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Home » Daher beträgt die durchschnittliche Länge \(\boxed5.5\) cm. - DNSFLEX

Daher beträgt die durchschnittliche Länge \(\boxed5.5\) cm. - DNSFLEX

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 Substitute \( x = 2 \): \( f(2) = 3(2)^2 - 2(2) + 1 = 12 - 4 + 1 = 9 \).

📌 Use the Pythagorean theorem: \( \text{base}^2 + 8^2 = 10^2 \).

📌 \( \text{base}^2 = 100 - 64 = 36 \).

📌 Base = \( \sqrt{36} = 6 \) meters.

📌 The sum of the first 10 terms of an arithmetic sequence is 155. If the first term is 5, find the common difference.

📌 The sum formula for an arithmetic sequence is \( S_n = \frac{n}{2} (2a + (n-1)d) \).

📌 Substituting known values: \( 155 = \frac{10}{2} (2 \times 5 + 9d) \).

📌 Simplifying: \( 155 = 5 (10 + 9d) \) → \( 155 = 50 + 45d \) → \( 105 = 45d \) → \( d = \frac{105}{45} = \frac{7}{3} \).

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