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#### 418.664 cubic meters - High Altitude Science

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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Alternatively, perhaps question is valid only for non-integer n, but n...
Therefore, no integer solution. But likely intended:
Try n = 8: 4×(10 + 21) = 124
n = 6: 3×(10 + 15) = 75
n = 9: 4.5×(10 + 24) = 4.5×34 = 153
So no solution — but if we solve quadratic:
n = [ -7 + √(49 + 2640) ] / 6 = [ -7 + √2689 ] / 6
√2689 ≈ 51.85 → n ≈ 44.85 / 6 ≈ 7.475 → not integer → no valid n?
But question must have solution.
Recompute: 3n² + 7n - 220 = 0

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11y = -32 \\
y = -\frac{32}{11}
Substitute $ y = -\frac{32}{11} $ into equation (2):
2x + 3\left(-\frac{32}{11}\right) = -6 \\
2x - \frac{96}{11} = -6 \\
2x = -6 + \frac{96}{11} = \frac{-66 + 96}{11} = \frac{30}{11} \\
x = \frac{15}{11}
Thus, the intersection point is $ \left( \frac{15}{11}, -\frac{32}{11}...
Final answer: $ \boxed{\left( \frac{15}{11}, -\frac{32}{11} \right)} $
Question: Factor the expression $ 16x^4 - 81y^4 $.

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