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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.
Classifying critical points : Let's classify critical points as relative maximums, relative minimums or neither minimums or maximums. Fermat's Theorem told us that all relative
X and Y are centers of circles of radius 9cm and 2cm and XY = 17cm. Z is the centre of a circle of radius 4 cm, which touches the above circles externally. Given that XZY=90 o , w
Properties of Logarithms 1. log a xy = log a x + log a y 2. = log a x - log a y 3. log a x n = n log
Fundamental Theorem of Calculus, Part I As noted through the title above it is only the first part to the Fundamental Theorem of Calculus. The first part of this theorem us
f(x)=sin x+cos x in the interval {0,90}
A 20-foot light post shows a shadow 25 feet long. At the similar time, a building nearby casts a shadow 50 feet long. determine the height of building? a. 40 ft b. 62.5 ft
Suppose that we know the logarithms of all numbers which are expressed to base 'a' and we are required to find the logarithms of all these numbers to base 'b'. We
If (a,1/a), (b,1/b),(c,1/c),(d,1/d) are four distinct points on a circle of radius 4 units then,abcd is equal to?? Ans) As they are of form (x,1/x) let eq of circle be x
If cos?+sin? = √2 cos?, prove that cos? - sin? = √2 sin ?. Ans: Cos? + Sin? = √2 Cos? ⇒ ( Cos? + Sin?) 2 = 2Cos 2 ? ⇒ Cos 2 ? + Sin 2 ?+2Cos? Sin? = 2Cos 2 ? ⇒
(a) Specify that the sum of the degrees of all vertices of a graph is double the number of edges in the graph. (b) Let G be a non directed gra
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