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Home » Divide by 2: \( x = 72 \) - Belip

Divide by 2: \( x = 72 \) - Belip

📅 May 2, 2026 👤 scraface

May 02, 2026

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📌 The inradius $ c $ of a right triangle is known to be

📌 Also, the area can be expressed in terms of the inradius and semi-perimeter $ s $:

📌 Solution: When a rectangle is inscribed in a circle, the diagonal of the rectangle is the diameter of the circle. The diagonal $ d $ of the rectangle with sides 8 m and 15 m is found using the Pythagorean theorem:

📌 Solution: We are given 9 patent applications: 4 from Company A (indistinguishable among themselves), 3 from Company B, and 2 from Company C. We are to count the number of distinct sequences in which these can be reviewed, where only the company of origin matters (not individual applications, and indistinguishability within companies).

📌 This is a multinomial arrangement problem. The total number of distinct sequences is given by:

📌 Question: An epidemiologist is modeling a disease that spreads over 6 days, with each day classified as low, medium, or high transmission. If exactly 2 days are low, 2 days are medium, and 2 days are high, how many distinct transmission sequences are possible?

📌 Solution: We are to count the number of distinct sequences of length 6, where there are 2 low, 2 medium, and 2 high transmission days. Since the days are ordered over time and the counts per category are fixed, this is a permutation of a multiset.

📌 The total number of such sequences is:

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