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Home » Solving for \( w \): \( w = 50 \) meters - RoadRUNNER Motorcycle Touring & Travel Magazine

Solving for \( w \): \( w = 50 \) meters - RoadRUNNER Motorcycle Touring & Travel Magazine

📅 April 30, 2026 👤 scraface

Apr 30, 2026

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📌 If the function \( f(x) = 3x^2 - 2x + 1 \), find \( f(2) \).

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

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