Use Duhamel’s principle as formulated for the wave equation in Section 2.5 to find the solution to utt − c2uxx = f(x, t), 0 < x < π, t > 0, u(0, t) = u(π, t) = 0, t>0, u(x, 0) = ut(x, 0) = 0, 0 < x < π.

1. find the area of the unshaded square 2. find the area of the large square 3. what is the area of the frame represented by the shaded region show

As voters exit the polls, you ask a representative random sample of voters if they voted for a proposition. if the true percentage of voters who vote for the proposition is 63%, what is the probability that, in your sample, exactly 5 do not voted for the proposition before 2 voted for the proposition? the probability is

The equation of line e is y  =  -4/9x  +  5/6.  line f is parallelto line e.  what is the slope of line f