ingridskoerber

18.03.2021 • 

Mathematics

(a) The linear or mean intercept method is one way to estimate the average grain diameter, d. If you have several cross-sections of your sample so you can determine whether the grains are equi-axed (approximately the same length in all directions), rod or columnar shaped, or platy (like a dinner plate), you can increase the accuracy of your estimate by including a shape factor in your calculation.(i) Use the mean intercept on the schematic microstructure for a hypothetical single phase metal below, to estimate the average grain size. Don’t worry about including a shape factor.Note: Mean intercept length, where LT = measured length of the line(s) on the micrograph, P = L=LTP, number of times the line(s) intersect a grain boundary and M = the magnification of the micrograph; you may need to determine this from the scale bar.(ii) If you use more than one line and you vary the orientation of your lines will you get a better estimate of the average grain size? Explain your answer in 1-3 bullets.(b) Determine the ASTM grain size number for the schematic microstructure below.(ci) Which method did you find easier to do? Explain why in 1-3 bullets?(ii) Which method would you prefer to use if your average grain size was 0.5 μm?

Ответ:

ryleigh1780

26.10.2021

Mathematics

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Hello from MrBillDoesMath!

See discussion below

Discussion:

A real brain teaser!

If f(x) = x^2 + 2x + 3, then

a. f(-x) = (-x)^2 + 2(-x) +3

         =  x^2    -2x      + 3

b. - f(x) = - (x^2 + 2x + 3)  = -x^2 -2x - 3

c. Using a) above

   -f(-x) = - (x^2 -2x + 3 ) = -x^2 + 2x - 3

Note that f(x) is not an even function ( f(x) = f(-x) ) or an odd function ( f(-x) = - f(x))

Thank you,

MrB

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