Numerical Methods - Engineering Mathematics - Aerospace Engineering Previous Year Questions

An approximate solution of the equation \(x^3 - 17 = 0\) is to be obtained using the Newton-Raphson method. If the initial guess is \(x_0 = 2\), the value at the end of the first iteration is \(x_1 = \) ____ (rounded off to two decimal places).

A furnace of 250 MW rating is used to melt and raise the temperature of aluminium from 25 °C to 900 °C. Aluminium has a solid-state specific heat, latent heat, and liquid-state specific heat of 0.9 kJ/kg·K, 390 kJ/kg, and 1.108 kJ/kg·K, respectively, and the furnace has 70% efficiency. The melting point of aluminium is 660 °C. The amount of aluminium that can be processed per hour is __________ kg (rounded off to 1 decimal place).