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Home » Given \( C(2) = 7 \), we set up the equation: - Groen Casting

Given \( C(2) = 7 \), we set up the equation: - Groen Casting

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 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

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a_1 = 3(1)^2 - 2(1) + 1 = 2
a_2 = 3(2)^2 - 2(2) + 1 = 9
a_3 = 3(3)^2 - 2(3) + 1 = 22
a_4 = 3(4)^2 - 2(4) + 1 = 41
a_5 = 3(5)^2 - 2(5) + 1 = 66
Sum of the first 5 terms:
+ 9 + 22 + 41 + 66 = 140
A rectangular prism has dimensions 4 cm, 5 cm, and 6 cm. If the dimens...
\times 5 \times 6 = 120 \text{ cubic centimeters}
New dimensions are \( 8 \), \( 10 \), and \( 12 \).

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