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📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 A rectangular prism has a volume of 108 cubic meters. Its length is twice its height, and its width is 3 meters more than its height. Find the dimensions.

📌 Let height \( h \), then length \( l = 2h \), width \( w = h + 3 \).

📌 Volume: \( lwh = 2h \cdot (h+3) \cdot h = 2h^2(h+3) = 2h^3 + 6h^2 = 108 \)

📌 Divide by 2: \( h^3 + 3h^2 - 54 = 0 \)

📌 Try rational roots: \( h = 3 \): \( 27 + 27 - 54 = 0 \) → works.

📌 So \( h = 3 \), \( l = 6 \), \( w = 6 \)

📌 #### Height: 3 m, Length: 6 m, Width: 6 m

📌 The function \( f(x) = \frac{2x - 1}{x + 4} \) has a horizontal asymptote at what value?

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