answer:Coalition building

answer:The Axiom of Infinity allows for the existence of an infinite set that contains all the natural numbers, which can be manipulated as a single object. In contrast, finitists accept the existence of an "unbounded amount" of natural numbers but reject the idea of treating this unbounded collection as a set that can be manipulated in the same way as finite sets.

answer:Classification: Ellipse Rewritten Equation: The equation can be standardized by completing the square for both x and y: 8 left(x^2 - frac{x}{1}right) + 6 left(y^2 - frac{y}{2}right) = 1 8 left(x^2 - x + frac{1}{4}right) + 6 left(y^2 - y + frac{1}{16}right) = 1 + 2 + frac{3}{8} 8 left(x - frac{1}{2}right)^2 + 6 left(y - frac{1}{4}right)^2 = frac{27}{8} Properties: - Center: left{frac{1}{2}, frac{1}{4}right} - Foci: Since the major axis is along the x-axis and a^2 = frac{27}{8} cdot frac{8}{8} = frac{27}{8} and b^2 = frac{27}{8} cdot frac{6}{8} = frac{81}{32}, the eccentricity e = sqrt{1 - frac{b^2}{a^2}} = frac{1}{2}. The distance from the center to the focus is ae, so the foci are at: left( begin{array}{cc} frac{1}{2} + frac{sqrt{3}}{4} & frac{1}{4} frac{1}{2} - frac{sqrt{3}}{4} & frac{1}{4} end{array} right) - Eccentricity: frac{1}{2} - Area Enclosed: The area A of an ellipse is given by A = pi a b, where a and b are the semi-major and semi-minor axes, respectively. Thus, A = pi cdot sqrt{frac{27}{8}} cdot sqrt{frac{81}{32}} = frac{9 sqrt{3} pi}{32}

answer:Upon multiplying and expanding p(x) and q(x), we get: -left(frac{44x^2}{pi} cdot frac{25x^2}{pi}right) - left(frac{44x^2}{pi} cdot frac{16x}{pi}right) + left(frac{44x^2}{pi} cdot frac{39}{pi}right) - left(frac{7x}{pi} cdot frac{25x^2}{pi}right) + left(frac{7x}{pi} cdot frac{16x}{pi}right) - left(frac{7x}{pi} cdot frac{39}{pi}right) + left(frac{38}{pi} cdot frac{25x^2}{pi}right) - left(frac{38}{pi} cdot frac{16x}{pi}right) + left(frac{38}{pi} cdot frac{39}{pi}right) Simplifying each term and combining like terms, the result is: -frac{1100x^4}{pi^2} - frac{704x^3}{pi^2} + frac{1652x^2}{pi^2} - frac{301x}{pi^2} + frac{1482}{pi^2} After further simplification, the final expanded form is: -frac{1100x^4}{pi^2} - frac{704x^3}{pi^2} + frac{654x^2}{pi^2} - frac{335x}{pi^2} + frac{1482}{pi^2}