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Home » \( R(2) = 17 \), a prime number. - Aurero

\( R(2) = 17 \), a prime number. - Aurero

📅 March 13, 2026 👤 scraface

Mar 13, 2026

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📌 \[ c = \sqrt{a^2 + b^2} = \sqrt{5^2 + 12^2} = \sqrt{25 + 144} = \sqrt{169} = 13 \text{ meters} \]

📌 Substitute the values into the formula for the radius:

📌 \[ r = \frac{5 + 12 - 13}{2} = \frac{4}{2} = 2 \text{ meters} \]

📌 Thus, the radius of the inscribed circle is \(\boxed{2}\) meters.

📌 Question:** A flood risk manager is designing a circular retention pond within a square plot to improve drainage in New Orleans. If the square plot measures 20 meters on each side, what is the circumference of the largest possible circle that can fit inside the square?

📌 The largest circle that can fit inside a square is one where the diameter of the circle is equal to the side length of the square. Hence, the diameter \( d = 20 \) meters. The radius \( r \) of the circle is:

📌 \[ r = \frac{d}{2} = \frac{20}{2} = 10 \text{ meters} \]

📌 The circumference \( C \) of the circle is given by:

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Define events:
\( T \): traditional methods
\( M \): modern methods
\( F \): crop failure
P(T) = 0.60, \quad P(M) = 0.40
P(F|T) = 0.25, \quad P(F|M) = 0.10
Use the Law of Total Probability to find \( P(F) \):
P(F) = P(F|T)P(T) + P(F|M)P(M) = (0.25)(0.60) + (0.10)(0.40) = 0.15 +...
Apply Bayes’ Theorem:
P(T|F) = \frac{P(F|T)P(T)}{P(F)} = \frac{0.15}{0.19} \approx 0.7895

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