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Home » Exactly 3: $ \binom43 = 4 $ - Dachbleche24

Exactly 3: $ \binom43 = 4 $ - Dachbleche24

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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Solve the second equation for \(x\): \(x = y + 3\).
Substitute into the first equation: \(2(y + 3) + 3y = 12\).
Simplify: \(2y + 6 + 3y = 12\), \(5y + 6 = 12\), \(5y = 6\).
Divide by 5: \(y = \frac{6}{5}\).
Substitute back: \(x = \frac{6}{5} + 3 = \frac{21}{5}\).
#### \(x = \frac{21}{5}, y = \frac{6}{5}\)
Find the derivative of \(f(x) = 4x^3 - 5x^2 + 2x - 7\).
Differentiate term by term: \(f'(x) = 12x^2 - 10x + 2\).
#### \(12x^2 - 10x + 2\)
If the sum of the first \(n\) natural numbers is 210, find \(n\).

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