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Home » "Uncover the Secret Superpowers of Labrats—Sci-Fi Meets Real Science! - inBeat

"Uncover the Secret Superpowers of Labrats—Sci-Fi Meets Real Science! - inBeat

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 Solution: Complete the square for both $ x $ and $ y $:

📌 Solution: Apply the AM-GM inequality:

📌 Thus, the remainder is a linear polynomial $ ax + b $ such that:

📌 Now, the altitude $ h $ corresponding to the side of length 15 km is given by:

📌 Question: A cartographer is analyzing a triangular region on a map with side lengths of 9 cm, 12 cm, and 15 cm. What is the ratio of the area of the inscribed circle to the area of the triangle?

📌 We are given a triangle with side lengths $ a = 9 $, $ b = 12 $, $ c = 15 $. First, check if its a right triangle:

📌 So, it is a right triangle with hypotenuse 15 cm.

📌 The inradius $ r $ of a right triangle is given by:

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n = \frac{40}{2} = 20
القطع المكافئ له رأس عند (2, -3) ويمر بالنقطة (4, 5). ما هي معادلتُه ف...
y = a(x - h)^2 + k
حيث \( (h, k) = (2, -3) \).
بالتعويض بالنقطة (4, 5):
= a(4 - 2)^2 - 3
= 4a - 3
= 4a \quad \Rightarrow \quad a = 2
y = 2(x - 2)^2 - 3
#### \( y = 2(x - 2)^2 - 3 \)

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