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- Determine the center of mass for the region bounded by y=ax-x2 curve and x=b and x=c lines. (a=12 , b=2 , c=4.2)b) Find the mean and the standard deviation of the times in the following table. Because the table contains all the winning times for this race (up to year 2012), the data set is a population. Olympic Women's 400-Meter Dash Results, in Seconds, 1969-2012 52.0 51.08 49.29 48.88 48.83 48.65 48.83 48.25 49.11 49.41 49.62 49.55Without integrating, what is the average value of ƒ(x, y, z) = sin x sin y sin z on the cube {(x, y, z): -1 ≤ x ≤ 1, -1 ≤ y ≤ 1, -1 ≤ z ≤ 1}?Use symmetry arguments.
- compute the mass along the x-axis, the moment (M) around x=0, and the center of mass given the data in exercise 6. Show full and complete procedure. the letter "ρ" represents the density functiion. meaning ρ is the density function of sin xEvaluate the integral over curve C. f(x, y) = x + y, C : x2 + y2 = 4 in the first quadrant from (2, 0) to (0, 2)Compute the area A under the parametrized curve c(t) = (e', 5t) for 0Recommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons IncProbability and Statistics for Engineering and th…StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage LearningStatistics for The Behavioral Sciences (MindTap C…StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage LearningElementary Statistics: Picturing the World (7th E…StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSONThe Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. FreemanIntroduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. FreemanMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons IncProbability and Statistics for Engineering and th…StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage LearningStatistics for The Behavioral Sciences (MindTap C…StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage LearningElementary Statistics: Picturing the World (7th E…StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSONThe Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. FreemanIntroduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. Freeman