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Home » Simplify: \(120v + 2400 + 180v = 5v^2 + 100v\). - Nelissen Grade advocaten

Simplify: \(120v + 2400 + 180v = 5v^2 + 100v\). - Nelissen Grade advocaten

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 A rectangular prism has dimensions 8 cm by 6 cm by 4 cm. If a cylindrical hole with a radius of 1 cm is drilled through the center along the longest dimension, what is the remaining volume?

📌 Volume of prism = 8 cm × 6 cm × 4 cm = 192 cubic cm

📌 Volume of cylindrical hole = π × (1 cm)^2 × 8 cm = 8π cubic cm

📌 Remaining volume = 192 cubic cm - 8π cubic cm

📌 #### 192 - 8π

📌 Volume of frustum = (1/3)πh(R^2 + r^2 + Rr) = (1/3)π × 7 × (5^2 + 3^2 + 5 × 3) = (1/3)π × 7 × (25 + 9 + 15) = (1/3)π × 7 × 49 = 343π/3 cubic cm

📌 #### 343π/3

📌 A rectangular plot of land measures 50 meters by 30 meters. A circular garden with a radius of 10 meters is planted in the center. What is the area of the plot not occupied by the garden?

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oxed{\sqrt{7}}
Question: If $x + rac{1}{x} = 4$, what is the value of $x^2 + rac{1}...
Solution: Start with the identity:
\left(x + rac{1}{x}
ight)^2 = x^2 + 2 + rac{1}{x^2}
Substitute $x + rac{1}{x} = 4$:
4^2 = x^2 + 2 + rac{1}{x^2} \Rightarrow 16 = x^2 + rac{1}{x^2} + 2
Solve for $x^2 + rac{1}{x^2}$:
x^2 + rac{1}{x^2} = 16 - 2 = 14
oxed{14}

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