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Take the carburizing of a steel bar to make a hard surface. To obtain the desired hardness, we require to control the diffusion of carbon into the surface and the phases obtained during heat treatment and cooling. The base steel has a composition of 0.2 wt%C. For mathematical simplicity we took an infinitely thick bar and a diffusivity that does not vary with concentration. All concentrations are in weight percent.
A) Use the graph you have make to estimate the times needed for a diffusion depth of 600 microns (i.e. 0.6 mm) for each of the three temperatures.
Determine the function f ( x ) . f ′ ( x )= 4x 3 - 9 + 2 sin x + 7e x , f (0) = 15 Solution The first step is to integrate to fine out the most general pos
1. (‡) Prove asymptotic bounds for the following recursion relations. Tighter bounds will receive more marks. You may use the Master Theorem if it applies. 1. C(n) = 3C(n/2) + n
4x+8=32
Case 1: Suppose we have two terms 8ab and 4ab. On dividing the first by the second we have 8ab/4ab = 2 or 4ab/8ab = (1/2) depending on whether we consider either 8ab or 4ab as the
Josephine is constructing an open box by cutting the squares off the corners of a sheet of paper sized 20cm by 16cm. She is considering options of 3cm, 4cm and 5cm squares in order
to which subset of the real number does the number 22 belong?
sin (cot -1 {cos (tan -1 x)}) tan -1 x = A => tan A =x sec A = √(1+x 2 ) ==> cos A = 1/√(1+x 2 ) so A = cos -1 (1/√(1+x 2 )) sin (cot -1 {cos (tan -1 x)}) = s
the number is 605176 the underline digit is 0
Verify Louisville''s formula for y "-y" - y'' + y = 0 in (0, 1) question..
A box contains 12 balls out of which x are black .if one ball is drawn at random from the box what is the probability that it will be a black ball ? If 6 more black balls are pu
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