(a) Apply the Newton-Raphson method to the function f (x) = tanh(x^2 − 9) to evaluate its known real root at x = 3. Use an initial guess of x_0 = 3.2 and take a minimum of three iterations.
(b) Did the method exhibit convergence onto its real root? Sketch the plot with the results for each iteration labeled.

The y form of iron is known as: a) ferrite b) cementite c) perlite d) austenite

Heat is added to a piston-cylinder device filled with 2 kg of air to raise its temperature 400 c from an initial temperature of t1 27 cand pressure of pi 1 mpa. the process is isobaric process. find a)-the final pressure p2 b)-the heat transfer to the air.

Aloaded platform of total mass 500 kg is supported by a dashpot and by a set of springs of effective stiffness 72 kn/m. it is observed that when the platform is depressed through a distance x = 12.5 cm below its equilibrium position and then released without any initial velocity; it reaches its equilibrium position in the shortest possible time without overshoot. find the position and velocity of the loaded platform 0.10 sec. after its release. if a further load of 400 kg is added to the platform, find, i) the frequency of damped vibrations, and i) the amplitude of vibration after 2 complete oscillations, given that the initial amplitude is 15 cm.