Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 81,706

Yes, there are a lot of ways to come at this problem analytically but that will not always be the case. That is when we separate the heavyweights from the lightweights, when geogebra will shine.

**In mathematics, you don't understand things. You just get used to them.I have the result, but I do not yet know how to get it.All physicists, and a good many quite respectable mathematicians are contemptuous about proof.**

**Online**

**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,811

Hi Bobby,

I used G (only) as my 'go to' prog for this and used its great abilities to quickly give a solution, but I also got some satisfaction in being able to find that alternative (I'd thought I wouldn't find one), which I did with trig and M and needed much more thinking time.

If you're there, I'm here, ready to continue from where we left off...but I'll need to go to bed soon-ish.

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 81,706

Okay, you want to know what we mean for the curve?

**In mathematics, you don't understand things. You just get used to them.I have the result, but I do not yet know how to get it.All physicists, and a good many quite respectable mathematicians are contemptuous about proof.**

**Online**

**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,811

Yes please...I'm clueless. That was never covered in 4th-year high.

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 81,706

Did they cover graphing a line and such?

**In mathematics, you don't understand things. You just get used to them.I have the result, but I do not yet know how to get it.All physicists, and a good many quite respectable mathematicians are contemptuous about proof.**

**Online**

**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,811

Not that I recall, but then I wasn't terribly attentive in class and my main aim was to drop out of school that year.

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 81,706

Without the jargon an equation is a thing where there are variables ( x, y, z, a... etc ) that are linked together by an equal sign.

x^2 + 5x + 2 = 0 is an equation. E=mc^2 is an equation, y = 16t^2 is an equation. x + y is not. Savvy?

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

**Online**

**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,811

Savvy, kemo sabe.

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 81,706

Sometimes an equation has only one variable and we must try to solve for it and sometimes it has more than one.

x - 5 = 0 is an equation with one variable. y = 3x - 8 is an equation with 2 variables. If you follow up to here we need to sort of define one term here...

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

**Online**

**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,811

Yes, I saw the multi-variable conic equations and didn't know what to do with them. I've used 'simultaneous equations' to eliminate variables...

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 81,706

When we say solve an equation we mean find the value of the variables that make the equation true.

x + 3 = 9

If we say that x = 6 then

6 + 3 = 9 is true so 6 is a solution to that equation. 5 or anything else is not.

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

**Online**

**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,811

Understood...

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 81,706

Sometimes an equation can have more than one solution! For instance y = 3x + 9, x = 1 and y = 12 is a solution because 12 = 3 + 9. x = 2 and y = 15 is a solution because 15 = 3(2) + 9. Savvy?

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

**Online**

**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,811

Yes, no probs with that.

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 81,706

Notice how each solution can be paired together to form what they call an ordered pair. How amazing.

We can get a lot of them (3,12), (6,15), (9,18)...

By the way they are called ordered pairs because they are a pair where the order counts, (6,12) is not the same as (12,6)

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

**Online**

**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,811

I think I may have heard that term, but I didn't know what it meant.

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 81,706

Now each one of those ordered pairs can be plotted on a piece of paper where y ( the second number) and x ( the first number ) are the vertical and horizontal axis. In geogebra enter ( 6 , 9 ).

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

**Online**

**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,811

Done. I've done that before with, eg, A = ( 6, 9 ).

*Last edited by phrontister (2014-04-01 03:07:53)*

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 81,706

Each ordered pair ( solution to the equation ) can be plotted just like that.

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

**Online**

**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,811

Yes...tried it.

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 81,706

If you draw a line through all 3 points then geogebra will give you a surprise.

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

**Online**

**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,811

Hang on...I've lost track. What is the equation we're working on? Is it the one in post #63: y = 3x + 9?

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 81,706

That is very good, I changed in the middle of this.

Let me get back on track, let's use the equation:

y = 3x + 9 and the 3 ordered pairs (1,12), (2,15), (3,18)

What do those 3 ordered pairs represent?

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

**Online**

**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,811

I'd anticipated that and entered the coordinates into G...which gave a straight line connecting the lot.

Oops. Sorry, but I didn't answer your Q. They're coordinates.

*Last edited by phrontister (2014-04-01 03:30:43)*

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 81,706

Look at the algebra pane and under Line, what is there?

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

**Online**