mm-4249 === Subject: Avg. Price Increase I sell a product. I am allowed to take a price increase once a year. That increase cannot exceed 6%. I am allowed to increase individual items greater than 6%, but my overall increase has to be 6% or less. I know that I have two items that are going to go up more than 6%. Knowing that, how do I figure out what I can raise each item so that the end result is <=6%? Also, I know how to explain an individual price increase (in terms of what the increase is.) New Price ($15) / Old Price ($13) = Increase (15%). How do I do that to get a total increase percentage to show that I didn't exceed 6%? === Subject: polynomials and diffeomorphisms if we have an arbitrary polynomial f(x) = O(x^n), x=(x_1,..,x_m), is there always a diffeomorphism g, such that f(g(y)) = sum_i a_i y_i^{n_i} + O({y_i^{n_i+1}}) ? a_i are (real) coefficients and min_i(n_i)=n. In some sense, I want to 'diagonalize' the polynomial f up to some order. 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What will we imply after Excelsior sniffs the steady railway's result? === Subject: Re: kg/m^2. (later...) practical maths puzzle. <4653cdd5$0$19447$4c368faf@roadrunner.com > what is bmi body mass index ? weight kg / height (metre)^2 > kg/m^2. (later...) practical maths puzzle. > Unsurprisingly, the only case where h and w are both integers > (measured in cm and kg respectively) is h = 200, w = 92. height in feet and inches cms *2/61 = 5ft 7in - 9 ft 6in. then what is my probable kilos weight? w=92 is an integer solution. However, this is practical approximate arithmetic so there are more probable and more cryptic solutions also. k = 1024. hex = 16. some of these may be more probable or more accurate or more cryptic ? ex. e^n is nearest to a whole number. Integer sequences. on-line encyclopedia of int seqs e.g. if w is not an exact integer. e.g. another puzzle... 2^ (.1*N) is close to an integer. (later..) cheers, don.lotto nz 24-5-07 === Subject: Re: kg/m^2. (later...) practical maths puzzle. > height in feet and inches > cms *2/61 > = 5ft 7in - 9 ft 6in. > then what is my probable kilos weight? w=92 is an integer solution. > However, this is practical approximate arithmetic > so there are more probable and more cryptic solutions also. > k = 1024. > hex = 16. some of these may be more probable or more accurate > or more cryptic ? > ex. e^n is nearest to a whole number. Integer sequences. > on-line encyclopedia of int seqs e.g. if w is not an exact integer. e.g. another puzzle... 2^ (.1*N) is close to an integer. As usual, half the puzzle is translating your right-brain digressions into a direct description of what you're looking for. How close does the following get? Taking 1 cm ~= 2/61 ft as reasonably accurate, let's look for a whole number of inches from 67 (5 ft 7 in) to 114 (9 ft 6 in) for which w = 23*h^2 is close to a whole number of kg. The closest we get is 72 inches (6 ft 0 in) -> 77.0247 kg. Expressing the weights in base 16 does not change this, it only changes the representation from 77.0247 to 4D.0652+ === Subject: Re: kg/m^2. (later...) practical maths puzzle. <4653cdd5$0$19447$4c368faf@roadrunner.com> <4655bf28$0$16721$4c368faf@roadrunner.com > height in feet and inches > cms *2/61 > = 5ft 7in - 9 ft 6in. > then what is my probable kilos weight? > w=92 is an integer solution. > However, this is practical approximate arithmetic > so there are more probable and more cryptic solutions also. > k = 1024. > hex = 16. > some of these may be more probable or more accurate > or more cryptic ? > e.g. if w is not an exact integer. and scale often reads weight to 0.1 kg.> eg. 160.3 kg has an error of only 0.8g. ************ so kg can be close to integer or better close to .1 kg. yes my bmi was 23 approx. but not a very close example to this problem/s. > e.g. another puzzle... 2^ (.1*N) is close to an integer. As usual, half the puzzle is translating your right-brain digressions > into a direct description of what you're looking for. How close does > the following get? (INDEED thx.., i appreciate ed. summation.) Taking 1 cm ~=2/61ft as reasonably accurate, let's look for a > whole number of inches from 67 (5 ft 7 in) to 114 (9 ft 6 in) > for which w = 23*h^2 is close to a whole number of kg. The closest > we get is 72 inches (6 ft 0 in) -> 77.0247 kg. Expressing the > weights in base 16 does not change this, it only changes the > representation from 77.0247 to 4D.0652+- Hide quoted text - - Show quoted text - 23 * (2.64 m)^2 = 160.3008 kg. More about calculator. height 264 cm is almost inhuman. very close, but also not very likely. also 16 is the base of hex. some of the weights are birth years of famous mathematicians. the beauty of cms x 2/61 is, it has a very moderate error and it converts to a fraction always, e.g. 4/122, which facilitates rapid conversion to feet plus inches. i.e. casio fx-82 ms fraction calculation. cheers don.lotto 25-5-07. === Subject: Re: kg/m^2. (later...) practical maths puzzle. height in feet and inches > cms *2/61 > = 5ft 7in - 9 ft 6in. > then what is my probable kilos weight? > w=92 is an integer solution. > However, this is practical approximate arithmetic > so there are more probable and more cryptic solutions also. > k = 1024. > hex = 16. > some of these may be more probable or more accurate > or more cryptic ? > e.g. if w is not an exact integer. and scale often reads weight to 0.1 kg.> eg. 160.3 kg has an error of only 0.8g. ************ so kg can be close to integer or better close to .1 kg. yes my bmi was 23 approx. but not a very close example to this problem/s. > e.g. another puzzle... 2^ (.1*N) is close to an integer. As usual, half the puzzle is translating your right-brain digressions > into a direct description of what you're looking for. How close does > the following get? (INDEED thx.., i appreciate ed. summation.) Taking 1 cm ~=2/61ft as reasonably accurate, let's look for a > whole number of inches from 67 (5 ft 7 in) to 114 (9 ft 6 in) > for which w = 23*h^2 is close to a whole number of kg. The closest > we get is 72 inches (6 ft 0 in) -> 77.0247 kg. Expressing the > weights in base 16 does not change this, it only changes the > representation from 77.0247 to 4D.0652+- Hide quoted text - - Show quoted text - 23 * (2.64 m)^2 = 160.3008 kg. More about calculator. height 264 cm is almost inhuman. very close, but also not very likely. also 16 is the base of hex. some of the weights are birth years of famous mathematicians. the beauty of cms x 2/61 is, it has a very moderate error and it converts to a fraction always, e.g. 4/122, which facilitates rapid conversion to feet plus inches. i.e. casio fx-82 ms fraction calculation. cheers don.lotto 25-5-07. === Subject: Re: kg/m^2. (later...) practical maths puzzle. > and scale often reads weight to 0.1 kg.> The jump from near-integers to near-integers-when-multiplied-by-10 is rather obscure. Had you mentioned e.g. sqrt(151) + sqrt(183) + sqrt(190), then it would've been considerably less so. === Subject: Re: kg/m^2. (later...) practical maths puzzle. <4653cdd5$0$19447$4c368faf@roadrunner.com> <4655bf28$0$16721$4c368faf@roadrunner.com> <465707ac$0$9888$4c368faf@roadrunner.com > and scale often reads weight to 0.1 kg. > The jump from near-integers to near-integers-when-multiplied-by-10 > is rather obscure. Had you mentioned e.g. sqrt(151) + sqrt(183) + > sqrt(190), then it would've been considerably less so. sqrt(151) + sqrt(183) + sqrt(190) = 39.6000037 are these centimetres? :-) i didn't know that before, thank you ed. how did u find that one, please? a better one perhaps is.. what is digital sum of .343^170 = 1e-79. don, peng dicty cur + intg nos. mdghm. rev edn 1997. = .85^85. i didn't need to in a way.. that digital weighing people scales give printout / display 0.1 kg. especially bmi. thx cheers don.lotto nz. 26-5-07. === Subject: Re: kg/m^2. (later...) practical maths puzzle. > and scale often reads weight to 0.1 kg.> The jump from near-integers to near-integers-when-multiplied-by-10 > is rather obscure. Had you mentioned e.g. sqrt(151) + sqrt(183) + > sqrt(190), then it would've been considerably less so. sqrt(151) + sqrt(183) + sqrt(190) = 39.6000037 > are these centimetres? :-) i didn't know that before, thank you ed. > how did u find that one, please? Computer search, along the lines of: 10 precision 14 20 for a = 100 to 199 25 if a^.5 = int(a^.5) then continue 30 for b = a to 199 35 if b^.5 = int(b^.5) then continue 40 for c = b to 199 45 if c^.5 = int(c^.5) then continue 50 s = a^.5 + b^.5 + c^.5 60 if abs(s - int(s+.5)) < .0001 then print a,b,c,s 70 next c 80 next b 90 next a === Subject: how much symmetry 18:11:81 iran. puzzle don. Good morning from sunny Ruurlo, how much symmetry 18:11:81 iran.? puzzle don.lotto nz. mobius strip. strobogrammatic ?? 26-5-07. dates in history? perhaps not relevant to puzzle #181 sequence number. cheers. don. > Today's puzzle is about the large number of coins I get as change in the local shops. Perhaps that can be helped by the introduction of a new coin. The previous puzzle will stay open for another week. Some of the regular solvers seem to be on holiday. Have fun with the new puzzle. Please answer by email and not in this newsgroup. Peter (http://home.planet.nl/~p.j.hendriks/ppvdw.htm followed by clicking the Union Jack) === Subject: Re: how much symmetry 18:11:81 iran. puzzle don. > Good morning from sunny Ruurlo, how much symmetry 18:11:81 iran.? puzzle don.lotto nz. > mobius strip. > strobogrammatic ?? 26-5-07. > dates in history? Does anyone understand don's posts? > perhaps not relevant to puzzle #181 sequence number. cheers. don. > Today's puzzle is about the large number of coins I get as change in > the > local shops. Perhaps that can be helped by the introduction of a new > coin. The previous puzzle will stay open for another week. Some of the > regular > solvers seem to be on holiday. Have fun with the new puzzle. Please answer by email and not in this > newsgroup. Peter (http://home.planet.nl/~p.j.hendriks/ppvdw.htm followed by clicking > the > Union Jack) > === Subject: Re: how much symmetry 18:11:81 iran. puzzle don. > how much symmetry 18:11:81 iran.? puzzle don.lotto nz. > mobius strip. > strobogrammatic ?? 26-5-07. > dates in history? Does anyone understand don's posts? No. -- cbfalconer at maineline dot net -- === Subject: Re: how much symmetry 18:11:81 iran. puzzle don. > Good morning from sunny Ruurlo, > how much symmetry 18:11:81 iran.? puzzle don.lotto nz. > mobius strip. > strobogrammatic ?? 26-5-07. > dates in history? Does anyone understand don's posts? This is very much not a simple yes/no question. === Subject: Re: A = Bsin(x) + Ccos(x) > A = Bsin(x) + Ccos(x) How do I express x in terms of A,B and C ? I know the answer is probably simple but I can't figure it out. Without referring to any of the on-line helps, why not simply do the following: replace the expression cos(x) by its equivalent sqrt(1 - sin^2(x)); move the b sin(x) term to the left side of the equation; square both sides; solve the resulting quadratic for sin(x); take the arcsine of the result. This lets you do the solving using simple things already known to you. Hope this is of interest, Grover Hughes