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Home » Volume of the smaller container = π × (2 meters)^2 × 6 meters = 24π cubic meters - go-checkin.com

Volume of the smaller container = π × (2 meters)^2 × 6 meters = 24π cubic meters - go-checkin.com

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 On Mars, a colony’s water recycling system recovers 85% of used water daily. If colonists consume 400 liters per day, how much new water must be imported after 7 days to sustain the colony, assuming no initial reserves?

📌 Each day, 15% of water is lost: 15% of 400 = 0.15 × 400 = 60 liters lost daily

📌 Total loss over 7 days = 60 × 7 = 420 liters

📌 So, 420 liters must be imported after 7 days to maintain supply

📌 An AI specialist trains a model to classify images. The model improves by reducing error rate by half each week. If the initial error rate is 32%, what will it be after 5 weeks?

📌 Error rate halves weekly: geometric sequence with ratio 0.5

📌 After n weeks: error = 32% × (0.5)⁵

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$ p(3) = 27a + 9b + 3c + d = 31 \Rightarrow 27a + 9b + 3c = 29 $
From (2): $ a + b + c = 3 $
Multiply by 2: $ 2a + 2b + 2c = 6 $
Subtract from (3):
Multiply (2) by 3: $ 3a + 3b + 3c = 9 $
Subtract from (4):
Now from (5): $ b = 2 - 3a $
Substitute into (6):
12a + 3(2 - 3a) = 10 \Rightarrow 12a + 6 - 9a = 10 \Rightarrow 3a = 4...
Then $ b = 2 - 3 \cdot \frac{4}{3} = 2 - 4 = -2 $

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