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Home » This Unbelievable Two-Face Story Will Make You Question the Dark Knight’s Fate! - jntua results

This Unbelievable Two-Face Story Will Make You Question the Dark Knight’s Fate! - jntua results

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 解: 直線 \(y = 2x + 3\) 上の点 \((1, 2)\) に最も近い点を見つけるには、点から直線までの垂直距離を最小化する必要があります。直線 \(y = 2x + 3\) の傾きは 2 なので、垂直な直線の傾きは \(-\frac{1}{2}\) です。

📌 点 \((1, 2)\) を通り傾き \(-\frac{1}{2}\) の直線の式は次のとおりです:

📌 y - 2 = -\frac{1}{2}(x - 1)

📌 y - 2 = -\frac{1}{2}x + \frac{1}{2} \implies y = -\frac{1}{2}x + \frac{5}{2}

📌 この直線と \(y = 2x + 3\) の交点を見つけるために、方程式を等しくします:

📌 2x + 3 = -\frac{1}{2}x + \frac{5}{2}

📌 分数をなくすために両辺に 2 を掛けます:

📌 4x + 6 = -x + 5

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oxed{(x^2 + 4)^2 - 16(y^2 - 2)(y^2 + 2)}
Question: An archaeologist analyzing ancient Andean crop yields finds...
Solution: Let the yields be $ a, ar, ar^2, ar^3 $, where $ r > 0 $.
a(1 + r + r^2 + r^3) = 120
Product:
a \cdot ar \cdot ar^2 \cdot ar^3 = a^4 r^{6} = 160000
From the product:
a^4 r^6 = 160000 = 16 \cdot 10000 = 16 \cdot 10^4 = (2^4)(10^4) = (2 \...
a^4 r^6 = 20^4 \Rightarrow (ar^{1.5})^4 = 20^4 \Rightarrow ar^{1.5} =...
Letâs write $ a = rac{20}{r^{1.5}} $. Substitute into the sum:

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