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Home » First discount: 15% of 120 = 0.15 × 120 = 18 → discounted price = 120 – 18 = 102 - AMAZONAWS

First discount: 15% of 120 = 0.15 × 120 = 18 → discounted price = 120 – 18 = 102 - AMAZONAWS

📅 March 6, 2026 👤 scraface

Mar 06, 2026

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📌 V_2 = \frac{4}{3} \pi (3r)^3 = \frac{4}{3} \pi \cdot 27r^3 = 27 \cdot \frac{4}{3} \pi r^3 = 27V_1

📌 Thus, the volume increases by a factor of \(\boxed{27}\).

📌 Question:** In a right triangle, one leg is 6 cm and the hypotenuse is 10 cm. Find the length of the shortest altitude.

📌 Let the triangle have legs \(a = 6\) cm, hypotenuse \(c = 10\) cm. Use the Pythagorean theorem to find the other leg \(b\):

📌 b = \sqrt{c^2 - a^2} = \sqrt{100 - 36} = \sqrt{64} = 8 \text{ cm}

📌 Area of the triangle:

📌 A = \frac{1}{2} \cdot 6 \cdot 8 = 24 \text{ cm}^2

📌 The altitudes corresponding to each side are found using \(A = \frac{1}{2} \times \text{base} \times \text{height}\).

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