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Home » Let \( t \) be the total years until the cliff erodes completely. - High Altitude Science

Let \( t \) be the total years until the cliff erodes completely. - High Altitude Science

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 oxed{(x^2 + 4)^2 - 16(y^2 - 2)(y^2 + 2)}

📌 Question: An archaeologist analyzing ancient Andean crop yields finds that in a sequence of four consecutive years, the yields increase by a constant ratio. The sum of the yields is 120, and the product of the four yields is $ 160000 $. What is the third term in the sequence?

📌 Solution: Let the yields be $ a, ar, ar^2, ar^3 $, where $ r > 0 $.

📌 a(1 + r + r^2 + r^3) = 120

📌 a \cdot ar \cdot ar^2 \cdot ar^3 = a^4 r^{6} = 160000

📌 From the product:

📌 a^4 r^6 = 160000 = 16 \cdot 10000 = 16 \cdot 10^4 = (2^4)(10^4) = (2 \cdot 10)^{4} = 20^4

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