# rational

1. ### Sum of rational cubes: I would like to know if this formula was already discovered (some book, references ..please...)

Hello People The problem finding sum of two rational cubes to give an integer is not an easy one: it has the general form a^3 + b^3 = n . c^3 example find (a/c)^3 + (b/c)^3 = 7 (or a^3 + b^3 = 7 . c^3 ) The are infinite solutions for this one, the first being (5/3)^3 + (4/3)^3 = 7 , (...
2. ### Irrational -> Rational Number

Hey, I was using guess and check to find a value, and it ended up being close to 15.83007499. I am certain it could be represented by an equation, but I can't find out what that would be. There is a good chance it would be a log natural. If you do find out what it is, I'd love to know. Thanks!!
3. ### How to prove that a rational algebraic expression is capable of all values?

Well, I want to express myself using an example from Higher Algebra by Hall and Knight . Find the limits between which a must lie in order that \frac{ax^2 - 7x +5} {5x^2-7x+a} may be capable of all values, x being any real quantity. Solution:- Put \frac{ax^2-7x+5} {5x^2-7x+a} = y...
4. ### why do we represent rational number by p/q?

why do we represent rational number by p/q, why can't you not use m/n, x/y, c/y, a/c, etc. is there any meaning by (p/q)?
5. ### Why is the set of rational numbers dense, and set of integers numbers not?

If we have two sets: Set one is the set of rational numbers with the usual less-than ordering Set two is the set of integers numbers with the usual less-than ordering Why is the set of rational numbers dense, and set of integers numbers not? Density is that for all choices of x and y with...
6. ### Rational Solutions of the tan function in the context of a video game

First of all, I'd like to note that I believe I've already solved the problem I'm about to pose (it just comes down to there being just two rational solutions to the tan function) and as such, am not really in need of help with it. I'm only posting this as a log of a "real-world" application to...
7. ### removable discontinuities in rational functions

So I was taught that $f(x) = \dfrac{(x+1)(x-2)}{x+1} = x-2$ is continuous. I'm reading online now that $x=-1$ is considered a removable discontinuity, i.e. a "hole" If this is the case what stops us from creating infinite holes in any continuous function by multiplying by 1 in the...
8. ### Number of rational points

The number of rational points on the circle with center $(\sqrt{2},-\sqrt{2})$ and which passes through $(1,-1)$ is
9. ### The rational number between rationals

How I can prove that between every two real number there is real number?
10. ### What is a Rational prime?

Hello When we say let $p$ be rational prime, automatically that does mean that p>0?? thanks
11. ### rational expression simplification

Hi everyone, I couldn't do this: (x^2-y^2-4y-4) / (x^2-y^2-4y+4) any idea?
12. ### Calculating The Nth Rational Number

Hallo If we specify a particular method for mapping the natural numbers to the rationals, could we also specify a "distance" between two consecutive terms in some general way? Also, are we able to calculate the nth term in such a progression, perhaps incorporating this distance function somehow...
13. ### Rational equation definition

Hi everyone, Stuck with this definition question. What is the meaning of a rational equation A) Two rational expressions having equal domains. B) The set of X values which satisfy two rational expressions. C) Two rational expressions which are equal to each other. D) Any equation having...
14. ### Help Proving Whether a Certain Rational Exists - Tried and I'm Stumped

Trying to solve this: Let $r \in \, (0,1\, )$ and $r \notin \mathbb{Q}$. Let $râ€™ \in \, (0,1\, )$, $râ€™>r$, $râ€™ \notin \mathbb{Q}$, and $râ€™-r \notin \mathbb{Q}$. Let $q \in A = \{ râ€™-r+p : p \in \, (r,r+1\, ) \cap \mathbb{Q} \}$ Finally, one of the following statements must be true...
15. ### A Rational Game

This post is to set forth a little game that attempts to demonstrate something that I find to be intriguing about the real numbers. The game is one that takes place in a theoretical sense only. It starts by assuming we have two pieces of paper. On each is a line segment of length two: [0,2]...
16. ### Natural, Rational, and Real, Numbers

Natural, Rational, and Real, Numbers m/n stands for mth of n, not division. Natural Numbers: 1,2,3,4,.........,n Rational Numbers: 1/n, 2/n, 3/n,.....n/n Real Numbers: n â†’ âˆž, (0,1] Or, you could start the natural numbers with zero: Natural Numbers: 0,1,2,3,.........,n-1 Rational...
17. ### How solve system 10 rational equations?

Equations are like\frac{a \cdot x_i+b\cdot y_1 + c}{1+d \cdot x_i + e \cdot y_i}. I tried it with multidimensional Newton-Raphson method but is unconvergent if I don't know rough solution. It need subdivision algorithm?
18. ### Need help with simplifying rational exponent

I have struggled for hours tonight attempting to eliminate a fractional exponent in the denominator. For instance, one problem has y^5/3 in the denominator. I have the correct answer so I know I am doing it incorrectly (since I am obviously getting the wrong answer). I thought I could simply...
19. ### Straight line that doesn't touch any rational

Does exist a straight line (in $\mathbb{R}^2$) that touches only irrational numbers?
20. ### Application for rational function

Please answer the following question. Consider the following context Jamal owns a painting company that includes two painters Bob and Anna. Jamal has modeled how long it takes each of them to paint a room where x = the number of square meters of the room. Bob takes ax-b minutes and Anna...