answer:Solution: Z = frac {2i}{1+i} = frac {2i(1-i)}{(1+i)(1-i)} = frac {2i+2}{2} = 1 + i, Then, overset{ -}{Z} = 1 - i, the coordinates of the corresponding point are (1, -1), which is located in the fourth quadrant. Therefore, the answer is: boxed{text{A}}. According to the rules of complex number operations, simplify the expression, and combine the conjugate complex number and the geometric meaning of the complex number to make a judgment. This question mainly examines the geometric meaning of complex numbers, and simplifying the expression according to the rules of complex number operations is the key to solving this problem.

answer:The equation of circle C: x^2+y^2-2x+4y+4=0 can be rewritten as (x-1)^2+(y+2)^2=1, which represents a circle with center C(1, -2) and radius equal to 1. For a line passing through point P(0, -1) and tangent to the circle, when the slope is undefined, the equation is x=0. When the slope exists, let the equation of the tangent line be y+1=k(x-0), i.e., kx-y-1=0. According to the distance from the center of the circle to the tangent line being equal to the radius, we get frac{|k+1|}{sqrt{k^2+1}}=1, solving this gives k=0. Therefore, the equation of the tangent line is y+1=0. In summary, the equations of the tangent lines to the circle are x=0, or y+1=0. Thus, the correct choice is: boxed{text{A}}. First, we find the standard equation of the circle to get the coordinates of the center and the radius. Then, we consider two cases: when the slope exists and when it does not, to find the equations of the tangent lines, thereby arriving at the answer. This problem mainly examines the standard equation of a circle and the use of the point-slope form to find the equation of a tangent line to a circle, reflecting the mathematical idea of case analysis, and is considered a medium-level question.

answer:Let's denote the number of golf balls Corey found on Saturday as S. According to the information given, Corey found 18 golf balls on Sunday. He still needs to find 14 more golf balls to reach his goal of 48. So, the total number of golf balls Corey has found so far is: S (Saturday) + 18 (Sunday) = 48 (goal) - 14 (still needed) S + 18 = 34 Now, we solve for S: S = 34 - 18 S = 16 Corey found boxed{16} golf balls on Saturday.

answer:Given the conditions frac{1}{a} + frac{1}{b} = 1 where a and b are positive numbers, we start by rewriting the equation as: [ frac{a + b}{ab} = 1 implies a + b = ab. ] Since a and b are positive, it follows that a, b geq 1. Next, we need to prove that for any positive integer n, the inequality [ (a+b)^{n}-a^{n}-b^{n} geq 2^{2n}-2^{n-1} ] holds true. Starting from the given transformation a + b = ab, we write: [ (a + b)^n - a^n - b^n = (ab)^n - a^n - b^n. ] Recognizing that a + b = ab, we can express this as: [ (a+b)^n - a^n - b^n = left(a^n - 1right)left(b^n - 1right) - 1. ] By expanding and rearranging terms, we have: [ (a^n - 1)(b^n - 1) = (a - 1)(b - 1)left(sum_{i=0}^{n-1} a^i right) left(sum_{j=0}^{n-1} b^j right). ] By the Cauchy-Schwarz inequality, it holds that: [ left( sum_{i=0}^{n-1} a^i right) left( sum_{j=0}^{n-1} b^j right) geq left[ sum_{k=0}^{n-1} sqrt{a^kb^k} right]^2. ] Knowing that ab = a + b geq 4 (from the fact that a geq 1 and b geq 1), we can use: [ left( sum_{i=0}^{n-1} a^i right) left( sum_{j=0}^{n-1} b^j right) geq left( sum_{k=0}^{n-1} 2^k right)^2. ] The sum of the geometric series sum_{k=0}^{n-1} 2^k is: [ sum_{k=0}^{n-1} 2^k = 2^{n} - 1. ] Thus, [ left( sum_{i=0}^{n-1} 2^i right)^2 = (2^n - 1)^2, ] leading us to: [ (a^n - 1)(b^n - 1) - 1 geq (2^n - 1)^2 - 1 = 2^{2n} - 2^{n+1} + 1 - 1 = 2^{2n} - 2^n. ] Therefore: [ (a + b)^n - a^n - b^n geq 2^{2n} - 2^{n-1}. ] Thus, the proven inequality holds: boxed{(a+b)^n - a^n - b^n geq 2^{2n} - 2^{n-1}}.