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Home » Let \( x \) be the number of units of Product A sold. - Network4

Let \( x \) be the number of units of Product A sold. - Network4

📅 May 20, 2026 👤 scraface

May 20, 2026

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📌 Since the rectangle is inscribed in a circle, its diagonal is the diameter of the circle.

📌 Find the length of the shortest altitude in a triangle with side lengths of 13 cm, 14 cm, and 15 cm.

📌 The shortest altitude corresponds to the longest side, which is 15 cm.

📌 Thus, the number of such triangles is the number of valid $ k $, which is $ 100 $.

📌 Therefore, each $ a = 7k $, $ k = 1 $ to $ 100 $, gives a valid triangle.

📌 Question: A palynologist observes that the number of pollen grains in successive layers of sediment follows a geometric sequence where the first term is $ 3 $ and the common ratio is a prime number. If the sum of the first $ 5 $ terms is divisible by $ 100 $, what is the smallest possible prime ratio?

📌 Let the prime ratio be $ p $. The sum of the first 5 terms of a geometric sequence is:

📌 Since $ 3 $ and $ 100 $ are coprime, divide both sides:

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