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Home » Time \( t \) = 3 years - Crosslake

Time \( t \) = 3 years - Crosslake

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 given that all roots are non-negative real numbers.

📌 Let \( x = \sqrt{u} \), so \( u = x^2 \) and \( u\sqrt{u} = x^2 \cdot x = x^3 \). Substitute:

📌 \[ x^3 - 5x^2 + 6x - 4 = 0 \]

📌 We solve this cubic equation. Try rational roots: \( \pm1, \pm2, \pm4 \).

📌 Test \( x = 1 \):

📌 \( 1 - 5 + 6 - 4 = -2

📌 Test \( x = 2 \):

📌 \( 8 - 20 + 24 - 4 = 8

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a_2 &= 2(2)^2 + 3(2) + 1 = 8 + 6 + 1 = 15,\\
a_3 &= 2(3)^2 + 3(3) + 1 = 18 + 9 + 1 = 28,\\
a_4 &= 2(4)^2 + 3(4) + 1 = 32 + 12 + 1 = 45,\\
a_5 &= 2(5)^2 + 3(5) + 1 = 50 + 15 + 1 = 66.
Now, sum these terms:
+ 15 + 28 + 45 + 66 = 160.
Thus, the sum of the first five terms is \(\boxed{160}\).
Question:** A middle school student is exploring functions and their c...
First, evaluate \(f(4)\):
f(4) = 3(4) - 2 = 12 - 2 = 10.

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