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Home » Thus, the sum of the real parts is: - AMAZONAWS

Thus, the sum of the real parts is: - AMAZONAWS

📅 March 7, 2026 👤 scraface

Mar 07, 2026

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📌 If \(a = 12\), then \(b + c = 2\). Possible pairs \((b, c)\) are \((1, 1)\), but \(\gcd(12, 1, 1) = 1\), which is valid.

📌 Thus, \(a = 12\) is feasible, giving the maximum erosion rate for one region as:

📌 6a = 6 \times 12 = 72

📌 Therefore, the maximum possible erosion rate for any one region is \(\boxed{72}\).

📌 A hydrologist is modeling water flow through a system of aquifers. If the flow rates through three distinct aquifers are three consecutive integers, and their sum is 90 cubic meters per hour, what is the flow rate through the aquifer with the highest rate?

📌 Let the flow rates through the three aquifers be \(x-1\), \(x\), and \(x+1\). The sum of these rates is:

📌 Solving for \(x\), we find:

📌 x = \frac{90}{3} = 30

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The area is \(12 \times 24 = 288\) square meters.
The sum of the first \(n\) terms of an arithmetic sequence is given by...
The \(n\)-th term \(a_n\) is given by \(a_n = S_n - S_{n-1}\).
\(S_{10} = 3(10)^2 + 5(10) = 300 + 50 = 350\).
\(S_9 = 3(9)^2 + 5(9) = 243 + 45 = 288\).
Thus, \(a_{10} = 350 - 288 = 62\).
A train travels 120 km at a speed of \(v\) km/h and then 180 km at \(v...
The time for the first part is \(\frac{120}{v}\) hours.
The time for the second part is \(\frac{180}{v+20}\) hours.
The total time is \(\frac{120}{v} + \frac{180}{v+20} = 5\).

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