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Home » Original rate: \( 240 \div 8 = 30 \) gadgets/hour - High Altitude Science

Original rate: \( 240 \div 8 = 30 \) gadgets/hour - High Altitude Science

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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🔥 Popular Posts

r^2 = 3^2 + 5^2 = 9 + 25 = 34
r = \sqrt{34}
The radius of the lake is $ oxed{\sqrt{34}} $ km.
Question: An astronomer observes a protoplanetary disk rotating unifor...
Solution: The central angle corresponding to the arc is $ 120^\circ $,...
c = 2R \sin\left(rac{ heta}{2}
Substituting $ heta = rac{2\pi}{3} $:
c = 2R \sin\left(rac{\pi}{3}
ight) = 2R \cdot rac{\sqrt{3}}{2} = R\sqrt{3}
The ratio of chord length to radius is:

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The ellipse is \( \frac{x^2}{16} + \frac{y^2}{9} = 1 \). Since \( |x|...
We seek integer \( x, y \) such that:
\frac{x^2}{16} + \frac{y^2}{9} = 1, \quad |x| \leq 4, \quad |y| \leq 3
Multiply both sides by \( 144 = 16 \cdot 9 \):
\cdot \left( \frac{x^2}{16} + \frac{y^2}{9} \right) = 9x^2 + 16y^2 = 1...
So we solve \( 9x^2 + 16y^2 = 144 \) in integers with \( |x| \leq 4 \)...
We try all integer \( x \) from \( -4 \) to \( 4 \), compute \( 9x^2 \...
\( x = 0 \): \( y^2 = \frac{144}{16} = 9 \) → \( y = \pm 3 \) → valid
\( x = \pm 1 \): \( 9(1) = 9 \), \( 144 - 9 = 135 \), \( y^2 = 135/16...
\( x = \pm 2 \): \( 9(4) = 36 \), \( 144 - 36 = 108 \), \( y^2 = 108/1...

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