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Home » Why All Celebrities Are Rocking the Marquise Ring—Designer Revealed Inside! - ToelettAPP

Why All Celebrities Are Rocking the Marquise Ring—Designer Revealed Inside! - ToelettAPP

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 5Question: A virtual reality game designer is creating a puzzle where players must align two rotating gears with 24 and 36 teeth respectively. What is the smallest number of full rotations each gear must make before both gears align in their starting position?

📌 Solution: To find when both gears align, we need the least common multiple (LCM) of their number of teeth, 24 and 36. First, factor both numbers:

📌 $24 = 2^3 \cdot 3$,

📌 $36 = 2^2 \cdot 3^2$.

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\frac{2a^2 + 2b^2}{a^2 - b^2} = 3
Factor out 2 in the numerator:
\frac{2(a^2 + b^2)}{a^2 - b^2} = 3
\frac{a^2 + b^2}{a^2 - b^2} = \frac{3}{2}
Question: Let $ g(x^2 + 1) = x^4 + 2x^2 + 2 $. Find $ g(x^2 - 1) $.
g(x^2 + 1) = x^4 + 2x^2 + 2
Let’s express the right-hand side in terms of $ x^2 + 1 $.
Let $ u = x^2 + 1 \Rightarrow x^2 = u - 1 $, so:
x^4 = (x^2)^2 = (u - 1)^2 = u^2 - 2u + 1
x^4 + 2x^2 + 2 = (u^2 - 2u + 1) + 2(u - 1) + 2

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