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Home » The rate of change of the area with respect to time is given by \( racdAdt = 2s racdsdt \). - Crosslake

The rate of change of the area with respect to time is given by \( racdAdt = 2s racdsdt \). - Crosslake

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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Sum of all terms: $ 4A + 6d $, square: $ 16A^2 + 48Ad + 36d^2 $.
Set equal:
2A^2 + 6Ad + 9d^2 = 16A^2 + 48Ad + 36d^2
\Rightarrow 0 = 14A^2 + 42Ad + 27d^2.
Divide by $ d^2 $: let $ x = \frac{A}{d} $, then:
14x^2 + 42x + 27 = 0.
Discriminant: $ 42^2 - 4\cdot14\cdot27 = 1764 - 1512 = 252 = 36 \cdot...
x = \frac{-42 \pm 6\sqrt{7}}{28} = \frac{-21 \pm 3\sqrt{7}}{14}.
Third term: $ A + 2d $, first: $ A $, so ratio:
\frac{A + 2d}{A} = 1 + 2\frac{d}{A} = 1 + 2\frac{1}{x} = 1 + \frac{2x}...

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