Chris Berry wrote:
It works out fine if you use more signigicant digits - I did all my calculations with only three significant digits, hence the non-exact match. Repeat my calculation with more significant digits and you will get a more accurate result.Moby wrote:Chris Berry wrote:Mark Lane wrote:I was a math major in a former life 10+ years. 1/2(e^x + e^-x) = 4 e^x + e^-x = 8 (e^x)^2 + 1 = 8e^x Let y = e^x such that x = ln(y). y^2 + 1 = 8y y^2 - 8y + 1 = 0Use quadratic formula, which is x = (-b +- sqrt(b^2 - 4ac))/2a, to solve fory in previous equation. Then x = ln(y)Pretty, but pure handwaving, you still didn't provide a value for x.To continue the handwaving some more then :)Using the quadratic formula and keeping only the positive value for y (y = e^x - as such y cannot be negative!) we get:y = (8 + 9.592) /2 = 8.796 This means e^x = 8.796 => x = ln(8.796) = 2.174That doesn't work out right when I plug it into my spreadsheet. *scratches head*I used: =1/2*(2.71828183^A1+2.71828183^(A1*-1)) and got 4.4536 not 4 I'm a little rusty though, did I miss something?
-- --Moby They that can give up essential liberty to obtain a little temporary safety deserve neither liberty nor safety. -- Benjamin Franklin First they came for the Jews and I did not speak out because I was not a Jew. Then they came for the Communists and I did not speak out because I was not a Communist. Then they came for the trade unionists and I did not speak out because I was not a trade unionist.Then they came for me and there was no one left to speak out for me. -- Pastor Martin Niemöller
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