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Home » Multiply numerator and denominator by the conjugate of the denominator \(2 + \sqrt5\): - go-checkin.com

Multiply numerator and denominator by the conjugate of the denominator \(2 + \sqrt5\): - go-checkin.com

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 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 \( f(x) = a \sin(bx + c) + d \).

📌 The amplitude \( a \) is given as 3.

📌 The period \( T \) is \( \pi \). For a sine function, the period is \( \frac{2\pi}{b} \), so:

📌 \frac{2\pi}{b} = \pi \implies b = 2

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