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Home » + 24x + 18x + 4x² = 180 - inBeat

+ 24x + 18x + 4x² = 180 - inBeat

📅 May 3, 2026 👤 scraface

May 03, 2026

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📌 Question: An ichthyologist observes a fish migration pattern forming a right triangle on a pollutant-affected zone, where the legs measure 15 km and 20 km. If a drone flies directly over the hypotenuse at a constant altitude, what is the distance it travels?

📌 Solution: Let the legs of the right triangle be $ a = 15 $ km and $ b = 20 $ km. The hypotenuse $ c $ is given by the Pythagorean theorem:

📌 c = \sqrt{a^2 + b^2} = \sqrt{15^2 + 20^2} = \sqrt{225 + 400} = \sqrt{625} = 25

📌 The drone travels a distance of $ \boxed{25} $ km.

📌 Question: A hydrologist models a reservoir as a cone with height 60 m and base radius 40 m. A smaller cone (representing a spillway) is similar to the reservoir and has height 15 m. What is the ratio of the volume of the spillway to the reservoir?

📌 Solution: Since the cones are similar, the ratio of their linear dimensions is $ \frac{15}{60} = \frac{1}{4} $. The volume ratio of similar solids is the cube of the linear ratio:

📌 \left(\frac{1}{4}\right)^3 = \frac{1}{64}

📌 The volume ratio is $ \boxed{\frac{1}{64}} $.

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