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Home » Fidelity after n layers: 100 × (√2)^n > 900 - Appfinity Technologies

Fidelity after n layers: 100 × (√2)^n > 900 - Appfinity Technologies

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 A projectile is launched from the ground with an initial velocity of 50 m/s at an angle of 30 degrees above the horizontal. Ignoring air resistance, calculate the maximum height reached by the projectile.

📌 The vertical component of the initial velocity is \( 50 \times \sin(30^\circ) = 25 \) m/s.

📌 Use the formula \( h = \frac{v^2 \sin^2 \theta}{2g} \), where \( g = 9.8 \) m/s².

📌 \( h = \frac{25^2 \times \sin^2(30^\circ)}{2 \times 9.8} = \frac{625 \times 0.25}{19.6} \approx 7.97 \) meters.

📌 A circle is inscribed in a square with a side length of 12 cm. Calculate the area of the shaded region outside the circle but inside the square.

📌 Area of the square is \( 12^2 = 144 \) cm².

📌 Radius of the inscribed circle is \( \frac{12}{2} = 6 \) cm.

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