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Deducing the Formula of a Unknown Function

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Hey guys,

I have a question about mathematics that I do not understand. How do I determine the function that can be used in volume of revolution? Do I have to assume the general form of the function?


 

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On 4/4/2016 at 10:48 PM, Tanque said:

Hey guys,
I have a question about mathematics that I do not understand. How do I determine the function that can be used in volume of revolution? Do I have to assume the general form of the function?

To convert an image to a function
1) Overlap a coordinate axis over the image. Ideally you want y axis to overlap with your 6.8m line, and x-axis with your base = 25 m line. You should keep in mind the conversion factor, eg 1m = 1 unit. For a photograph you can just write 1 pixel = some length in real life. 

2) Take some points on the curve and note down their coordinates. More points is gives you greater accuracy. 
3) In a curve fitting program, such as MS Excel, LoggerPro (or the LoggerLite free version), you can use software to find the best curve that fits the points. You have to specify whether you want a polynomial or power or whichever fit. The program uses an algorithm similar to linear regression, which is derived from calculus beyond HL, specifically the second derivative test in 3-D. If you don't need very good fit you can just throw in coefficients and essentially "guess" the equation until you get a good fit.
4) When you calculate the volume keep in mind your initial conversion factor and remember you should take it to the exponent 3 to convert from linear factor to volume factors. So for example if your grid to real life linear ratio is 1 : 10, then the volume ratio is actually 1 : 1000. 

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