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Home » \[ S_n = racn2(2 imes 3 + (n-1) imes 2) = 210 \] - Crosslake

\[ S_n = racn2(2 imes 3 + (n-1) imes 2) = 210 \] - Crosslake

📅 February 28, 2026 👤 scraface

Feb 28, 2026

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📌 5### Frage 1

📌 Ein Unternehmen entwirft ein neues Produkt und muss die Kombination von Materialien bestimmen, um die Kosten zu minimieren, während eine bestimmte Festigkeitsanforderung erfüllt wird. Material A kostet 50 $ pro Einheit und bietet 10 Einheiten Festigkeit, während Material B 30 $ pro Einheit kostet und 7 Einheiten Festigkeit bietet. Wenn das Produkt insgesamt mindestens 85 Festigkeits-Einheiten erfordert, welchen minimalen Kostenpunkt stellt die kostengünstigste Kombination von Materialien A und B dar?

📌 Sei \( x \) die Anzahl der Einheiten von Material A und \( y \) die Anzahl der Einheiten von Material B.

📌 Die Festigkeitsbeschränkung ist \( 10x + 7y \geq 85 \).

📌 Die Kostenfunktion ist \( C = 50x + 30y \).

📌 Wir wollen \( C \) unter der Festigkeitsbeschränkung minimieren.

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Simplifying, \( 2(4w) = 64 \) leads to \( 8w = 64 \).
Solving for \( w \), we find \( w = 8 \).
Thus, the length is \( 3 \times 8 = 24 \).
The area is \( w \times \text{length} = 8 \times 24 = 192 \) square me...
A car travels 150 miles in 3 hours. If it continues at the same speed,...
The speed of the car is \( \frac{150 \text{ miles}}{3 \text{ hours}} =...
In 7 hours, the distance traveled is \( 50 \times 7 = 350 \) miles.
The sum of the first \( n \) odd numbers is 625. What is \( n \)?
The sum of the first \( n \) odd numbers is \( n^2 \).
So, \( n^2 = 625 \).

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