mm-410 === Subject: (Please check my answer) please give a hint on this X Hello: thanks to your help in kick starting me, I'm slowly (but surely) getting the hang of this.. So I prooved that 1^3 + 2^3 + .. n^3 = (1 + 2 + .. n)^2 by the following: ((n(n + 1))/2)^2 and ended up with (n^4)/4 + (2n^3)/4 + (n^2)/4 and plugging in the values of n > 2 worked (thank you again)... For the (n + 1) case I ended up with ( ((n + 1)(n + 2))/2 )^2 in which I then let k = (n + 1) which allowed me to view it as: (k^4)/4 + (2k^3)/4 + (k^2)/4 to proove to myself that the equation still retains it's original form which it does. Going back and then rewritting, I get: ( ((n+1)^4)/4 + (2(n+1)^3)/4 + ((n+1)^2)/4 Then figuring out what the value 3 would get evaluated, I let n = 2 and plug it in which yielded 36 which ends up giving me the same answer if I let n = 3 and plug that into (n^4)/4 + (2n^3)/4 + (n^2)/4. I'm pretty sure this has prooved it. thanks again all for your help. This took me a better part of 3 hours just to figure this out with your help and browsing the internet sites for induction. I still plan ALOT of practice because I'm not quite yet comfortable with this yet. === Subject: Re: (Please check my answer) please give a hint on this > 1^3 + 2^3 + .. n^3 = (1 + 2 + .. n)^2 1^3 + 2^3 + .. n^3 = [n(n+1)/2]^2 n = 1 ok. n+1 step needs to show: 1^3 + 2^3 + .. n^3 + (n+1)^3 = [(n+1)(n+2)/2]^2 [n(n+1)/2]^2 + (n+1)^3 = [(n+1)(n+2))/2]^2 [n(n+1)/2]^2 + (n+1)^3 = [n(n+1)/2 + (n+1)]^2 (n+1)^3 = n(n+1)(n+1) + (n+1)^2 (n+1)^3 = n(n+1)^2 + (n+1)^2 so work it backwards, since no divisions by zero or square rooting, and fill in the gaps as I did no, no's, ie more than one step at a time. === Subject: Re: (Please check my answer) please give a hint on this Content-transfer-encoding: 8bit > X > Hello: > thanks to your help in kick starting me, I'm slowly (but surely) > getting the hang of this.. > So I prooved that > 1^3 + 2^3 + .. n^3 = (1 + 2 + .. n)^2 by the following: > ((n(n + 1))/2)^2 and ended up with > (n^4)/4 + (2n^3)/4 + (n^2)/4 Right ((n(n + 1))/2)^2 = (n^4)/4 + (2n^3)/4 + (n^2)/4. As a rule though, it is wiser to not multiply things out without a good reason. > and plugging in the values of n > 2 worked (thank you again)... I don't know what you meant by that. > For the (n + 1) case I ended up with > ( ((n + 1)(n + 2))/2 )^2 in which I then let k = (n + 1) which > allowed me to view it as: > (k^4)/4 + (2k^3)/4 + (k^2)/4 > to proove to myself that the equation still retains it's original form > which it does. Well yes but where does that get you? > Going back and then rewritting, I get: > ( ((n+1)^4)/4 + (2(n+1)^3)/4 + ((n+1)^2)/4 > Then figuring out what the value 3 would get evaluated, I let n = 2 > and plug it in which yielded 36 which ends up giving me the same > answer if I let n = 3 and plug that into (n^4)/4 + (2n^3)/4 + (n^2)/4. > I'm pretty sure this has prooved it. I don't think so. If I'm reading you correctly, you've just shown that the equation is correct for n = 3. You need to show it is correct for _any_ unknown n. > thanks again all for your help. This took me a better part of 3 hours > just to figure this out with your help and browsing the internet sites > for induction. I still plan ALOT of practice because I'm not quite yet > comfortable with this yet. Here is a big hint. ((n + 1)*(n + 2)/2)^2 = (n + 1)^2*(n + 2)^2/4 = (n + 1)^2*(n^2 + 4*n + 4)/4 = n^2*(n + 1)^2/4 + (n + 1)^2*(4*n + 4)/4 And here is a sample: Prove 1 + 2 +...+ n = n*(n + 1)/2 for all integer n > 0. Step 1. Let n = 1. 1 = 1*(1 + 1)/2 Step 2. Suppose we know 1 + 2 +... + n = n*(n + 1)/2. Can we show, without knowing n, that 1 + 2 + 3 +...+ n + (n + 1) = (n + 1)*(n + 2)/2? 1 + 2 + ... + n + (n + 1) = [1 + 2 + ... + n] + (n + 1) = [ Using our supposition] [n*(n + 1)/2] + (n + 1) = [Add 'em up] (n*(n + 1) + 2*(n + 1))/2 = [Factor n + 1 in the numerator] (n + 1)*(n + 2)/2 Paul Sperry Columbia, SC (USA) === Subject: Re: help solve this riddle please by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id i2H2kZW04823; >The beginning of every end. The end of every place. The beginning of >eternity. The end of time and space. please! help me solve this riddle >for my daughter for school thank you ANSWER: God === Subject: Re: help solve this riddle pleEase >The beginning of every end. The end of every place. The beginning of >eternity. The end of time and space. please! help me solve this > riddle >for my daughter for school thank you > ANSWER: God How about the letter e? As in End, placE, Eternity, timE, and spacE. === Subject: Re: AIR by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id i2H2kY204795; >This is an open chat room for Academy At Ivy Ridge students only. For >math questions only, not for chatting but for getting answeres. Okay lets see what is 2+2? === Subject: Re: AIR >This is an open chat room for Academy At Ivy Ridge students only. For >math questions only, not for chatting but for getting answeres. > Okay lets see what is 2+2? 5! Well, at least, for large enough values of 2... === Subject: Re: AIR >This is an open chat room for Academy At Ivy Ridge students only. For >>math questions only, not for chatting but for getting answeres. > Okay lets see what is 2+2? > 5! Well, at least, for large enough values of 2... If you want to use 5 to denote the successor of the successor of 2 then fair enough. Just don't come running to us when your tax return gets audited. P.A.C. Smith The vast majority of Iraqis want to live in a peaceful, free world. And we will find these people and we will bring them to justice. === Subject: Re: AIR >>This is an open chat room for Academy At Ivy Ridge students only. For >>math questions only, not for chatting but for getting answeres. >Okay lets see what is 2+2? >5! Well, at least, for large enough values of 2... > If you want to use 5 to denote the successor of the successor of 2 then > fair enough. Just don't come running to us when your tax return gets > audited. Hey, I don't work about it. I use the same large value for 2 in my social security number, phone number and mailing address. And, my bank account number which would explain why I haven't gotten a tax return in...uh...2 years... === Subject: Re: Please help thx:) > Hi guys! I need help for a final in my math92 course tomorrow and I am > stuck on one study prob in particular, so if someone could give me the > answer and maybe show me how they got that would be awesome. > Problem: A police department knows that city growth and the number of > burglaries are related by a linear equation. City records show 585 > burglaries were reported in a year when the local pop. was 67500, and > 685 were reported when the pop. was 77500. How many burglaries can be > expected when the pop. reaches 100,000? A linear equation for y in terms of x must be expressible in the form y = a*x + b, where x represents the population in a given year and y represents the number of robberies in that same year, and a and b are numbers to be determined to fit the data given. According to your data, you must have (1) 585 = a*67500 + b, and (2) 685 = a*77500 + b. Then subtracting the first equation from the second gives (3) (685 - 585) = a*(77500-67500) + (b - b), and (4) 100 = a*10000 + 0, so (5) a = 1/100 Substituting a = 1/100 into equations (1) and (2) gives (6) 585 = (1/100)*67500 + b and (7) 685 = (1/100)*77500 + b both of which reduce to (8) b = -90 Now substituting a = 1/100 and b = -90 gives (9) y = (1/100)*x + (-90) For the last step, substitute 100,000 in place of x and work out what y should be. === Subject: Re: Please help thx:) > Problem: A police department knows that city growth and the number of > burglaries are related by a linear equation. City records show 585 > burglaries were reported in a year when the local pop. was 67500, and > 685 were reported when the pop. was 77500. How many burglaries can be > expected when the pop. reaches 100,000? When the population went up by 10,000, burglaries went up by 100. This means you get 100/10,000 = .01 new burglaries for each new person. So in going from 77,500 to 100,000, there are .01*22,500 = 225 new burglaries. Add that to 685 and you have your total. === Subject: Re: Please help thx:) alt.math.undergrad: >Hi guys! I need help for a final in my math92 course tomorrow and I am >stuck on one study prob in particular, so if someone could give me the >answer and maybe show me how they got that would be awesome. >Problem: A police department knows that city growth and the number of >burglaries are related by a linear equation. City records show 585 >burglaries were reported in a year when the local pop. was 67500, and >685 were reported when the pop. was 77500. How many burglaries can be >expected when the pop. reaches 100,000? You have two x-y pairs, where x is population and y is number of burglaries. Plot those points on a grid of suitable scale. Draw a line through them and extending to the right. Since you have two points, you can find the equation of that line. Do so. Plug x=100000 into your equation and find y. Stan Brown, Oak Road Systems, Cortland County, New York, USA http://OakRoadSystems.com An expense does not have to be required to be considered necessary. -- IRS Form 1040 line 23 instructions === Subject: Re: Can anyone slove this? by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id i2HDlWd05761; >I have an equation for Vout given AH (absolute humidity in g/m3) and T >(temperature in Deg. C.) as follows >Vout = (a * AH * AH + b * AH) * (c * T * T + d * T + e) * f >Constants: a = -0.00067742 b = 0.17704445 c = -0.000017156 d = -0.00088115 e >= 1.11463 f = 1.062806 >I need it worked to give an equation for AH given Vout and T. >Ed Donovan Hi Ed, if you write the equation as a*(AH)^2 + b*(AH) - Vout/(f*(c*T^2+d*T+e)) = 0, you see that it is a quadratic equation in AH. The solution is given by AH = -b/(2*a) +/- sqrt( b^2/(4*a^2) + Vout/(a*f*(c*T^2+d*T+e)) ) (Look which of the two solutions makes sense) Best wishes Torsten.. === Subject: advanced calculus by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id i2HGviA32114; I am really in need of help, I have to present this math problem in class, and I have no idea how to present it. Consider the set {x + 1/x: x is an element of the reals and x>0} the infimum of this set is a. 0, b. 1, c. 2, d. Squareroot of 3, e. e. I know the correct answer is c. 2, but I just don't know how to present it to the class, if anyone could help I would appriciate it! :) Lisa === Subject: Re: advanced calculus > Consider the set {x + 1/x: x is an element of the reals and x>0} the > infimum of this set is > a. 0, b. 1, c. 2, d. Squareroot of 3, e. e. > I know the correct answer is c. 2, but I just don't know how to > present it to the class, if anyone could help I would appriciate it! > :) > Lisa To prove that m is the infimum of set S, you need to prove two things: 1. m <= x for all x in S (i.e. m is a lower bound) 2. for all positive epsilon, there is an x in S such that x < m + epsilon (i.e., no number greater than m is a lower bound) For the first part you need to prove that x + 1/x >= 2 for all positive real x (1 - x)^2 >= 0 1 + x^2 >= 2x 1/x + x >= 2 For the second part you need to prove that for any 2 + epsilon there is an x such that x + 1/x < 2 + epsilon. This is true because 1 + 1/1 = 2 < 2 + epsilon hth meeroh If this message helped you, consider buying an item from my wish list: I am really in need of help, I have to present this math problem in > class, and I have no idea how to present it. > Consider the set {x + 1/x: x is an element of the reals and x>0} the > infimum of this set is > a. 0, b. 1, c. 2, d. Squareroot of 3, e. e. > I know the correct answer is c. 2, but I just don't know how to > present it to the class, if anyone could help I would appriciate it! > :) You can minimize f by setting f' = 0, is that what they had in mind? === Subject: Re: advanced calculus by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id i2HJGTI16875; >I am really in need of help, I have to present this math problem in >class, and I have no idea how to present it. >Consider the set {x + 1/x: x is an element of the reals and x>0} the >infimum of this set is >a. 0, b. 1, c. 2, d. Squareroot of 3, e. e. >I know the correct answer is c. 2, but I just don't know how to >present it to the class, if anyone could help I would appriciate it! >:) >Lisa ============================================== Just look at the differeence: x+(1/x)-2 = [(x-1)^2]/x and this is always nonnegative. Done. === Subject: Magic Square 3x3 by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id i2HIZdn12012; I would be very very gratful if anyone could help thank you: Questions: Make a 3 by 3 grid int hem are to be Whole numbers that along the lines must add up to 55, the same down the colums and on the diagonal, so the magic square must equal 55 in all lines using ONLY WHOLE numbers. tytyty Paul === Subject: Re: Magic Square 3x3 by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id i2HKiel27530; >I would be very very gratful if anyone could help thank you: >Questions: >Make a 3 by 3 grid int hem are to be Whole numbers that along the >lines must add up to 55, the same down the colums and on the diagonal, >so the magic square must equal 55 in all lines using ONLY WHOLE >numbers. >tytyty >Paul a b c d e f g h i a+e+i = 55 b+e+h = 55 c+e+g = 55 3e+ ( a+b+c )+( g+h+i ) = 3*55 3e+ ( 2*55 ) = 3*55 3e = 55 no solution === Subject: Re: MU System by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id i2HJ40V15609; I got an answer too. And I think your reasoning is correct... I was actually online looking to see if there was any info, or if anyone else got an answer. >Did anyone read Godel, Escher, Bach? >I thought I found an answer to the MU formal system, but there isn't >supposed to be any. >Rules: >1. If xI is a theorem, so is xIU. >2. If Mx is a theorem so is Mxx. >3. Ifn any theorem III can be replaced by U. >4. UU can be dropped from any theorem. >Axiom: MI >Goal: To get MIU >What I did: >Use Rule 2 to double I 32 times to get M followed by 42957296 (or >8589934592, etc). 2 raised 32 is a multiple of 3. >Use Rule 3 to rplace the Is with 1431655765 Us. >Use Rule 4 to drop all Us but one, leaving MU. >Do you see any errors? >Is this in the right section? === Subject: Re: MU System alt.math.undergrad: > I got an answer too. And I think your reasoning is correct... I was > actually online looking to see if there was any info, or if anyone > else got an answer. >Did anyone read Godel, Escher, Bach? >I thought I found an answer to the MU formal system, but there isn't >supposed to be any. >Rules: >1. If xI is a theorem, so is xIU. >2. If Mx is a theorem so is Mxx. >3. Ifn any theorem III can be replaced by U. >4. UU can be dropped from any theorem. >Axiom: MI >Goal: To get MIU >What I did: >Use Rule 2 to double I 32 times to get M followed by 42957296 (or >8589934592, etc). 2 raised 32 is a multiple of 3. No power of 2 is a multiple of 3, so the derivation fails right here. However, there is a trivial derivation by applying Rule (2) twice, followed by Rule (3). MI > MII > MIIII > MIU. However, you have misstated the goal: the real goal is to derive MU. This is impossible, by the following simple argument. Rules (1) and (4) do not change the number of I's in the string, Rule (2) doubles the number of I's, and Rule (3) decreases the number of I's by 3. Suppose that at some point in your derivation you have a word with n I's in it, and suppose further that n is not a multiple of 3. Applying Rule (1) or Rule (4) leaves the number of I's unchanged, so it is still not a multiple of 3. Applying Rule (2) changes the number of I's to 2n, but if n is not a multiple of 3, neither is 2n. Finally, applying Rule (3) changes the number of I's to n - 3, but again, if n is not a multiple of 3, neither is n - 3. (In fact they have the same remainder, 1 or 2, when divided by 3.) Thus, none of the rules can create a string with a multiple of 3 I's from one that did not already have a multiple of 3 I's. The starting string, MI, does not have a multiple of 3 I's, so no string derivable from it by Rules (1) - (4) can have a multiple of 3 I's. In particular, since 0 is a multiple of 3, MU cannot be derived from MI. [...] Brian === Subject: Poisson's Equation Here is the problem I am working on. http://server6.uploadit.org/files/aka002-untitled.JPG I have don't the first bit, but I can't do the second bit. Any help === Subject: Re: Indian maths methods?? by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id i2HMNKt06857; >Couple of years ago I was introduced to ancient Indian techniques in >the field of maths, which unfortunatly can't remember the name of. >As far as I can remember it was focused around approaching formulas >and equations in an, for the Western world, unconventional way. And >had got some recognition in the West for being method of teaching >fundamental maths. >Can anybody help me out with the name of these techniques and maybe >even point me to some web resources on the matter? >Fredrik I think they are called vedic mathematics... mostly on the quick methods of calculating value of expressions like finding the square root, cube root... I think the books are available in many bookstores === Subject: Re: Recursive Help.. by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id i2HMNKM06853; >How do I define recursively the set of bit strings that have more >zeros than ones. using the standard Backus-Naur Form, <1>|<1><0>|<1><1>|<0><0>|<00>|<0 = <0><1>|<1><0>|<0><0 = <0><1>|<1><0>|<1><1 Hopefully this helps... === Subject: Random Variable Questions by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id i2I0Etf19330; a) A total of 4 buses carrying 148 students from the same school arrives at a football stadium. The buses carry, respectively, 40, 33, 25, and 50 students. One of the students is randomly selected. Let X denote the number of students that were on the bus carrying this randomly selected student. One of the 4 bus drivers is also randomly selected. Let Y denote the number of students on her bus. -which of the E[X] or E[Y] do you think is larger? why? -compute E[X] and E[Y] -find Var(X) and Var (Y) for X and Y. b) On a multiple-choice exam with 3 possible answers for each of the 5 questions, what is the probability that a student would get 4 or more correct answers just by guessing? c) A man claims to have extrasensory perception. As a test, a fair coin is flipped 10 times, and the man is asked to predict the outcome in advance. He gets 7 out of 10 correct. What is the probability that he would have done at least this well if he had no ESP? d) A communications channel transmits the digits 0 and 1. However, due to static, the digit transmitted is incorrectly received with probability .2. Suppose that we want to transmit an important message consisting of one binary digit. To reduce the chance of error, we transmit 00000 instead of 0 and 11111 instead of 1. If the receiver of the message uses majority deciding, what is the probability that the message will be wrong when decoded? What independence assumptions are you making? e) A satellite system consists of n components and functions on any given day if at least k of the n components function on that day. On a rainy day each of the components independently functions with probability p1, whereas on a dry day they each independently function with probability p2. If the probability of rain tomorrow is w, what is the probability that the satellite system will function? f) A student is getting ready to take an important oral examination and is concerned about the possibility of having and on day or and off day. He figures that if he has an on day, then each of his examiners will pass him independently of each other with probability .8, whereas if he has on off day this probability will be reduced to .4. Suppose that the student will pass the examination if a majority of the examiners pass him. If the student feels that he is twice as likely to have an off day as his is to have an on day, should he request an examination with 3 examiners or 5 examiners? g) Suppose that it takes at least 9 votes from a 12-member jury to convict a defent. Suppose that the probability that a juror votes a guilty person innocent is .2, whereas the probability that the juror votes an innocent person guilty is .1. If each juror acts independently and if 65 percent of the defents are guilty, find the probability that the jury renders a correct decision. What percentage of defents is convicted? h) Suppose that a biased coin that lands on heads with probability p is flipped 10 times. Given that a total of 6 heads result, find the conditional probability that the first 3 outcomes are: -H,T,T (meaning that the first flip is heads, the second is tails and the third is tails) -T,H,T i) A box contains 5 red and 5 blue marbles. Two marbles are withdrawn randomly. If they are the same color, then you win $1.10; if they are different colors, the you win -$1.00 (that is, you lose $1.00). Calculate - the expected value of the amount you win - the variance of the amount you win j) A newsboy purchases papers at 10 cents and sells them at 15 cents. However, he is not allowed to return unsold papers. If his daily demand is a binomial random variable with n=10, p=1/3, approximately how many papers should he purchase so as to maximize his expected profit? k) To determine whether or not they have a certain disease, 100 people are to have their blood tested. However, rather than testing each individual separately, is has been decided first to group the people in groups of 10. The blood samples of the 10 people in each group will be pooled and analyzed together. If the test is negative, on test will suffice for the 10 people; whereas, if the test is positive each of the 10 people will also be individually tested and, in all, 11 tests will be made on this group. Assume the probability that a person has the disease is .1 for all people, independently of each other, and compute the expected number of tests necessary for each group. (Note that we are assuming that the pooled test will be positive if at least one person in the pool has the disease). === Subject: Re: Random Variable Questions Let's see, (a) through (k). Evidently you have eleven homework problems today. Why don't you post what you've done to try to solve them? Stan Brown, Oak Road Systems, Cortland County, New York, USA http://OakRoadSystems.com An expense does not have to be required to be considered necessary. -- IRS Form 1040 line 23 instructions === Subject: Re: please give a hint on this by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id i2I0Ete19334; (Recognize the left side as 1 + 2 + 3 + ... + n = n(n+1)/2) The base case is fine, assume kth step holds. Square both sides of the equation, with the hint above, and substitute k+1. (Maybe this will help (?)). Good luck, Hello: >I'm completely stumped and thought I had this figured out but realized I >did not. >Problem is >Show by induction that: >1 + 2 + 3 + 4 + .. n = (1^3 + 2^3 + 3^3 + 4^3 + .. n^3)^1/2 >I tried to show for (n + 1) and >ended up with a formula (had to square both sides) which worked for n=0, >n=1, and n=2. However, it fails once n > 2 >My formula after a bunch of algebra including squaring both sides >(although this is wrong): >4n^2 + 4n + 1 = n^3 + 3n^2 + 2n + 1 >I've spent over 2 hours stewing on this and am having a mental block on >how next to proceed. If anyone can lend a hint on what step(s) I >should take, I'd much appreciate it. I'm missing the boat somewhere on >this. >thanks! === Subject: Re: please give a hint on this X thank you for your replies. It's given me a base point from where to start. I was totally stumped on this one and you guys gave me a kick start so now I can try this problem over again. I originally got the step of squaring both sides in order to get rid of the radical. I made the mistake of trying to square n + (n+1) and make it = to 1^3 + .. (n+1)^3. I came up with an equation that did not satisfy n > 2. Hopefully I will now with the hints/help you gave me. thanks again