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Home » Cite Fast: Say Goodbye to Slow Citations — Get Results Instantly! - Aurero

Cite Fast: Say Goodbye to Slow Citations — Get Results Instantly! - Aurero

📅 March 13, 2026 👤 scraface

Mar 13, 2026

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📌 \( \frac{9}{25} + \cos^2(\theta) = 1 \)

📌 \( \cos^2(\theta) = \frac{16}{25} \)

📌 \( \cos(\theta) = \frac{4}{5} \) (positive in first quadrant)

📌 #### \( \frac{4}{5} \)

📌 A rectangular garden has a perimeter of 60 meters and a length 5 meters more than twice its width. Find the dimensions.

📌 Let width = \( w \), length = \( 2w + 5 \)

📌 Perimeter: \( 2(w + 2w + 5) = 60 \)

📌 \( 2(3w + 5) = 60 \)

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### Solution to Problem 1:
Perimeter: \( 2(w + 3w) = 80 \)
\( 2(4w) = 80 \Rightarrow 8w = 80 \Rightarrow w = 10 \)
Length = \( 3 \times 10 = 30 \)
Area = \( 10 \times 30 = 300 \) square meters.
### Solution to Problem 2:
Use exponential growth: \( P = P_0(1 + r)^t \)
\( P = 250000(1.12)^4 \)
\( 1.12^4 \approx 1.5735 \)
\( P \approx 250000 \times 1.5735 = 393,375 \)

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