B: Study the stability of critical points of ODES: *+(x²-2x²-1)x+x=0 and draw the phase portrait.
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- Data on alcohol content and wine quality was collected from variants of a particular wine. From a sample of 48 wines, a model was created using the percentages of alcohol to predict wine quality. The data are modeled by Yi=−0.357+0.5392Xi, where Xi is the alcohol content (%) and Yi is the rated quality of the wine. For these data,SYX=0.9852,X=10.31,and hi=0.095564 when X=8. Complete parts (a) through (c). Only answer part 1(A). Question content area bottom Part 1 a. Construct a 90% confidence interval estimate of the mean wine quality rating for all wines that have 8%alcohol. ≤μY|X=8≤Consider the discrete-time dynamical system xt+1 = 5xt(1-xt).If xt = 4/5, xt +1 = _____Is x1 = 4/5 an equilibrium for this system? ______Write the updating function rule as f(x) = 5x(1-x).Compute the derivative: f'(x) = ______Evaluate the derivative at the equilibrium: ___________Is the equilibrium stable, unstable or neither? ________