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Home » \( = 2(100) - 30 + 1 \) - High Altitude Science

\( = 2(100) - 30 + 1 \) - High Altitude Science

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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Simplify the fractions:
\frac{x^2}{16} - \frac{y^2}{9} = 1.
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Calculate \( f(2) \):
f(2) = 2^3 - 4(2) + 1 = 8 - 8 + 1 = 1.
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R(2) &= 3(4) + 4 + 1 = 12 + 4 + 1 = 17, \\
R(3) &= 3(9) + 6 + 1 = 27 + 6 + 1 = 34, \\
R(4) &= 3(16) + 8 + 1 = 48 + 8 + 1 = 57, \\
R(5) &= 3(25) + 10 + 1 = 75 + 10 + 1 = 86, \\
R(6) &= 3(36) + 12 + 1 = 108 + 12 + 1 = 121, \\
R(7) &= 3(49) + 14 + 1 = 147 + 14 + 1 = 162, \\
R(8) &= 3(64) + 16 + 1 = 192 + 16 + 1 = 209, \\
R(9) &= 3(81) + 18 + 1 = 243 + 18 + 1 = 262, \\
R(10) &= 3(100) + 20 + 1 = 300 + 20 + 1 = 321.
We are to find \( \gcd(R(1), R(2), \ldots, R(10)) = \gcd(6, 17, 34, 57...

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