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Home » Let \( x = \sin \theta \), so: - Ready Digital AB

Let \( x = \sin \theta \), so: - Ready Digital AB

📅 March 7, 2026 👤 scraface

Mar 07, 2026

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📌 First, compute the denominator:

📌 \[ (2)^2 - (\sqrt{5})^2 = 4 - 5 = -1 \]

📌 Now, expand the numerator:

📌 \[ (3)(2) + (3)(\sqrt{5}) + (\sqrt{5})(2) + (\sqrt{5})(\sqrt{5}) = 6 + 3\sqrt{5} + 2\sqrt{5} + 5 = 11 + 5\sqrt{5} \]

📌 \[ \frac{11 + 5\sqrt{5}}{-1} = -11 - 5\sqrt{5} \]

📌 \(\boxed{-11 - 5\sqrt{5}}\)

📌 ---**Question: A volcanologist is analyzing the seismic waves produced by a volcanic eruption. Let \( f(t) \) be a polynomial representing the amplitude of a seismic wave over time \( t \). Find the remainder when \( t^4 + 3t^2 + 2 \) is divided by \( t^2 + 1 \).

📌 To find the remainder when \( t^4 + 3t^2 + 2 \) is divided by \( t^2 + 1 \), we use polynomial long division or the remainder theorem. We express \( t^4 + 3t^2 + 2 \) in the form:

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