mm-253 === Subject: Req equation of Interpolation acceleration........http://www.acad.polyu.edu.hk/~02471629d/ HMA001.jpgthis pic's Interpolation acceleration must be wrong because even all 5y are the same (eg. =90) , interpolation acceleration is still notzero.what is the correct equation ? === acceleration........> http://www.acad.polyu.edu.hk/~02471629d/HMA001.jpg> this pic's Interpolation acceleration must be wrong because even all 5> y are the same (eg. =90) , interpolation acceleration is still not> zero.> what is the correct equation ? >.,> .... > K2 = a + b + c> K1 = a b + b c + c a> K0 = a b c That is, a, b, and c are the three roots of the cubic equationx^3 - (K2)(x^2) + (K1)x - K0 = 0.To see this, multiply out (x - a)(x - b)(x - c) and compare the coefficients. > I want to acheive 2a - b - c, 2b - a - c, 2c - a - b using any> combinations of K2, K1, K0 using any operations (+, -, *, , roots, logs,> etc.) under real numbers. Since 2a - b - c = 3a - K2, and you know K2, finding 2a - b - c is essentially the same problem as finding a separately. Similarly finding your other two expressions amounts to find b and c. So you're really after the solution of a general cubic equation, which you can find at various web sites such as:http://www.sosmath.com/algebra/factor/fac11/fac11.htmlhttp: //mathworld.wolfram.com/C/CubicEquation.html Ken === Suppose:> K2 = a + b + c> K1 = a b + b c + c a> K0 = a b c> I want to acheive 2a - b - c, 2b - a - c, 2c - a - b using any> combinations of K2, K1, K0 using any operations (+, -, *, , roots, logs,> etc.) under real numbers.> 1) How do I know if such combinations of K2, K1, K0 will get me to 2a -b -> c?> 2) If such a combination exists, how would I figure it out?> ClaudioSymmetric functions can always be expressed in terms ofthe elementary symmetric polynoms, e.g. a^2 + b^2 + c^2is a combination of K0, K1 and K2.As 2a -b -c is not symmetric, I think, you cannot finda combination in K0, K1 K2.Bye, Norbert === Suppose:> K2 = a + b + c> K1 = a b + b c + c a> K0 = a b c> I want to acheive 2a - b - c, 2b - a - c, 2c - a - b using any> combinations of K2, K1, K0 using any operations (+, -, *, , roots, logs,> etc.) under real numbers.> 1) How do I know if such combinations of K2, K1, K0 will get me to 2a - b -> c?> 2) If such a combination exists, how would I figure it out?You have three equations in three unknowns.Solve for a, b, and c in terms of K0, K1, and K2.Note: this will be a very messy result, with multiplecases depending upon the values that the variablestake on.After you have each of a, b, and c as functions of K0, K1, and K2,you can write any combination of === 20(square)+2 =22(square)+2 =66(square)+2 = 38 ectGive the next number in the seequence 2; 6; ... . Give 3 possibilities.> The first 2 are the obvious arithmetical and geometrical sequences. === SequencesGive the next number in the seequence 2; 6; ... . Give 3possibilities.> The first 2 are the obvious arithmetical and geometrical sequences. Any> ideas for the third one ?> Deon1, 2, 3 are all good possibilities (as are all integers)For example 2,6,2,6,2,6... is a nice sequence where the third term is 2.This is a nice question: finding a wrong === show me how to interpolate values in engineering tables?Say for example I have a tributary load width of 26 feet. Using a 2x4 inchbeam I am allowed a maximum span of 6' 9 (6 feet 9 inches).The table then jumps to a load width of 30'. That 2x4 beam now has a maximumspan of 6' 4.If I have a load width of === here show me how to interpolate values in engineering tables?> Say for example I have a tributary load width of 26 feet. Using a 2x4 inch> beam I am allowed a maximum span of 6' 9 (6 feet 9 inches).> The table then jumps to a load width of 30'. That 2x4 beam now has amaximum> span of 6' 4.> If I have a load width of 27.5' how would I find the max. span of that2x4> -Allenhttp://numericalmethods.eng.usf.edu/mws/gen/05inp/mws_ gen_inp_ppt_ndd.ppt