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July 6th, 2017, 12:01 PM   #1
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I have few math questions ?

OK, I have three questions . . .
I was a computer science student, so I am a bit confused about some terms.

What is a variable x?

x is a quantity
x is binary
x is a point mass object
x is digital logic
x is electrons


The other is when you try to find the "pairs of factors" of a whole number. You can either find its composite factor or prime factors, right?

I hope that is what it is really called, "pairs of composite factors" and "pairs of prime factors"

Third one is when you try to solve a rational equation involving polynomials, you try to factor the polynomials in the numerator and the denominator, then find the LCM from the factors, right?

Can somebody give me an example of that?

Last edited by skipjack; July 6th, 2017 at 12:09 PM.
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July 6th, 2017, 12:25 PM   #2
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A variable is usually a letter representing a number (usually) called the value of the variable, where the value is not known or is not fixed.

If a whole number, such as 35, has a known factor, such as 5, dividing by that factor gives another factor (usually different from the known factor). In this example, the other factor is 7. If the known factor is 35, the other factor is 1, which is neither composite nor prime.

For examples of solving rational equations involving polynomials, do a web search for rational equations.
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July 6th, 2017, 12:25 PM   #3
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Can you solve

$$\frac{x^2-4x+4}{x^2+4x-12}\ge0$$

for $x$?
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July 6th, 2017, 01:12 PM   #4
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Quote:
Originally Posted by skipjack View Post
A variable is usually a letter representing a number (usually) called the value of the variable, where the value is not known or is not fixed.

If a whole number, such as 35, has a known factor, such as 5, dividing by that factor gives another factor (usually different from the known factor). In this example, the other factor is 7. If the known factor is 35, the other factor is 1, which is neither composite nor prime.

For examples of solving rational equations involving polynomials, do a web search for rational equations.
Thanks .

Quote:
Originally Posted by greg1313 View Post
Can you solve

$$\frac{x^2-4x+4}{x^2+4x-12}\ge0$$

for $x$?
Not sure how to do that , could you show me the steps ?




In the above two examples ,

I don't understand taking the LCM part properly ?
What are the steps involved to find LCM like that ?
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July 6th, 2017, 01:18 PM   #5
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Quote:
Originally Posted by awholenumber View Post
What is a variable x?

That is really a very philosophical question that's deeper than it seems. For example take a simple quadratic expression like $ax^2 + bx + c$. We are told that $a$, $b$, and $c$ are "constants" and $x$ is a "variable." What does that mean? They are all letters of the English alphabet that stand for numbers. But $a$, $b$, and $c$ stand for particular fixed numbers during the evaluation of the expression, while $x$ "ranges over" some domain like the real numbers.

And what can all that possibly mean? How can a man from Mars sort out the meaning? After all, $a$, $b$, and $c$ do in fact freely range over the real numbers. I think we need a philosopher to sort this out. I don't think this is as clear as we all think it is. Maybe it has something to do with free and bound variables but I'm not actually sure.

As an example, we might ask the question: If we equate the quadratic expression to $0$, what condition on $a$, $b$, and $c$ results in $x$ being a real number? The answer is that the discriminant $b^2 - 4ac \geq 0$. But in this question $a$, $b$, and $c$ are the "unknowns," they're the things we're trying to find out about.

The more I think about the question of what is a variable, the less I understand it.
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Last edited by Maschke; July 6th, 2017 at 01:24 PM.
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July 6th, 2017, 01:57 PM   #6
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Thanks ,
In computer science this is a variable



x is electrons
x is a quantity
x is binary
x is a point mass object
x is digital logic
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July 6th, 2017, 02:02 PM   #7
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Is LCD and LCM the same thing ?

One definition here says that ,

https://2012books.lardbucket.org/boo...and-equat.html

Quote:
It is not always the case that the LCM is the product of the given denominators. Typically, the denominators are not relatively prime; thus determining the LCM requires some thought. Begin by factoring all denominators.
The LCM is the product of all factors , with the highest power
Quote:
By factoring denominators to the form (x-a)(x-b)(x-c).
If both denominators contain (x-a), then the LCM
has (x-a) only once.








I still don't understand this completely

Last edited by awholenumber; July 6th, 2017 at 02:11 PM.
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July 6th, 2017, 02:35 PM   #8
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Steps to Find the LCM of Two or More Rational Expressions

1. Factor all denominators completely.
2. The LCM is the product of unique prime factors from the denominators,
where each factor is raised to the highest power to which it appears in
any denominator.



Can somebody show me the steps involved ?
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July 6th, 2017, 03:47 PM   #9
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Things are different in computer science and in mathematics.

In compsci you write the assignment statement, where x is being used as an indexing variable,

x = x+1

and this is quite allright because the equals sign means something different from the mathematics equality statement, where the equation would lead to difficulty.

More subtle in mathematics is the difference between an equality (equation) and an identity, both using the variable x.

The equality statement f(x) = 0 is true for some particular value or values of the variable x, whereas

The identity statement $\displaystyle f\left( x \right) \equiv 0$
is true for every value of x.

The old established and long held view about the quadratic expression
$\displaystyle a{x^2} + bx + c$

is that

a, b and c are 'That which is known' or the data

and x is 'That which is to be determined' or the unknown quantity

Interestingly, this originated in India and spread to Europe in the middle ages.

John Derbyshire's book 'Unknown Quantity' is a fascinating history of the development.

Last edited by studiot; July 6th, 2017 at 03:54 PM.
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July 6th, 2017, 04:09 PM   #10
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In computer things looks like these .





Thanks , i will try to get that book someday
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