12) is true before the first iteration of the loop. c. Explain how the correctness proof for the Euclidean algorithm together with the results of (a) and (b) above allow you to conclude that given any integers A and B with A > B ≥ 0, there exist integers u and v so that gcd(A, B) = u A + vB. d. By actually calculating u, v, s, and t at each stage of execution of the Euclidean algorithm, find integers u and v so that gcd(330, 156) = 330u + 156v.

Suppose an astronomer discovers a large, spherical-shaped body orbiting the sun. the body is composed mostly of rock, and there are no other bodies sharing its orbit. what is the best way to categorize this body? a. planet b. moon c. comet d. asteroid

You're programming an infinite loop. what must you include in your code to prevent crashes? in roblox

Anew author is in the process of negotiating a contract for a new romance novel. the publisher is offering three options. in the first option, the author is paid $5,000 upon delivery of the final manuscript and $20,000 when the novel is published. in the second option, the author is paid 12.5% of the net price of the novel for each copy of the novel sold. in the third option, the author is paid 10% of the net price for the first 4,000 copies sold, and 14% of the net price for the copies sold over 4,000. the author has some idea about the number of copies that will be sold and would like to have an estimate of the royal- ties generated under each option. write a program that prompts the author to enter the net price of each copy of the novel and the estimated number of copies that will be sold. the program then outputs he royalties under each option and the best option the author could choose. (use appropriate named constants to store the special values such as royalty rates and fixed royalties.