Solution

In a certain cryptographic system, the decoding speed $v$ (in units per second) is related to the security delay function $d(v) = \dfrac{v^2}{20 + v}$, where $d(v)$ represents the decoding delay in milliseconds. For secure transmission, the system requires a decoding delay of $50$ milliseconds. Use Newton–Raphson Method with initial guess $v_0 = 35$ to determine the decoding speed $v$ that satisfies $d(v) = 50$, correct to three decimal places.