answer:The given equation can be factored similarly to the original problem: [ x^3y - 2x^2y + xy = (x^2 - 2x + 1)xy = (x - 1)^2xy ] We substitute x = 201 into the equation: [ (201 - 1)^2 cdot 201y = 804000 ] Simplifying further: [ 200^2 cdot 201y = 804000 ] [ 40000 cdot 201y = 804000 ] Solving for y: [ 201y = frac{804000}{40000} = 20.1 ] [ y = frac{20.1}{201} = frac{201}{2010} = frac{1}{10} ] So, y = boxed{frac{1}{10}}.

answer:Since the company produces three models of sedans, there are significant differences between the models. Therefore, it is appropriate to use the stratified sampling method. Hence, the correct choice is boxed{C}.

answer:Since x > 1 and y > 1, it follows that lg x > 0 and lg y > 0. Therefore, 4 = lg x + lg y geqslant 2 sqrt{lg x cdot lg y}, which simplifies to lg x cdot lg y leqslant 4. Equality holds if and only if lg x = lg y = 2, that is, when x = y = 100. Hence, the maximum value of lg x lg y is 4. Therefore, the correct answer is: boxed{B}. This problem can be solved using the basic inequality and the properties of logarithms. It tests the understanding of basic inequalities and logarithmic operations, and is considered a fundamental question.

answer:1. In triangle ABC, we have cos(2C - 3cos(A + B)) = 1. This simplifies to 2cos^2(C) - 1 + 3cos(C) = 1, which can be rewritten as 2cos^2(C) + 3cos(C) - 2 = 0. Factoring, we get (2cos(C) - 1)(cos(C) + 2) = 0. This gives us cos(C) = frac{1}{2} or cos(C) = -2 (which is extraneous). Since 0 < C < pi, we have C = frac{pi}{3}. 2. From part 1, we know that C = frac{pi}{3}, c = sqrt{7}, and b = 3a. Using the cosine rule, we have cos(C) = frac{a^2 + b^2 - c^2}{2ab}. Substituting the known values, we get frac{1}{2} = frac{a^2 + 9a^2 - 7}{2 times a times 3a}. Solving this equation gives us a = sqrt{2}, and thus b = 3sqrt{2}. The area of triangle ABC is given by S = frac{1}{2}absin(C). Substituting the known values, we get S = frac{1}{2} times sqrt{2} times 3sqrt{2} times sin(frac{pi}{3}) = boxed{frac{3sqrt{3}}{2}}.