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When x = 1 y = C so the particular solution is y(x)=(x ? 1)ex + 3. (b) If y = 2sin xcosx

This tutorial introduces the mathematics of rotations using two formalisms: (1) Euler angles are the angles of rotation of a three-dimensional coordinate frame.

Problem 1: For each of the following functions do the following: (i) Write the function as a piecewise function and sketch its graph (ii) Write the 

Therefore s2 is a biased estimator of the population variance and

Example 7 Show that the probability density function of a chi square distribution with ? degrees of freedom is f(x) = 1. 2?/2?(?/2).

Math 215 HW #8 Solutions. 1. Problem 4.2.4. By applying row operations to produce an upper triangular U compute det.. 1. 2. ?2 0. 2.

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that the time series processes are stationary. 7. An autoregressive distributed lag model is estimated as yt =11+0.7yt?1 ? 0.4yt?2 + 9xt + 

v(0) = ?A. (1. 2 ? cos ?0 + ? sin(??0). ) =0 =? ?0 = 0.125. Therefore A = 2.02 and the full solution for the damped oscillator without a driving force is x( 

the electronic version). When filled with water to within a distance of the top the volume V of water is r h. 2. 2. 2. 2 1/2. 0.5 arcsin( / ) (. ).