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Home » - \frac151 = \frac5151 - \frac151 = \frac5051 - Get link 4share

- \frac151 = \frac5151 - \frac151 = \frac5051 - Get link 4share

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 Now, substitute $ y = x^2 + 1 $ to find $ g(x^2 + 1) $:

📌 g(x^2 + 1) = 2(x^2 + 1)^2 - (x^2 + 1) - 2 = 2x^4 + 4x^2 + 2 - x^2 - 1 - 2 = 2x^4 + 3x^2 - 1.

📌 The final answer is $ \boxed{2x^4 + 3x^2 - 1} $.

📌 Question: An angel investor analyzes a medical startup's growth, modeled by the polynomial $ g(x) $, where $ g(x^2 + 2) = 3x^6 - 4x^4 + 5x^2 - 2 $. Find $ g(x^2 - 2) $.

📌 Solution: Let $ y = x^2 + 2 $. Then $ x^2 = y - 2 $. Express $ g(y) $ in terms of $ y $:

📌 g(y) = 3x^6 - 4x^4 + 5x^2 - 2 = 3(x^2)^3 - 4(x^2)^2 + 5x^2 - 2 = 3(y - 2)^3 - 4(y - 2)^2 + 5(y - 2) - 2.

📌 3(y^3 - 6y^2 + 12y - 8) - 4(y^2 - 4y + 4) + 5y - 10 - 2 = 3y^3 - 18y^2 + 36y - 24 - 4y^2 + 16y - 16 + 5y - 12 = 3y^3 - 22y^2 + 57y - 52.

📌 Thus, $ g(x^2 - 2) = 3(x^2 - 2)^3 - 22(x^2 - 2)^2 + 57(x^2 - 2) - 52 $. Expanding:

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Usa trigonometría:
\[ \text{Altura} = 10 \times \sin(60^\circ) = 10 \times \frac{\sqrt{3}...
#### \(5\sqrt{3}\)Frage: Ein Quadrat hat eine Fläche von \( 144 \, \te...
Lösung:
Sei die Seitenlänge des ursprünglichen Quadrats \( s \). Da die Fläche...
s^2 = 144 \implies s = \sqrt{144} = 12 \, \text{cm}
Wenn jede Seite um 2 cm verkleinert wird, wird die neue Seitenlänge:
s_{\text{neu}} = 12 \, \text{cm} - 2 \, \text{cm} = 10 \, \text{cm}
Die neue Fläche des Quadrats ist:
s_{\text{neu}}^2 = 10^2 = 100 \, \text{cm}^2

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