Sketch the phase portrait for the competing species system: yi = y1(1 – Y1 – 2y2) Y2 = Y2 (1 – Y2 – 2y1) -

The goal of this problem is to fit a trigonometric function of the form f(t) = co + c1 sin(t) to the data points (0, –9.5), (5,–11.5), (7, –9.5), (*,-1.5), using least squares. (a) The problem is equivalent to finding the least squares solution to the system Xc= y where X = У — and c = (c1, c2]" (b) Find the coefficients of the best fit by finding the least squares solution to the system in part (a) Co C1

Give Z(G), the center of G, for G = S3

Part a,b and c please

Consider the non-linear system: x = -x(x² + y² - 2ax - B) - y y = y(x² + y² - 2ax - B) + x What is the correct polar coordinate form of this system? (r = -r (r² - 2ar cos(0) - B) 20 θ = α (r = -r(r² - 2ar sin(0) - B) 0 = : 1 Ofr = -r(r² - 2ar cos(0) – B) {* = - U (r = -r(r² - 2ar sin(0) - B) 10 = θ = α