answer:Let's denote the man's speed in still water (without the current of the stream) as ( v ) kmph. When the man goes downstream, the speed of the stream adds to his speed in still water, so his downstream speed is ( v + 2.5 ) kmph. When the man goes upstream, the speed of the stream subtracts from his speed in still water, so his upstream speed is ( v - 2.5 ) kmph. We are given that the man's upstream speed is 8 kmph. Therefore, we can set up the following equation: [ v - 2.5 = 8 ] Now, we solve for ( v ): [ v = 8 + 2.5 ] [ v = 10.5 ] kmph So, the man's speed in still water is 10.5 kmph. Now, to find the man's downstream speed, we add the speed of the stream to his speed in still water: [ text{Downstream speed} = v + 2.5 ] [ text{Downstream speed} = 10.5 + 2.5 ] [ text{Downstream speed} = 13 ] kmph Therefore, the man's downstream speed is boxed{13} kmph.

answer:The three basic logic structures in a flowchart are: 1. Sequence structure - where actions are performed in a linear step-by-step manner. 2. Condition structure - where actions depend on certain conditions being met (often represented by decision-making processes). 3. Loop structure - where actions are repeated until a certain condition is met. In the list provided, "Decision structure" is a term that does relate to the concept of decision-making. However, in the context of basic logic structures, decision-making is typically represented within the broader category of "Condition structure." Therefore, it is not considered a separate basic logic structure. So the correct answer is: boxed{C}

answer:First examine the expression M = xz + 2yz + 4zv + 8zw = z(x + 2y + 4v + 8w). Utilizing Cauchy-Schwarz, [ x + 2y + 4v + 8w leq sqrt{(1 + 4 + 16 + 64)(x^2 + y^2 + v^2 + w^2)} = sqrt{85(x^2 + y^2 + v^2 + w^2)} = sqrt{85(2025 - z^2)} = 15sqrt{17(2025 - z^2)}. ] Therefore, z(x + 2y + 4v + 8w) leq 15zsqrt{17(2025 - z^2)} = 15sqrt{17z^2(2025 - z^2)}. By AM-GM, [ z^2(2025 - z^2) leq left(frac{z^2 + (2025 - z^2)}{2}right)^2 = 1012.5^2, ] implying [ 15sqrt{17z^2(2025 - z^2)} leq 15sqrt{17 cdot 1012.5^2} = 3075sqrt{17}. ] Equality occurs when x : y : v : w = 1 : 2 : 4 : 8, z^2 = 1012.5, and x_M = y_M = v_M = w_M = z_M = sqrt{1012.5} for simplicity. Thus, [ M + x_M + y_M + z_M + v_M + w_M = 3075sqrt{17} + 5sqrt{1012.5} = boxed{3075sqrt{17} + 5sqrt{1012.5}}. ]

answer:① Since alpha parallel beta and line l perp plane alpha, it follows that line l perp plane beta. Given that line m is contained in plane beta, it implies l perp m. Therefore, proposition ① is true. ② If alpha perp beta and line m is contained in plane beta, then m could either be perpendicular or not perpendicular to alpha. Only if m perp alpha would it result in l parallel m. Therefore, proposition ② is false. ③ Given l parallel m and line l perp plane alpha, it implies line m perp plane alpha. Since line m is contained in plane beta, it follows that alpha perp beta. Therefore, proposition ③ is true. Hence, the correct choice is boxed{text{C}}.