Rational Definition and 616 Threads

1. Let a and b be rational numbers. Prove or provide counterexample that A) a+b is a rational number. B) Is ab necessarily a rational number? 2. How can you prove that the sume of two rational number is rational? Well I am not really good at math 3. This is what I've tryed to...

please... i need a help in integrating the partial fractions i can't proceed to the integration part if i don't understand the patter in finding the constant... that is... if the given is: ʃ ( (x^5+1) / ((x^3)(x+1)) )dx then; ʃ ( x-2 + ( 4x^3+1 ) / ( x^4 + 2x^3) ) ʃ ( x-2 + (...

In my calc class we are reviewing rational and polynomial functions before we start with the actual calculus part of the course. In my book we had 3 problems that we had to do for homework and none of my classmates could understand why the book answered them a certain way. Question: State...

I've programmed an algorithm to numerically compute the logarithm of numbers in phinary base easily. I could avoid float multiplications if I can find a pair of rational numbers x and y such that x^{\sqrt{5}}=y Is it possible? Probably not, but I cannot prove it :(

Homework Statement ∫1/ x^3-1 dx, ok how would i do this Homework Equations ∫dx/ x^2+a^2= 1/a tan^-1 (x/a) +c i tried to simplify x^3-1 = (x+1)(x-1)(x+1)

Homework Statement ∫ 10/(x-1)(x^2+9) would i change this into 10/ (x-1) (x+3) (x+3) then= A/ x-1 + B/ X+3 + C/ x+3

It can easily be shown that the recurring decimal x = 1.123123... is rational, as follows: 10^{3}x-x = 1123.123...-1.123123...=1122 => x = \frac{1122}{999} \in Q Show that the recurring decimals 0.3712437127... and 0.9999999...are rational numbers. 3. The Attempt at a Solution...

Evaluate the Integral: \int \frac {2x+1}{(x^{2}+9)^{2}} My attempt: \frac {2x+1}{(x^{2}+9)^{2}} = \frac {Ax+B}{x^{2}+9} + \frac {Cx+D}{(x^{2} + 9)^{2}} = (Ax+B)(x^{2} + 9)^{2} + (Cx+D)(x^{2} + 9) = Ax^{5} + Bx^{4} Dx^{3} + (18A + E)x^{2} + (81A+9D+18B)x + 9E + 81B I'm not sure what...

1. x/20 = (3/8)-(4/5) 2. solve 3. My attempt as far as I can tell there is no LCM so 3/8 becomes 15/40 4/5 becomes 32/40 (15/40)-(32/40)= 17/40 which equals 8.5/20 which means x=8.5 For some reason I don't think I got the right answer?

I've been working through "A Course of Pure Mathematics" and there is one problem I'm really stuck on. I'm wondering if anyone could help me out. To avoid typing it all out, I here's a link...

Hi, this is a question to the members with some knowledge in algebraic geometry: 1. what are rational curves with self-intersection -2? How do they look like? 2. do you know why these correspond to the vertices of some of the Dynkin diagrams? 3. just something that's bothering me...

I've been thinkng about this one for a while. Is i rational or irrational. i is an imaginary number, so logically, it would be irrational. But \frac{-1}{i} = i so it has a fractional equivilant. But then, it doesn't have a real number decimal equivilant... So, what is it? Is i rational or...

and, consequently, infinitely many. I am new to proofs so could you please check if this proof is correct? Let x be an irrational number in the interval I[SIZE="1"]n = [a[SIZE="1"]n, b[SIZE="1"]n], where a[SIZE="1"]n and b[SIZE="1"]n are both rational numbers, in the form p/q. Let z be...

Please tell me one of the bases for the infinite dimenional vector space - R (the set of all real numbers) over Q (the set of all rational numbers). The vector addition, field addition and multiplication carry the usual meaning.

Homework Statement I have volunteered to help a friend's son with his Algebra 2 (thinking - no problem, I've had Calc 1-3, differential equation, complex variables, probability / stats and so on. So I start to help and the first questions: Why aren't these rational expressions...

Homework Statement Suppose there are two polynomials over a field, f and g, and that gcd(f,g)=1. Consider the rational functions a(x)/f(x) and b(x)/g(x), where deg(a)<deg(f) and deg(b)<deg(g). Show that if a(x)/f(x)=b(x)/g(x) is only true if a(x)=b(x)=0. Homework Equations None The Attempt at...

I want to integrate: 1/[(x + 1)*(x^2 + x +1)] dx Now the quadratic has complex routes, and we have not done any integration with that yet, so I broke it up into its partial fractions. A/(x +1) + (Bx + C)/(x^2 + x +1) But I cannot seem to find the numbers A B C. mamybe I am just...

Can someone pls help me on "rational and Irrational numbers". Esp. on Decimals. I can't classify if it is rational or irrational.

Homework Statement Find asymptotes for f(x) = (x^2 -1) / (x - 1). (if exist) Homework Equations g(x) is a (horizontal or oblique) asymptote if lim |f(x) - g(x)| = 0 (here, lim is to be limit as x goes to infinity. don't know how to type it) or if q(x)/p(x) = g(x) + r(x)/p(x)...

\frac{5x-5y-bx+by}{5x-5y+bx-by} i can't cancel anything i can't factor anything please help

1) Prove that the acute angle whose cosine is 1/10 cannot be trisected with straightedge and compass. ... I worked it out and at the end found out that , if I can prove that the cubic polynomial 40x3 - 30x -1 has no rational roots, then I am done. Now, is there any way to prove (e.g...

Homework Statement Is there a non-empty perfect set that contains no rational number? Homework Equations None The Attempt at a Solution I thought the answer was no, but my professor said that there is. My reasoning is as follows (please let me know if I'm wrong here): If p is an...

Homework Statement Show that the square root of 3 is not rational Homework Equations The Attempt at a Solution A number is irrational if χ is not ε. Q=p/q: p, q ε z and q is not=0, z=integers If p/q: p, q is not ε or q=0, then square 3 is rational. If p=square root of 3 and q...

I'm a new comer, even in Math. I need hands for this (simple, may be for most people) question: Can a subset of Rational Number Set be open (and closed)? If does, how can it be? If not,why? thks! Ka Yan:smile:

Homework Statement \frac{5(y-2)}{y+1} x \frac{y+1}{10} Homework Equations The Attempt at a Solution Does this equal 5(y-2)(y+1)/10(y+1) ? Or are there no brackets on that first y+1 ?

First Question If: f(x) = (x^2+1)/x Then: f(x) = x + (1/x) From my understanding, x would be the oblique/slant asymptote. Why is that? Second Question Why and how can horizontal asymptotes be crossed?

Homework Statement Factor the following over the set of rational numbers. Simplify if possible. cos³ x-1 I do not know how to deal with the cubic cosine. Help is greatly appreciated.

Homework Statement Determine all positive rational solutions of x^y=y^x.Homework Equations The Attempt at a Solution Obviously, x=y will always work. I think that is the only solution. If I can show that x^y must be rational, I think it will be easy because then both x and y must have the same...

i'm trapped with a problem: \int\frac{dx}{x\sqrt{2-x-x^2}}. i think this problem could be solved by subtitutions: \ x+\frac{1}{2}=\frac{3}{2}sint and \ u=tan\frac{t}{2}. and finally we would get an expression in \ u: \frac{\sqrt{2}}{4} log\left|\frac{2\sqrt{2}+u-3}{2\sqrt{2}-u+3}\right| (am...

[SOLVED] functions on rational numbers Homework Statement Find all functions from Q to Q which satisfy the following two conditions: i)f(1)=2 ii)f(xy)=f(x)f(y)-f(x+y)+1 for all x,y in Q Homework Equations The Attempt at a Solution I can show by integers that if x is an...

Homework Statement Queuing Theory (study of lines for stores) says that for a drive through window at a Macdonalds, the function f(x)= 9/(x(x-9)) represents the average time in hours a customer will wait in line. X=average number of people an hour. How long will a customer have to...

Hello, this question is for anyone who is kind enough to shed some light. I am not actually taking a physics class currently, but a philosophy of science course. One of the guest lecturers we've had this semester spoke on QM; EPR and Bells. My question is basically this, I am not doubting...

Homework Statement Find two constants for 'a' and 'b' such that the verticle asymptote will be \pm \frac{3}{5} y=\frac{ax^2+7}{9-bx^2} I rearranged so that it becomes -bx^2+8 in the denominator since i know that there are two roots that are \pm it must be a square and since 3 is the...

How do you find the point where the graph crosses the oblique asymptote?

I have trouble with Graphing rational functions, please help me,test is tomorrow I do not know how to use horizontal , vertical , oblique asymptotes to graph a rathional functions. like y=2x+3+3/x+1; y=x^2-4/x-4 thank you very much

How do I find the sup of rationals (p/q, where q is even) that is less than sqrt(10)? gcd(p,q)=1

if two rational numbers added together is still rational then wouldn't an infinite sume of rational numbers that converge also be rational and if that is the case then an irrational number is therefore rational which makes no sense though. i don't see where the flaw in this lies because it is...

This isn't really a question about homework specifically, it's more just that I don't understand part of my chapter...I am just starting Principles of Mathematical Analysis by Ruben... Here is what I don't understand: It is proving that p^2 = 2 is not satisfied by any rational p. And it...

Homework Statement Proved that the set of all rational numbers of the form 3^m *6^n are integers , is a group under multiplicationHomework Equations No equations for this particular proof The Attempt at a Solution Assume that all rational numbers are in the form 3^m *6^n . Therefor 3^m*6^n =...

Hi, here is the question, if A is a closed set that contains every rational number r: [0,1], show that [0,1] is a subset of A. But, how could A be closed? If A is closed, R^n-A is open, so any point in R^n-A would have a open sphere around it and this open sphere wouldn't intersect A...

http://planetmath.org/encyclopedia/CPlace.html, how do I rewrite (2) to get the third equation R(z)=... ? thank you

can anyone show me step by step of how to evaluate the integral of [x^m/(x^n+a^n)^p](dx) from negative infinity to positive infinity. all i know is that contour integration is required to solve this problem.

Homework Statement Integrate (dx)/(-4 + x^2) Homework Equations Trig substitution? The Attempt at a Solution How would you integrate something like this? I don't need answers, I just need some guidelines to start off.

Hello, here is my problem: how can i prove that if a\in\mathbf{Q} and t\in\mathbf{I}, then a+t\in\mathbf{I} and at\in\mathbf{I}? My original thought was to show that neither a+t or at can be belong to N, Z, or Q, thus they must belong to I. However I'm not certain if that train of thought...

Homework Statement How are you able to determine if a solution is rational or irrational Homework Equations - The Attempt at a Solution - :confused: I'm pretty sure it will be something basic I'm forgetting, thanks for any help.

Homework Statement the indefinite integral of x/(x^4+x^2+1) Homework Equations n/a The Attempt at a Solution I didn't see an obvious u-substitution and it didn't look like a partial fractions candidate to me since the bottom is not easily factored. It doesn't look like any of the...

Excuse my typography - I'm new here... a, b, and c are rational numbers. I want to prove that * IF S = root(a) + root(b) + root(c) is rational THEN root(a), root(b) and root(c) are rational in themselves. Now I have done as follows: I reverse the problem and try to show that: * IF...

Homework Statement (n + 1) / (3n - 1) Homework Equations A_n = L The Attempt at a Solution lim n-> infinity (n/n + 1/n) / (3/n - 1/n) = (1 + 0) / (3 - 0) = 1/3 Thats the solution, however i have questions.. 1.) If a series is in rational form like this, is it...

Does anyone have an idea how to prove the following (or prove that it is not true): For any positive integer k, you can find k points on a circle such that each point is a rational distance from every other point.

Given 2 points on a plane, if you arbitrarily place a third, is there any way to determine the closest approximation to this triangle where all sides of the approximation are rationally related? The only thing I can think of would be to draw a small circle around the third point that...