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Originally Posted By: paul
Quote:

2x * 3x = 6x^2 ( that's 6*(x^2) )

wrong
Quote:

2m * 3m = 6m^2 (like measuring the area of a room)

wrong


What are your answers?

Do you agree with everything else in the list? Once you agree with something we can put it behind us and waste less time.

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Quote:
25 sq ft
25 ft^2
25 square foot

ARE ALL EXACTLY THE SAME AREA


no , 25 ft^2 is

25 ft * 25 ft = 625 sq ft



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Originally Posted By: paul
no , 25 ft^2 is
25 ft * 25 ft = 625 sq ft


Look at the Wikipedia link I gave. It directly says you're wrong.

If you disagree with Wikipedia, find a reference saying you're right.

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paul Offline OP
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Quote:
2x * 3x = 6x^2 ( that's 6*(x^2) )


2x * 3x = 6x

not 6x^2

6x^2 = 36x

Quote:
2m * 3m = 6m^2 (like measuring the area of a room)


2m * 3m = 6m

not 6m^2

6m^2 = 36 sq meters





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paul Offline OP
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the wiki article is using the wrong units for sq ft
it is using ft^2 like you do.

Quote:
The square foot (plural square feet; abbreviated ft² or sq ft)


its wrong!

probably made by someone who also doesnt know the difference.
most likely because he was taught it that way.

I would hope that you understand what a square measurement is.

1 sq ft = an area of 12 in * 12 in

12 in^2 = 1 sq ft

12 * 12 = 1 sq ft

to square a number you simply multiply the number by itself.

you might not even understand what cubed means because your understanding of a 2 dimensional measurement is flawed.

1 ft^3 = 12 in * 12 in * 12 in
1 ft^3 = 1 ft * 1 ft * 1 ft

a 3 dimensional measurement might confuse you I just thought you might want to consider how it would be affected by your use of a two dimensional measurement.





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Originally Posted By: paul
the wiki article is using the wrong units for sq ft
it is using ft^2 like you do.


Summary:
I say 5 square feet = 5 ft^2

You say 5 square feet = 25 ft^2

Again, can you find a reference? Or any documented case of anyone anywhere using your way? Try looking at advertisements for apartments. I did.

Hang on! Why are we talking about this? Let's just not use words "square feet" or "square meters" or "square anythings". That'll solve it.

Going back to my list. Which do you agree with?

2x * 3x = 6x^2 [Paul says no]
2m * 3m = 6m^2 [Paul says no]

2x * 3 = 6x [Paul says ??]
2N * 3 = 6N [....]

2x * 3y = 6xy
2N * 3s = 6Ns
2gallons * 3seconds = 6gallon-seconds

2m/s * 3s = 6m
2gallons/second * 3seconds = 6gallons
2kg.m/s/s * 3s = 6kg.m/s

Last edited by kallog; 10/01/11 03:47 AM.
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Quote:
Summary:
I say 5 square feet = 5 ft^2

You say 5 square feet = 25 ft^2


point me to the post where I said 5 sq ft = 25 ft^2

I know better than that.

your summary is also wrong.

this is what I meant when I said that you dont say things that are true very often.

and that you take things out of context.






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Originally Posted By: paul

1 ft^3 = 12 in * 12 in * 12 in
1 ft^3 = 1 ft * 1 ft * 1 ft


Yes

I ignored the other cases because they used "sq .." which is half of our trouble. We don't need that notation anywhere, so let's just never use it.

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Originally Posted By: paul
[quote]
point me to the post where I said 5 sq ft = 25 ft^2


Sorry, my mistake. Anyway let's stop using "square.." or "sq .." entirely. We don't need them. Stick to ft^2 or other usual math notation.

Back to the list. I added one at the bottom:

2x * 3x = 6x^2 [Paul says no]
2m * 3m = 6m^2 [Paul says no]

2x * 3 = 6x
2N * 3 = 6N

2x * 3y = 6xy
2N * 3s = 6Ns
2gallons * 3seconds = 6gallon-seconds

2m/s * 3s = 6m
2gallons/second * 3seconds = 6gallons
2kg.m/s/s * 3s = 6kg.m/s

1ft^3 = 1ft * 1ft * 1ft [Paul says yes]

Last edited by kallog; 10/01/11 04:00 AM.
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Quote:
I ignored the other cases because they used "sq .."


thats because we were dealing with squares.

how many square feet are on the surface area of a 1 ft^3 cube?

there are 6 sq ft on its surface area.

how many square feet are on the surface area of a 2 ft^3 cube?

12 sq ft

if it was a origami cube and you opened it up.

there would be a piece of paper that has a 12 sq ft area on it.








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Originally Posted By: paul
there are 6 sq ft on its surface area.


OK, but let's completely stop using:
sq ft
square feet
feet squared

because we don't follow the same conventions for their meanings. Instead use the unambiguous:

ft^2
or
ft
or whatever is appropriate.

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Quote:
1ft^3 = 1ft * 1ft * 1ft [Paul says yes]


because its a cube.

there are 6 sq ft on that cubes surface.

1 sq ft * 1 sq ft * 1 sq ft = 1 ft^3

correct?

now suppose we use 2ft^2 * 2 ft^2 * 2 ft^2 = 64 sq ft area = 8ft^2 area


thats like saying

4 sq ft * 4 sq ft * 4 sq ft = 64 sq ft = 8ft^2 area




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Paul,
I'm trying to understand how you're thinking about this.

Do you think that mathematicians, engineers, and scientists
1) agree with you on what you're saying?
OR
2) agree with us - but you also think they're wrong as well?
OR
3) don't know and don't care what they think or why they think it?

I'd like to keep this with the simplest example that illustrates the principle.

I say that 2x * 2x = 4x^2
You say 2x * 2x = 4x

I'm not asking you to accept something you don't agree with. I'm just asking you to check your math. That equal sign means that the left and right sides result in the same value, regardless of the value selected for x. So just pick a few values of x and see which one, if either, works.

I can think of a simpler example:
Do you agree that 1x * 1x is the same as x * x?
And do you think that x * x = x^2 (by definition)?

Last edited by TheFallibleFiend; 10/01/11 04:38 AM.
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Quote:
Do you think that mathematicians, engineers, and scientists


Im only going by the evidence that I see in the math mistakes.

such as yours and kallogs mistakes.

if you have a yard stick.

place it on the floor , now mark its length.

now turn it 90 degrees from where it is.

now mark its length again.

mark off the 4 corners of the squared area you just measured.

why do you use 4 corners? , because a square is square and a square has 4 corners.

calculate the number of square feet inside the square.

now if you had 3ft^2 how many sq feet is that?

is it 3 sq ft?

or is it 9 sq ft?

I say its 9 sq ft = 3ft^2

just look at the ^2 and think about what it represents...

it means that its squared.

10^2 = 100
















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Originally Posted By: paul
Quote:
Do you think that mathematicians, engineers, and scientists


Im only going by the evidence that I see in the math mistakes.

such as yours and kallogs mistakes.



But how do you know we're mistaken? All of this is covered in the first few weeks of an algebra 1 class. I'm guessing you have never taken algebra 1. Is that correct?

When I tell you that all the other mathematicians and scientists agree with what we're saying, do you think we're lying or mistaken?

Have you checked a book? Do you care what the books say?

If I pointed you to a professional PhD mathematician, would you accept his answer?

I'm asking you
a) Do you agree that 1x * 1x = x * x?
b) Do you agree that x * x = x^2?

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Originally Posted By: paul

calculate the number of square feet inside the square. (one yard on a side)

now if you had 3ft^2 how many sq feet is that?


It's not 3ft^2. Its (3ft)^2 =3ft * 3 ft = 9 ft^2.

Seriously. Check ANY algebra 1 book.










[/quote]

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paul Offline OP
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Quote:
It's not 3ft^2. Its (3ft)^2 =3ft * 3 ft = 9 ft^2.


did you even try the calculator out to see what it says?

when you remove notation from a number by squaring it you remove the ^ notation symbol

just like .8000 -3

with the notation removed = 800.0

notice there's no trailing - notation

so 2^2 without notation = 4

thats why a 2 becomes 4 when you square it.

try it with your calculator.

put a 2 in it , then square the 2

it will say 4 because the 2 is now squared !!!

2 x 2 = 4

a number that is squared is that number multiplied by itself.








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here's a chart on wiki
http://en.wikipedia.org/wiki/Square_number

Quote:
It's not 3ft^2. Its (3ft)^2 =3ft * 3 ft = 9 ft^2.


find 9^2 below

0^2 = 0
1^2 = 1
2^2 = 4
3^2 = 9
4^2 = 16
5^2 = 25
6^2 = 36
7^2 = 49
8^2 = 64
9^2 = 81
10^2 = 100

9^2 = 81

Quote:
3ft * 3 ft = 9 ft^2.


Quote:
No, 4 is not 2^2 without notation.


count the square feet , are there 81 sq ft in a 3 ft x 3 ft area?

you guys really could use a good refresher course.
TFF , your students may need one also.






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Originally Posted By: thefalliblefiend
It's not 3ft^2. Its (3ft)^2 =3ft * 3 ft = 9 ft^2.


Originally Posted By: paul

did you even try the calculator out to see what it says?


It doesn't help to type into a calculator, if you don't type in the right thing. I get my students to solve problems without the calculator.

Originally Posted By: paul

when you remove notation from a number by squaring it you remove the ^ notation symbol

just like .8000 -3

with the notation removed = 800.0
notice there's no trailing - notation

Do you understand what that "trailing notation" means?
It's called "engineering notation." Not every calculator types it out exactly the same way.

.8000 -3 means .8000 times 10^-3

Some calculators will right it as .8000E-3
No kidding. Check the manual with your calculator.

Originally Posted By: paul

so 2^2 without notation = 4
thats why a 2 becomes 4 when you square it.


No, 4 is not 2^2 without notation. It's got nothing to do with the representation on a calculator. It's that 2^2 MEANS 2 times 2, or 2*2.


Originally Posted By: paul

put a 2 in it , then square the 2
it will say 4 because the 2 is now squared !!!
2 x 2 = 4
a number that is squared is that number multiplied by itself.

Okay, all that stuff is correct. Over the course of my life I've computed squares thousands of times and used many different kinds of calculators (and have programmed them).

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Quote:
It doesn't help to type into a calculator, if you don't type in the right thing. I get my students to solve problems without the calculator.


that darn calculator might tell on you !!!

it should at least be used to check answers.


3/4 inch of dust build up on the moon in 4.527 billion years,LOL and QM is fantasy science.
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