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Home » \[ 9a + 3b + c = 5 \] — (Equation 3) - Groen Casting

\[ 9a + 3b + c = 5 \] — (Equation 3) - Groen Casting

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 5Ein zylindrischer Behälter mit einem Radius von 5 cm ist bis zu einer Höhe von 12 cm mit Wasser gefüllt. Wenn eine Kugel mit einem Radius von 4 cm vollständig in das Wasser getaucht wird, um wie viel steigt der Wasserspiegel?

📌 Das Volumen der Kugel beträgt (4/3)πr³ = (4/3)π(4³) = (256/3)π cm³.

📌 Das Volumen des Zylinders ist V = πr²h, also beträgt die Höhe Zunahme h = V / (πr²) = (256/3)π / (π×5²) = (256/3) / 25 = 256/75 ≈ 3,41 cm

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So $ \frac{a + 2b}{a - 2b} = 1 \Rightarrow a + 2b = a - 2b \Rightarrow...
Now compute $ \frac{a^2 + 4b^2}{a^2 - 4b^2} $. Since $ b = 0 $, this b...
\frac{a^2}{a^2} = \boxed{1}
Question: A polynomial $ f(x) $ satisfies $ f(x + 1) - f(x) = 6x + 4 $...
Solution: Since the difference $ f(x+1) - f(x) $ is linear, $ f(x) $ m...
f(x+1) = a(x+1)^2 + b(x+1) + c = a(x^2 + 2x + 1) + b(x + 1) + c = ax^2...
f(x+1) - f(x) = (ax^2 + 2ax + a + bx + b + c) - (ax^2 + bx + c) = 2ax...
f(x+1) - f(x) = 6x + 4
2a = 6 \Rightarrow a = 3, \quad a + b = 4 \Rightarrow 3 + b = 4 \Right...
Thus, the leading coefficient of $ f(x) $ is $ \boxed{3} $.

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