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Home » How This Stunning Gown Made Her the Sweet Sixteen Royalty in One Night! 💫 - DNSFLEX

How This Stunning Gown Made Her the Sweet Sixteen Royalty in One Night! 💫 - DNSFLEX

📅 March 12, 2026 👤 scraface

Mar 12, 2026

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📌 Solution: The angle of elevation is $ 45^\circ $, and the adjacent side (distance from the boat to the base) is 100 meters. Using $ \tan(45^\circ) = \frac{\text{opposite}}{\text{adjacent}} $, we have $ 1 = \frac{h}{100} $. Solving gives $ h = 100 $ meters. Thus, the height of the lighthouse is $\boxed{100}$ meters.

📌 Question: A spherical buoy used by an oceanographer has a radius of $ 2x $, while a hemisphere-shaped sensor has a radius of $ 3x $. What is the ratio of their volumes?

📌 Solution: The volume of the sphere is $ \frac{4}{3}\pi (2x)^3 = \frac{32}{3}\pi x^3 $. The volume of the hemisphere is $ \frac{2}{3}\pi (3x)^3 = 18\pi x^3 $. The ratio is $ \frac{32/3}{18} = \frac{32}{54} = \frac{16}{27} $. The ratio of their volumes is $\boxed{\dfrac{16}{27}}$.

📌 Question: A right triangle formed by ocean currents has sides of length 9 km, 12 km, and 15 km. What is the length of the shortest altitude?

📌 Solution: The area of the triangle is $ \frac{1}{2} \times 9 \times 12 = 54 $ km². The altitudes corresponding to each side are $ \frac{2 \times 54}{9} = 12 $, $ \frac{2 \times 54}{12} = 9 $, and $ \frac{2 \times 54}{15} = 7.2 $. The shortest altitude is $ 7.2 $ km, or $ \frac{36}{5} $. Thus, the length is $\boxed{\dfrac{36}{5}}$ km.

📌 Question: A circular throughfall in a coral reef has a diameter equal to the diagonal of a 6 cm by 8 cm rectangular coral fragment. What is the circumference of the throughfall?

📌 Solution: The diagonal of the rectangle is $ \sqrt{6^2 + 8^2} = 10 $ cm. The circumference is $ \pi \times \text{diameter} = 10\pi $ cm. The circumference of the throughfall is $\boxed{10\pi}$ cm.**Question:** A bag contains 7 red marbles and 8 blue marbles. If four marbles are drawn at random, what is the probability that exactly two are red?

📌 To solve this problem, we use combinations to determine the number of ways to draw marbles with the specified conditions.

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