Consider an elastic string of length l. the end x = 0 is held fixed, while the end x = l is free; thus the boundary conditions are u(0,t) = 0 and u_x(l, t) = 0. the string is set in motion with no initial velocity from the initial position u(x, 0) = f{x), where f(x) = {1, 0, l/2 - 1 < x l/2 + 1 (l > 2), otherwise. find the displacement u(x, t).

Abag contains 3 red marbles 4 white marbles and 5 blue marbles if one marble is drawn from the bag what is the probability that the marble will be blue

This is the number of parts out of 100, the numerator of a fraction where the denominator is 100. submit

Suppose you just purchased a digital music player and have put 8 tracks on it. after listening to them you decide that you like 4 of the songs. with the random feature on your player, each of the 8 songs is played once in random order. find the probability that among the first two songs played (a) you like both of them. would this be unusual? (b) you like neither of them. (c) you like exactly one of them. (d) redo () if a song can be replayed before all 8 songs are played.