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Home » ight) = c r - racr^3c - ClickBalance

ight) = c r - racr^3c - ClickBalance

📅 May 17, 2026 👤 scraface

May 17, 2026

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📌 Question: A triangle has sides of lengths 13 cm, 14 cm, and 15 cm. What is the length of the shortest altitude?

📌 Solution: To find the shortest altitude, we first compute the area using Herons formula. Let the sides be $ a = 13 $, $ b = 14 $, $ c = 15 $. The semi-perimeter is:

📌 Question: A right circular cylinder is inscribed in a sphere of radius 10 cm. If the height of the cylinder is equal to its diameter, what is the volume of the cylinder in cubic centimeters?

📌 Solution: Let the radius of the cylinder be $ r $ and its height be $ h = 2r $. The cylinder is inscribed in a sphere of radius 10, so the diagonal from the center of the sphere to the top rim of the cylinder forms a right triangle with legs $ r $ and $ r $, and hypotenuse equal to the radius of the sphere, 10 cm.

📌 $$Question: A programmer is developing an AI application that generates 5-character codes using the characters A, B, C, D, and E. What is the probability that exactly two of the characters are As, assuming each character is chosen independently and uniformly?

📌 Question: A hydrologist is modeling groundwater flow through 6 distinct aquifers and needs to assign 3 unique intensity levels to them. What is the number of ways to distribute the intensity levels if each level is applied to exactly 2 aquifers?

📌 Question: A paleontologist is analyzing 4 fossilized teeth and 5 fossilized bones from a dinosaur site. If the fragments are arranged in a line, what is the probability that all 4 teeth appear consecutively?

📌 Substitute into the given expression:

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