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Home » Pa5 Controller Shock: The Feature That’s Making Other Controllers Look Obsolete! - Carbonext

Pa5 Controller Shock: The Feature That’s Making Other Controllers Look Obsolete! - Carbonext

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 v(v - 2)(v - 3) = 0.

📌 So, \( v = 0, 2, 3 \). Since \( u = v^2 \), the corresponding roots are:

📌 All roots are non-negative, so valid.

📌 Sum of roots: \( 0 + 4 + 9 = 13 \).

📌 Define \( M(u) = u - \frac{u^4}{4} \) for all real \( u \). If \( n \) is a positive integer, define \( b_n \) by \( b_1 = 1 \) and \( b_{n} = M(b_{n-1}) \) for \( n \geq 2 \). Compute \( b_3 \).

📌 We compute recursively:

📌 \( b_2 = M(b_1) = M(1) = 1 - \frac{1^4}{4} = 1 - \frac{1}{4} = \frac{3}{4} \)

📌 \( b_3 = M(b_2) = M\left(\frac{3}{4}\right) = \frac{3}{4} - \frac{\left(\frac{3}{4}\right)^4}{4} \)

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r = 31.4 / (2 × 3.14) = 5 meters
Area = πr² = 3.14 × 5² = 3.14 × 25 = 78.5 square meters.
#### 78.5Question: Let $ a $ and $ b $ be complex numbers such that $...
Solution: We are given that $ a^2 + b^2 = 1 $ and $ ab = \frac{1}{2} $...
We start by using the identity:
a^4 + b^4 = (a^2 + b^2)^2 - 2a^2b^2
We already know $ a^2 + b^2 = 1 $ and $ ab = \frac{1}{2} $, so
a^2b^2 = (ab)^2 = \left(\frac{1}{2}\right)^2 = \frac{1}{4}
Substituting into the identity:
a^4 + b^4 = 1^2 - 2 \cdot \frac{1}{4} = 1 - \frac{1}{2} = \frac{1}{2}

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