Consider the system r(s)-g(sx(s) with transfer function g(s) 4/s^2 +3s +2 . let r(t) and x(t) be the inverse laplace transform of r(s) and x(s), respectively. (similar to example 3.1) 1a. find the differential equation corresponding to the transfer function g(s). (500) lb. find the characteristic equation and the poles of the system. (590) 1 c. find the damping ratio ç , the natural frequency a,, and the steady-state step response xss of the system. (5%) ld. is the system overdamped? critically damped? underdamped? or undamped? (590) le. assume the initial conditions x(0) 0 and (0)-0, and let the input r(t) be an unit step function. find the output response x(t). (15%) if. plot the constant term, the two exponential terms of x(t) and the sum of these three terms versus t on the same graph. discuss how these two exponential terms relate to the system poles, and how the constant terrm relates to ' (15%)

What is the value of x in the this question ?

Over which interval is the graph of f(x) = x2 + 5x + 6 increasing?

Name and describe the three most important measures of central tendency. choose the correct answer below. a. the mean, sample size, and mode are the most important measures of central tendency. the mean of a data set is the sum of the observations divided by the middle value in its ordered list. the sample size of a data set is the number of observations. the mode of a data set is its highest value in its ordered list. b. the sample size, median, and mode are the most important measures of central tendency. the sample size of a data set is the difference between the highest value and lowest value in its ordered list. the median of a data set is its most frequently occurring value. the mode of a data set is sum of the observations divided by the number of observations. c. the mean, median, and mode are the most important measures of central tendency. the mean of a data set is the product of the observations divided by the number of observations. the median of a data set is the lowest value in its ordered list. the mode of a data set is its least frequently occurring value. d. the mean, median, and mode are the most important measures of central tendency. the mean of a data set is its arithmetic average. the median of a data set is the middle value in its ordered list. the mode of a data set is its most frequently occurring value.