The free lower end of the rope is struck sharply at time t=0. what is the time t it takes the resulting wave on the rope to travel to the ceiling, be reflected, and return to the lower end of the rope? express your answer in terms of l and constants such as g (the magnitude of the acceleration due to gravity), π, etc.

7. see worksheet 1 for values of variables x1, x2 and x3 and answer the following questions: a. for each variable find the mean, median, coefficient of skewness, range and population standard deviation. b. compared to variable x1, how are the mean and median affected by extreme values (outliers) seen in x2 and x3. c. is the median or mean the better measure of location for x2 and x3? explain. d. explain the differences in the magnitudes of the skewness coefficients for the three variables. e. what is the relationship between the range and standard deviation looking across the three variables?