answer:Mike bought 200 acres for 70 per acre, so his initial cost was 200 x 70 = 14,000 He sold half of the acreage, which is 200/2 = 100 acres, for 200 per acre, so he made 100 x 200 = 20,000 His profit is the amount he made from selling the land minus his initial cost, so 20,000 - 14,000 = 6,000 6000 The answer is: 6000

answer:We can rewrite the expression as frac{x^2 + 2xy + y^2}{x^2 + y^2}. This can be further simplified as 1 + frac{2xy}{x^2 + y^2}. Since x and y are positive, we know that 2xy is positive. Therefore, the maximum value of frac{2xy}{x^2 + y^2} is 1, when 2xy = x^2 + y^2. This occurs when x = y. So, the maximum value of the expression is 1 + 1 = boxed{2}. The answer is: 2

answer:Let r_1 and r_2 be the roots of the equation. By Vieta's formulas, we have r_1 + r_2 = 13 and r_1r_2 = 4. The sum of the reciprocals of the roots is frac{1}{r_1} + frac{1}{r_2} = frac{r_1 + r_2}{r_1r_2} = frac{13}{4}. Therefore, the answer is boxed{frac{13}{4}}.The answer is: frac{13}{4}

answer:We complete the square for x and y by adding (2/2)^2 = 1 and (-4/2)^2 = 4 to both sides, resulting in x^2 - 2x + 1 + y^2 - 4y + 4 = 33, or (x-1)^2 + (y-2)^2 = 33. This is the equation of a circle with center (1, 2) and radius sqrt{33}, so the center of the circle is boxed{(1, 2)}. The answer is: (1,2)