Let p1 = 2, p2 = 3, . . be the list of primes, in increasing order. consider products of the form (p1 × p2 × ·· ·× pn) + 1 (compare with the proof of corollary 1.3.4). show that this number is prime for n = 1, . . , 5. show that when n = 6 this number is not prime. [use your answer to exercise 1.3.1. a calculator will speed the work of checking divisibility.]

Determine the damped natural frequencies and the steady state response of a decoupled damped forced two degrees of freedom system. 10ä1 + 2q1 20q1 10 cos t; 10q2 +4q2 + 40q2 10 cos t

Analyze the factors that influence the choice between the following pairs of processes to make the products indicated: i) sand casting versus die casting of an electric-motor housing ii) thread rolling versus machining of a bolt for high-strength application. (co3/c5)

Aseries piping system conveys methyl alcohol. the system consists of 70 m of 1- nominal pipe follow by 50 m of 2-nominal pipe, both schedule 40 commercial steel. the 1-nominal pipe contains 3 90° elbows (regular) anda fully open gate valve, all threaded. the pressure drop through the system is 150 kpa. determine the volume flow rate through the system that is horizontally laid.