Consider the equation utt = c 2uxx for 0 < x < l, with the boundary conditions ux(0, t) = 0, u(l, t) = 0. (a) Find all eigenfunctions. (The answer is cos[(n + 1 2 )πx/l], which n?) (b) Write the series expansion for a solution u(x, t) in terms of the initial data and (·, ·)L2 .

How long must $542 be invested at a rate of 7% to earn $303.52 in interest? in a easier way

It takes an ant farm 3 days to consume 1/2 of an apple. at that rate, in how many days will the ant farm consume 3 apples

In a study of the relationship between socio-economic class and unethical behavior, 129 university of california undergraduates at berkeley were asked to identify themselves as having low or high social-class by comparing themselves to others with the most (least) money, most (least) education, and most (least) respected jobs. they were also presented with a jar of individually wrapped candies and informed that the candies were for children in a nearby laboratory, but that they could take some if they wanted. after completing some unrelated tasks, participants reported the number of candies they had taken. it was found that those who were identiď¬ed as upper-class took more candy than others. in this study, identify: (a) the cases, (b) the variables and their types, (c) the main research question, (d) identify the population of interest and the sample in this study, and (e) comment on whether or not the results of the study can be generalized to the population, and if the ď¬ndings of the study can be used to establish causal relationships.