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How many cubic meters of helium are required to lift a balloon with a 400-kg payload to a height of 8 000 m? (Take ρ_He = 0.180 kg/m3.) Assume that the balloon maintains a constant volume and that the density of air decreases with the altitude z according to the expression ρ_air= ρ₀e^-z/8000, where z is in meters and ρ₀ = 1.25 kg/m³ is the density of air at sea level.

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