Ahmed Elkazaz
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What is the formula?
- Thread starter Ahmed Elkazaz
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D
Deleted member 4993
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Please show us what you have tried and exactly where you are stuck.Please help
I need the formula of these values. Which equation or formula used to find the next values?!
Please follow the rules of posting in this forum, as enunciated at:
https://www.freemathhelp.com/forum/threads/read-before-posting.109846/#post-486520
Please share your work/thoughts about this assignment.
HallsofIvy
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To have a function, you need pairs of values. Here you have only single values. Are we to assume that these are y values with x 0,1, 2, 3, 4, 5, 6, 7, 8, 9?
Or were these given as pairs that you have accidently separated?
In any case, given any finite number of pairs there exist an infinite number of functions that could give those pairs. One way to get a function is to assume straight lines between every consecutive pair of (x, y) values. Or, given any n+1 set of (x, y) pairs there exist a unique nth degree polynomial giving all n+ 1 pairs.
There does not exist a single, correct, solution to your problem.
I just noticed that you said "formula", not "function". That's even worse! Every "function" is a "formula" but there exist "formulas" that are not "functions". If by formula you mean the (very restricted) idea of a single "equation" then, as I said before, given any n+1 set of (x, y) pairs there exist a unique nth degree polynomial giving all n+ 1 pairs. Assuming that you mean pairs (0, 233.25), (1, 100.5375), etc., taking that polynomial to be \(\displaystyle a+ bx+ cx^2+ dx^3+ ex^4+ fx^5+ gx^6+ hx^7+ ix^8+ jx^9\) then you need to find a, b, c, d, e, f, g, h, i, j such that j= 233.25, a+ b+ c+ d+ e+ f+ g+ h+ i+ j= 100.5375, etc. 9 equations to solve for 9 numbers. Or you can use "Newton's divided difference method" (yes, that Newton) https://www.r-bloggers.com/divided-differences-method-of-polynomial-interpolation/
Either way, it's going to be a lot of work!
Or were these given as pairs that you have accidently separated?
In any case, given any finite number of pairs there exist an infinite number of functions that could give those pairs. One way to get a function is to assume straight lines between every consecutive pair of (x, y) values. Or, given any n+1 set of (x, y) pairs there exist a unique nth degree polynomial giving all n+ 1 pairs.
There does not exist a single, correct, solution to your problem.
I just noticed that you said "formula", not "function". That's even worse! Every "function" is a "formula" but there exist "formulas" that are not "functions". If by formula you mean the (very restricted) idea of a single "equation" then, as I said before, given any n+1 set of (x, y) pairs there exist a unique nth degree polynomial giving all n+ 1 pairs. Assuming that you mean pairs (0, 233.25), (1, 100.5375), etc., taking that polynomial to be \(\displaystyle a+ bx+ cx^2+ dx^3+ ex^4+ fx^5+ gx^6+ hx^7+ ix^8+ jx^9\) then you need to find a, b, c, d, e, f, g, h, i, j such that j= 233.25, a+ b+ c+ d+ e+ f+ g+ h+ i+ j= 100.5375, etc. 9 equations to solve for 9 numbers. Or you can use "Newton's divided difference method" (yes, that Newton) https://www.r-bloggers.com/divided-differences-method-of-polynomial-interpolation/
Either way, it's going to be a lot of work!
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