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beautiful things out of dust lyrics - Silent Sales Machine

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 y^3 < 12000

📌 Take cube roots of both sides:

📌 y < \sqrt[3]{12000}

📌 22^3 = 10648,\quad 23^3 = 12167

📌 Since \( 12167 > 12000 \), \( y < 23 \). The largest multiple of 5 less than 23 is 20. Verify:

📌 20^3 = 8000 < 12000

📌 Thus, the largest possible value of \( y \) is \(\boxed{20}\).**Question:** A linguist studying phonetic transformations models a sound wave as \( f(x) = a \sin(bx + c) + d \). Given that the maximum amplitude is 3, the period is \( \pi \), and the wave passes through the origin, find the values of \( a, b, c, \) and \( d \).

📌 The general form of the sinusoidal function is \( f(x) = a \sin(bx + c) + d \).

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Solve the logarithmic equation \(\log_2(x+3) + \log_2(x-1) = 3\).
Combine logs:
\log_2[(x+3)(x-1)] = 3
Convert to exponential form:
Expand and solve:
x^2 + 2x - 3 = 8
x^2 + 2x - 11 = 0
x = \frac{-2 \pm \sqrt{4 + 44}}{2} = \frac{-2 \pm \sqrt{48}}{2}
x = \frac{-2 \pm 4\sqrt{3}}{2} = -1 \pm 2\sqrt{3}
Valid solution (since \(x > 1\)):

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