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Home » Solve: 10000 / (1 + 99e^(−0.5t)) > 5000 - Belip

Solve: 10000 / (1 + 99e^(−0.5t)) > 5000 - Belip

📅 May 6, 2026 👤 scraface

May 06, 2026

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📌 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.

📌 Total ways to draw 4 marbles from 15:

📌 The total number of ways to draw 4 marbles from a bag containing 7 red and 8 blue marbles is given by:

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