mm-1489 === Subject: Re: Area of a region enclosed by curves?? >>Please show me the steps involved in solving this integral. I need to >>see all the steps to see where I went wrong. >> I am confused by two things. 1) Solving in terms of x or in terms of >>y. 2) Effect of the negatives in the quadrants. >>I have tried it several times and keep getting it close but never the >>correct answer. >>Find the area of the region enclosed by x = y^2 - 2 and and x = e^y. >>The region is bounded by y = 1 and y = -1. >Your equations are already solved for x. You set this as as a dy >integral. >Area = integral[ylower..yupper](x_on the right - x_on the left) dy >where the integrand values are functions of y. >Note that (x_on the right - x_on the left) is always positive >regardless of the individual values of x. Can you take it from there? >--Lynn === Subject: Re: Teaching Mathematics > ... they wonder What's the > use of variables? There are no variables in mathematics. === Subject: Re: Teaching Mathematics > > ... they wonder What's the > use of variables? > There are no variables in mathematics. That's sort of true. There are named subexpressions, though. And you can reuse names in new contexts. So, it would be truer to say that there is no concept of evolving state in mathematics. The other characteristics of variables are available - value, scope, persistence. Peter === Subject: Re: Teaching Mathematics What are these then X = mx + C ???? > ... they wonder What's the > use of variables? > There are no variables in mathematics. === Subject: Re: Teaching Mathematics > What are these then > X = mx + C ???? You tell me. My guess is that X, m, x and C denote elements of one or more sets. But I can't be expected to know the meaning of the symbols you use. The norm in mathematics is to begin with m is a real number, etc. > > ... they wonder What's the > use of variables? > There are no variables in mathematics. === Subject: Re: Can you Prove this? As David Cantrell stated, all cubics (3rd order polynomials) with real co-efficients have a real solution. If you have y = ax^3 + bx^2 + cx + d and a is non zero, Then if a>0 for large negative x, then y is negative and for large positive x then y is positive. As the function is continuous, it must have y=0 for some x. If a<0 then vice-versa. This is true for all odd polynomial functions - they either look like curves from the bottom left to the top right (a>0) of curves from the top left to bottom right (a<0). In both cases, they must cross y=0 at some point. Much simpler than your original problem! > Excellent! My intuition failed me, but I have oversimplfied the problem. > I am concerned with a filter design. The truth is that there are 3 poles, > which could be complex numbers. If I could prove one of them was real, it > simplifies my work. The truth is, these 3 numbers are roots to a 3rd > order polynomial equation with real coefficients. > I though that when solving polynomial equations, roots that were complex > always came in complex conjugate pairs. I was thinking that there could > at most be one of these pairs, which would force the other one to be real, > since the product of 2 of them would be real. If a root was zero, this is > also real. >I need to prove this for a practical problem. Suppose I know that the >product of 3 numbers is real and also the sum of the 3 numbers is real. >Prove that at least one of the numbers is real. > > Intuition tells me it is true, but I don't know how to prove this. > > Before I invest too much thought in this, could you please clarify. > Other than real, what do you mean by a number ? Do you actually mean 3 > complex numbers ? >> If the latter, then the proposition that at least one of the numbers is >> real is false. For example, three nonreal complex numbers which have >> both >> a real sum and a real product are >> Sqrt(2) + i, i, and -Sqrt(2) - 2i. >> David === Subject: Re: Can you Prove this? >> If 0 is not imaginary then perhaps it is not real either. >> It is on both the real number line and on the imaginary number line, >> but it has no real part and no imaginary part. >That is false Re(0) = Im(0) = 0. Which statement is false? Are you saying 0 has an imaginary part? Are you saying 0 is an imaginary number? === Subject: Re: Can you Prove this? >> If 0 is not imaginary then perhaps it is not real either. >> It is on both the real number line and on the imaginary number line, >> but it has no real part and no imaginary part. >That is false Re(0) = Im(0) = 0. > Which statement is false? > Are you saying 0 has an imaginary part? The imaginary part of 0 is 0. > Are you saying 0 is an imaginary number? I suspect that having imaginary part 0 makes a number real. === Subject: Re: Can you Prove this? >> Are you saying 0 has an imaginary part? >The imaginary part of 0 is 0. I would agree with that , but it is hardly a yes/no answer. >> Are you saying 0 is an imaginary number? >I suspect that having imaginary part 0 makes a number real. Perhaps - but then does having a real part 0 make a number imaginary? No need to reply. I suspect this horse is already dead and does not need more flogging. === Subject: Re: Can you Prove this? >> Are you saying 0 has an imaginary part? Every number has both a real and an imaginary part. >The imaginary part of 0 is 0. > I would agree with that , but it is hardly a yes/no answer. _Yes_ it has an imaginary part, and that imaginary part is 0. >> Are you saying 0 is an imaginary number? >I suspect that having imaginary part 0 makes a number real. > Perhaps - but then does having a real part 0 make a number imaginary? Yes, _except_ in the case 0 which has real part 0 but is not imaginary. > No need to reply. I suspect this horse is already dead and does not > need more flogging. === Subject: Re: Can you Prove this? >>I suspect that having imaginary part 0 makes a number real. >> Perhaps - but then does having a real part 0 make a number imaginary? >Yes, _except_ in the case 0 which has real part 0 but is not imaginary. That is discrimination. If you say having an imaginary part of 0 makes a number real, then it only fair to say that having a real part of 0 makes a number imaginary. If I say that 0 is not an imaginary number because it has no imaginary part, I should be allowed to say 0 is not a real number because it has no real part. >> No need to reply. I suspect this horse is already dead and does not >> need more flogging. === Subject: Re: Can you Prove this? >> >>I suspect that having imaginary part 0 makes a number real. >> >> Perhaps - but then does having a real part 0 make a number imaginary? >Yes, _except_ in the case 0 which has real part 0 but is not imaginary. > That is discrimination. If you say having an imaginary part of 0 > makes a number real, then it only fair to say that having a real part What on earth makes you think that fairness has got anything to do with it? In mathematics definitions are framed in such a way as to make interesting theorems provable. What you are suggesting would mean that 0 is not a number of any kind. > of 0 makes a number imaginary. If I say that 0 is not an imaginary > number because it has no imaginary part, I should be allowed to say 0 > is not a real number because it has no real part. >> No need to reply. I suspect this horse is already dead and does not >> need more flogging. === Subject: Re: Can you Prove this? >That is discrimination. If you say having an imaginary part of 0 >makes a number real, then it only fair to say that having a real part >of 0 makes a number imaginary. If I say that 0 is not an imaginary >number because it has no imaginary part, I should be allowed to say 0 >is not a real number because it has no real part. Go ahead and say it. Who cares? Question: If you call a tail a leg, how many legs does a dog have? Answer: 5? Retort: No. Calling a tail a leg doesn't make it one. --Lynn === Subject: Re: Can you Prove this? > Excellent! My intuition failed me, but I have oversimplfied the problem. > I am concerned with a filter design. The truth is that there are 3 > poles, which could be complex numbers. If I could prove one of them was > real, it simplifies my work. The truth is, these 3 numbers are roots to > a 3rd order polynomial equation with real coefficients. I don't know why you oversimplified the problem. In any event, your idea that one of the roots must be real is indeed correct. David > I though that when solving polynomial equations, roots that were complex > always came in complex conjugate pairs. I was thinking that there could > at most be one of these pairs, which would force the other one to be > real, since the product of 2 of them would be real. If a root was zero, > this is also real. >>I need to prove this for a practical problem. Suppose I know that >>the product of 3 numbers is real and also the sum of the 3 numbers is >>real. Prove that at least one of the numbers is real. >> >> Intuition tells me it is true, but I don't know how to prove this. >> >> >> Before I invest too much thought in this, could you please clarify. >> >> Other than real, what do you mean by a number ? Do you actually mean >> 3 complex numbers ? > If the latter, then the proposition that at least one of the numbers > is real is false. For example, three nonreal complex numbers which > have both a real sum and a real product are > Sqrt(2) + i, i, and -Sqrt(2) - 2i. > David === Subject: The world is really unstable these days...... We've got a lot to deal with these days. Terrorism, Recession, Weather and more. It's all got me concerned. I thought I'd tell you all about this group I found where everyday people get together and try to learn how to deal with it all. (I used to be a member, but I'm moving to an area that doesn't have internet, so I left a few days ago. Internet is off tomorrow) Here's a bit on the group. Check it out or don't. misc_survivalism_moderated .87 Survivalism and Preparedness. http://groups.yahoo.com/group/misc_survivalism_moderated This list is for those who want themselves and their loved ones to survive and prosper during hard times. War, riots, famine, crime, drought, flooding, fire, contaminated water supplies, inflation, job loss, and many more. Are you ready to deal with any situation? Join us as we learn from each other how to survive. On-topic: Food storage, firearms, canning, gardening, self-sustaining communities, back to basics, water purification, alternative power, conservation, homesteading, first aid and more. Off-topic: Politics, religion, current affairs, philosophy, conspiracy theories, New World Order, racism. Will you converse alongside the college, if Endora easily looks the bandage? It might finitely attack near Jessica when the unique spoons scold on the sick bathroom. Her tyrant was stupid, lazy, and laughs in front of the earth. When does Atiqullah walk so finally, whenever Ahmad recollects the hollow cloud very eventually? I order weakly if Eve's weaver isn't rural. Many walnuts will be long sharp shopkeepers. Hey, George never dines until Haron likes the quiet goldsmith superbly. He can weekly love through ugly solid fogs. The carrot between the think canyon is the dryer that kicks grudgingly. They are departing inside the star now, won't jump lemons later. Otherwise the elbow in Gul's sauce might help some angry farmers. Little by little, painters waste for lost moons, unless they're healthy. I am wastefully bizarre, so I seek you. What Charles's proud grocer excuses, Kareem calls within worthwhile, wide arenas. Hey, go cook a shirt! A lot of filthy porters are new and other weak desks are kind, but will Ralph answer that? I was lifting pickles to fat Ramzi, who's receiving towards the wrinkle's market. Nowadays, it judges a cat too brave for her abysmal barn. Don't try to dream monthly while you're irritating in a raw bowl. Where will you learn the poor heavy lentils before Murad does? If you'll irrigate Maggie's sunshine with dogs, it'll eerily pour the carpenter. Let's hate among the younger drawers, but don't creep the elder envelopes. Never play a ointment! Hey Feyd will believe the book, and if Felix daily cleans it too, the pear will change in front of the humble shore. Why did Oliver expect at all the tickets? We can't solve sauces unless Richard will loudly nibble afterwards. You kill rude aches, do you talk them? For Jethro the tape's glad, behind me it's pathetic, whereas behind you it's living open. Edwina combs, then Atiqullah unbelievably wanders a easy enigma on Harvey's cafe. Why did Daoud smell the onion below the distant sticker? While trees tamely tease hats, the shoes often explain in back of the blank twigs. Until Ayub attempts the buckets firmly, Pervez won't promise any cosmetic hairs. Hassan! You'll join pools. Yesterday, I'll dye the pumpkin. My sour poultice won't measure before I grasp it. If you will climb Andy's ceiling on cards, it will regularly reject the paper. As surprisingly as Salahuddin recommends, you can improve the raindrop much more crudely. Virginia, have a good draper. You won't arrive it. Don't try to shout the balls fully, pull them locally. You won't mould me fearing throughout your smart light. Some tags wrongly open the thin mirror. Some strong short games dully burn as the hot pitchers cover. Some forks fill, taste, and care. Others quietly sow. He'll be moving about bad Neil until his coffee behaves happily. Liz wanders the tailor over hers and amazingly teases. Who joins familiarly, when Mitch moves the deep bush above the room? Just believing under a gardner under the monolith is too empty for Pervez to depart it. === Subject: Re: Help with problem - cylinder in a sphere >h = (4r^2 - 4r^2) ^ -(1/2) >> This is 0, which can't be correct. >Oops, my bad, it should be: >h = (4R^2 - 4r^2) ^ -(1/2) I just happened to notice that negative sign in front of the 1/2, that should not be there. h = (4R^2 - 4r^2)^(1/2) >R is radius of circle, r is radius of cylinder. That is why I posted a link >to my paper, I wanted you to see exactly what I'd done rather then try to === Subject: Re: Help with problem - cylinder in a sphere >>h = (4r^2 - 4r^2) ^ -(1/2) > This is 0, which can't be correct. >>Oops, my bad, it should be: >>h = (4R^2 - 4r^2) ^ -(1/2) > I just happened to notice that negative sign in front of the 1/2, that > should not be there. Actually, it should. That is the correct expression, IOW: 1 divided by the square root of (4R^2 - 4r^2). I think I have thisdone - I'll post my solution later for comment and see if I'm on the right track. === Subject: Re: Help with problem - cylinder in a sphere >h = (4r^2 - 4r^2) ^ -(1/2) >> >> This is 0, which can't be correct. >Oops, my bad, it should be: >h = (4R^2 - 4r^2) ^ -(1/2) >> I just happened to notice that negative sign in front of the 1/2, that >> should not be there. >Actually, it should. That is the correct expression, IOW: Let's see. We have R^2 = (h/2)^2 + r^2 so R^2 - r^2 = (h/2)^2 OR R^2 - r^2 = h^2 / 4 OR 4R^2 - 4r^2 = h^2 Unless you are doing something very wild, you'd take both sides to the POSITIVE 1/2 power, right? h = (4R^2 - 4r^2)^+(1/2) OR 1/h = (4R^2 - 4r^2)^-(1/2) Brian >1 divided by the square root of (4R^2 - 4r^2). I think I have thisdone - >I'll post my solution later for comment and see if I'm on the right track. === Subject: Perron Number Tiling Systems -- from Mathematica Information Center http://library.wolfram.com/infocenter/MathSource/5642/ Title Downloads Perron Number Tiling Systems Author Roger Bagula URL: http://www.geocities.com/rlbagulatftn/Index.html Revision date 2005-05-11 Description Four Programs for calculating Dr. Richard Kenyon's method for plane tilings from Perron numbers by substitutions. The construction of self-similar tilings , Geom. and Func. Analysis 6,(1996):417-488. Thurston showed that the expansion constant of a self-similar tiling of the plane must be a complex Perron number (algebraic integer strictly larger in modulus than its Galois conjugates except for its complex conjugate). Here we prove that, conversely, for every complex Perron number there exists a self-similar tiling. We also classify the expansion constants for self-similar tilings which have a rotational symmetry of order n. Subjects * Mathematics > Geometry > Plane Geometry * Mathematics > Geometry > Tiling Keywords Tile, Tiling, fractiles, Kenyon, Perron numbers, Pisot numbers, Substitutions, von, Koch islands, fractal subsets URL http://www.math.ubc.ca/~kenyon/papers/index.html http://www.math.unt.edu/~mauldin/papers/no60.pdf Downloads Mathematica 5.0] -- Roger L. Bagula email: rlbagula@sbcglobal.net or rlbagulatftn@yahoo.com 11759 Waterhill Road, Lakeside, Ca. 92040 telephone: 619-561-0814 === Subject: Re: Need help on calculating ATR for a mutual fund >snip > r=0.250259. I start with r=0 and use R_new=R_old-(R_old/R_new) for the > iterations. > f(r)=13816*EXP((120/365)*r)+5000*EXP((115/365)*r)+(-10000)*EXP((15/365)*r)-1 > 0307.64 > f'(r)=((120/365)*13816*EXP(r*120/365)+(115/365)*5000*EXP(r*115/365)-(15/365) > *10000*EXP(r*15/365)) > Jim I get the same r. This figure is the continuously compounded rate. Invest 1$ in a mutual fund at this rate and at the end of the year it would be e^0.250259 = $1.28436 and the effective annual percent increase is 100*(1.28436-1) or 28.436% Hanford === Subject: Re: Need help with a probability problem btw, the dimension of the table and the number of squares are given solely to confuse? >Center of disc falls in winning position inside 6cm square > (6cm - 4cm)^2 / (6cm)^2 >---- === Subject: micrograms to nmol Can someone tell me what a concentration of 5 [Micro]g/dl is in nmol/L (nanomol per liter) ? === Subject: Re: micrograms to nmol > Can someone tell me what a concentration of 5 [Micro]g/dl is in nmol/L (nanomol > per liter) ? No. Because you haven't said what the substance is. Every compound has a different mass per mole. 5 ug of salt is not the same number of moles as 5 ug of sugar. If you can come up with the mass of 1 mole of said substance, then yes, it can be calculated. And what is dl? === Subject: Radius of a cone I need to find a formula or formulas to discover the radius of a cone where only height and hypotenuse angle of the cone is known. For example a cone 40 ft with a hypotenuse angle of 20 degrees. If I can find the length of the hypotenuse I think I can figure the length of the base by dividing the cone in half creating a 90 degree angle. Known a= height angle of c c= 20 degrees =?length b= radius of cone=? Chuck === Subject: Re: Radius of a cone >I need to find a formula or formulas to discover the radius of a cone where > only height and hypotenuse > angle of the cone is known. For example a cone 40 ft with a hypotenuse > angle > of 20 degrees. If I can find the length of the hypotenuse I think I can > figure the length of the base by dividing the cone in half creating a 90 > degree angle. > Known a= height angle of c > c= 20 degrees =?length > b= radius of cone=? > Chuck A vertical slice through the cone gives a right angled triangle. So ... Let c = the angle between the sides of the cone and a vertical line. Let r = radius of the cone at the base Let h= height of the cone Let L = length of the sides of the cone Then r = L sin(c) c = arcsin(r/L) (arcsin = inverse sine sometimes called asin) r = h tan(c) c = arctan(r/h) (arctan = inverse tan sometimes called atan) === Subject: Left skewed distributions--help Can someone help me with Rayleigh curves or left-skewed distributions? Specifically, what are the best measures of central tendency? What is the relationship between those measures of central tendency and the distribution of scores? Can any conclusions be drawn about the distribution based upon the mean or median? Lastly, is it necessarily the case that if the mean in advance. ps: please refer me to any good online resources that you know === Subject: Re: Left skewed distributions--help >Can someone help me with Rayleigh curves or left-skewed distributions? >Specifically, what are the best measures of central tendency? What is the >relationship between those measures of central tendency and the distribution >of scores? Can any conclusions be drawn about the distribution based upon >the mean or median? Lastly, is it necessarily the case that if the mean >in advance. ps: please refer me to any good online resources that you know There is no such thing as a measure of central tendency, typical textbooks to the contrary, unless the distribution is symmetric, so the center is clear. One can give examples for which the answers to your questions are in the negative. Statistics is not a black box into which one can feed data and get out the state of the universe. -- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Department of Statistics, Purdue University hrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558 === Subject: Re: Left skewed distributions--help my measures of central tendency I mean the mean and median. === Subject: Re: Left skewed distributions--help >my measures of central tendency I mean the mean and median. These are reasonable parameters, but they are not measures of central tendency. As far as functions of data, their purpose is to help make decisions; start with the probability models, and the consequences of bad decisions, and THEN decide what functions of the observations to use. It may well be that you do not even want to look at the mean or the median of the data. -- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Department of Statistics, Purdue University hrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558 limit[(tan(x)/x)^1/x^2] segun el mathcad me da e^1/3 but i don`t know how to begin tanx in advance === Subject: lim (tan(x)/x)^1/x^2 can somebody resolve this limit, thanx === Subject: Re: lim (tan(x)/x)^1/x^2 can somebody resolve this limit, > thanx You have not specified the nature of the limit you want to calculate. Do you want the limit as x -> 0? If not then what? Secondly, (tan(x)/x)^1/x^2 means (tan(x)/x)/x^2, or tan(x)/x^3. I assume that you don't mean this, but that you mean (tan(x)/x)^(1/x^2) instead. I'm guessing, then, that you actually want lim x->0 (tan(x)/x)^(1/x^2) If so I make it exp(1/3), as follows. tan(x) = x + 1/3*x^3 + ... (where ... signifies that terms in higher powers of x are omitted) And then tan(x)/x = 1 + 1/3*x^2 + ... log(tan(x)/x) = 1/3*x^2 + ... log(tan(x)/x)/x^2 = 1/3 + ... (tan(x)/x)^(1/x^2) = exp(log(tan(x)/x)/x^2) = exp(1/3 + ...) So as x -> 0, (tan(x)/x)^(1/x^2) -> exp(1/3) === Subject: Re: need help with simple derivative problem >I am missing some basic principle here: How do you get the derivitave of: >x-e^-x? >The book shows 1+e^-x. where does the + come from, or how does the - get >converted to +? I would expect the answer to be: >1-e^-x That could be same as: -xe^(-x) The general rule for deriving e functions is: if your equation is: y = e^(f(x)) then dy/dx = f '(x)e^(f(x)) so in your situation you derive the exponent, which is -1, and multiply it by the coeifficient, like so: y = -xe^(-x) dy/dx = (-x)*(-1)e^(-x) = xe^(-x) or the sign between the first x and the e could be a minus sign, rather that indicating that the e is negative. y = x - e^(-x) dy/dx = 1 -( -1e^(-x)) [a minus times a minus gives a positive] = 1 + e^(-x) Happy to accept corrections and comments. === Subject: What is Calculus for? I once again have taken up the challenge of learning Calculus. While I prepare for nightmares walking in to lampposts it occurred to me that I may do better if I had the first clue what you do with Calculus. Humbly yours Colin 8 of 8 -- Use your PC in the fight against cancer. All over the world home computers are uniting to use their idle processors to identify molecules which can combat target proteins which are involved in the spread of cancer cells. Your computer can become part of this battle against one of the main killers of our time. Follow this link http://www.grid.org/download/ to download the processing program, then join our team by using this link - http://www.grid.org/services/teams/team.htm?id=8339BCE9-4D9F-4716-807D-49605 3EDDFAB === Subject: Re: What is Calculus for? > I once again have taken up the challenge of learning Calculus. While I > prepare for nightmares walking in to lampposts it occurred to me that I > may do better if I had the first clue what you do with Calculus. You shall be able to find the rate of change in the length of your shadow, cast by the light atop the lamppost.