Difference Quotient and real world applications??

[CuriosOne]

What are some real physical world applications "examples" that use the Difference Quotient?

Yes I know they relate the slope of secants and tangent relationships, but how do these model a real physical world scenario?? 

Edited December 10, 2020 by CuriosOne

[HallsofIvy]

Velocity and acceleration are "difference quotients"!

 

[CuriosOne]

21 minutes ago, HallsofIvy said:

Velocity and acceleration are "difference quotients"!

 

Understood...

"But" isn't velocity a direction?? or a "variable?"

And acceleration "gravity" influenced?

Meaning a ball falling or "orbiting" around a "circular" object??

"Or atleast the ones in solar systems are circular."

 

How does 2 points connect all this together?

Edited December 11, 2020 by CuriosOne

[MigL]

Velocity HAS a direction, otherwise it is 'speed'.
Velocity can be a variable if it varies ( notice the connection ? )
Accelerations are influence by gravity, or any other force, according to     a = F/m
where a = acceleration,          F = force        and m = mass 
( bolded letters imply a vector quantity; IOW, it has a direction, usually denoted by an arrow above the letter )

[swansont]

20 hours ago, CuriosOne said:

 

"But" isn't velocity a direction?? or a "variable?"

Of course it’s a variable. What would be the point of finding a difference quotient for constants?

[CuriosOne]

14 hours ago, MigL said:

Velocity HAS a direction, otherwise it is 'speed'.
Velocity can be a variable if it varies ( notice the connection ? )
Accelerations are influence by gravity, or any other force, according to     a = F/m
where a = acceleration,          F = force        and m = mass 
( bolded letters imply a vector quantity; IOW, it has a direction, usually denoted by an arrow above the letter )

Understood, I'm just trying to figure out if speed is radiant or ominous, and if velocity acts as a ray "for example" in a linear direction..The acceleration part I fully understand....But now comes the numbers and physics part im trying to comprehend in the Difference Quotient..

4 hours ago, swansont said:

Of course it’s a variable. What would be the point of finding a difference quotient for constants?

When you say constants, are these:

G,g, pi, h etc etc???

""But"" they all use base ten...

Are we talking about ""decimal values"" of the constants???

 

[swansont]

13 minutes ago, CuriosOne said:

Understood, I'm just trying to figure out if speed is radiant or ominous,

You will need to clarify this. Radiant? Ominous? 

 

13 minutes ago, CuriosOne said:

 

G,g, pi, h etc etc???

Those are constants. As is a=2, or b=16.3

 

13 minutes ago, CuriosOne said:

""But"" they all use base ten...

Are we talking about ""decimal values"" of the constants???

It doesn’t matter. Base 10 is the usual way of expressing numbers in a lot of fields, but you could express a constant in any base, and certain disciplines use other bases. d= 10110 is a constant expressed in base 2, for example.

[MigL]

A 'constant' is constantly the same value; it does not change.
The value of Pi is 3.141… in base 10
And 11.001… in base 2

The ratio of a circle's circumference to its diameter doesn't change in different number bases.

 

[studiot]

7 minutes ago, MigL said:

A 'constant' is constantly the same value; it does not change.
The value of Pi is 3.141… in base 10
And 11.001… in base 2

The ratio of a circle's circumference to its diameter doesn't change in different number bases.

 

Careful or our numerologist will introduce the golden ratio Pi.

 

[CuriosOne]

18 minutes ago, MigL said:

A 'constant' is constantly the same value; it does not change.
The value of Pi is 3.141… in base 10
And 11.001… in base 2

The ratio of a circle's circumference to its diameter doesn't change in different number bases.

 

This is exactly what I was looking for..

The ratio of a circle's circumference to its diameter does not change in different bases..

"""""IT'S BASE MUST BE INFINITE???"""""

But as far as typical bases goes..

Example using some random numbers here..

111.000 is base 3 ?

7656.0877 is base 4 ?

6567566.099 is base 7 ?

Etc etc??

 "base" is another word for distance...

""""""Base 10 must be special""""""🤣😂

No Wonder!

Edited December 12, 2020 by CuriosOne

[Dord]

11 minutes ago, CuriosOne said:

 

""""""Base 10 must be special""""""🤣😂

 

I was taught that the reason we use base 10 is simply because we have 10 fingers and thumbs.

 

[HallsofIvy]

1 hour ago, CuriosOne said:

This is exactly what I was looking for..

The ratio of a circle's circumference to its diameter does not change in different bases..

"""""IT'S BASE MUST BE INFINITE???"""""

But as far as typical bases goes..

Example using some random numbers here..

111.000 is base 3 ?

7656.0877 is base 4 ?

6567566.099 is base 7 ?

Etc etc??

 "base" is another word for distance...

""""""Base 10 must be special""""""🤣😂

No Wonder!

  It looks to  me  like you don't know what "base" means here.

The ratio of a circle's circumference to its diameter does not change in different bases..

"""""IT'S BASE MUST BE INFINITE???"""""

Doesn't even make sense.  A NUMBER does NOT have a specific base.  When it is written as a specific NUMERAL it must be written in a specific base.  

111.000 is base 3 ?

7656.0877 is base 4 ?

6567566.099 is base 7 ?

Are you thinking that "base" is the number of digits before the decimal point?  That's the only way I can see to get "3", "4", and "7"!  Those numerals can be in any base but would represent different number in different bases.

IF 111.000 were in base 3 then it would mean 1(3^2)+ 1(3^1)+ 1(3^0) which would be the same as the number, in base 10, 9+ 3+ 1= 13.  If it were in base 10 then it would "one hundred eleven" .  If it were in base 5 then it would mean 1(5^2)+ 1(5^1)+ 1(5^0) which be the same as the number in base 10,  25+ 5+ 1 31.

 

No, "base" is NOT "distance".  And the only thing special about "base 10" is that our standard "numeration system" is base 10.  And, as Dord said, the reason we use base 10 is probably because we started counting on our fingers- and we have 10 fingers.

(I have read that Native Americans along the north Pacific coast counted using the gaps between the fingers- and so had what was effectively as "base 8" number system.)

[MigL]

I also asked you previously
What do you think 'base' means ?

Give us your understanding/interpretation.
You seem to think we are all telling you something different than what the rest of us all understand we are telling you.
YOU is the common denominator to this misunderstanding.
( do you know what a denominator is ?  )

[CuriosOne]

4 hours ago, HallsofIvy said:

  It looks to  me  like you don't know what "base" means here.

 

 

Neither does anyone else for that matter, as bases seize to exists through the use of pi ratio....

[Sensei]

6 hours ago, CuriosOne said:

The ratio of a circle's circumference to its diameter does not change in different bases..

Nothing, but visual representation of a number, changes in different numeral systems ("bases")..Regardless if it is PI, or any other number.

255 = 0xFF = $FF = %11111111 = CCLV

It is still the same value, just differently written..

You should start from reading Wikipedia article about numeral systems ("bases") first.

https://en.wikipedia.org/wiki/Numeral_system

"A numeral system (or system of numeration) is a writing system for expressing numbers; that is, a mathematical notation for representing numbers of a given set, using digits or other symbols in a consistent manner."

[CuriosOne]

4 hours ago, MigL said:

I also asked you previously
What do you think 'base' means ?

Give us your understanding/interpretation.
You seem to think we are all telling you something different than what the rest of us all understand we are telling you.
YOU is the common denominator to this misunderstanding.
( do you know what a denominator is ?  )

A base is obviously a conversion factor by 1, and a dominator is a distance from 0 to 1.....It works in reverse...

A more confusing way of thinking about it is right here, copied from wikipedia..

The same sequence of symbols may represent different numbers in different numeral systems. For example, "11" represents the number eleven in the decimal numeral system (used in common life), the number three in the binary numeral system (used in computers), and the number two in the unary numeral system (e.g. used in tallying scores).

The number the numeral represents is called its value.

2 minutes ago, Sensei said:

Nothing, but visual representation of a number, changes in different numeral systems ("bases")..Regardless if it is PI, or any other number.

255 = 0xFF = $FF = %11111111 = CCLV

It is still the same value, just differently written..

You should start from reading Wikipedia article about numeral systems ("bases") first.

https://en.wikipedia.org/wiki/Numeral_system

"A numeral system (or system of numeration) is a writing system for expressing numbers; that is, a mathematical notation for representing numbers of a given set, using digits or other symbols in a consistent manner."

I sure will read and study this...And give it the benifit of a doubt...ThnXxxxx

5 hours ago, HallsofIvy said:

  It looks to  me  like you don't know what "base" means here.

 

 

Ok, "Can You Show An Example?"

10 hours ago, swansont said:

You will need to clarify this. Radiant? Ominous? 

 

Those are constants. As is a=2, or b=16.3

 

It doesn’t matter. Base 10 is the usual way of expressing numbers in a lot of fields, but you could express a constant in any base, and certain disciplines use other bases. d= 10110 is a constant expressed in base 2, for example.

I'm very very sorry to say this, but it sounds like theoretical number theory..

This is what's confusing...

Edited December 13, 2020 by CuriosOne

[Sensei]

17 hours ago, CuriosOne said:

When you say constants, are these:

[..] g [....] etc etc???

BTW, g is not constant...

Simplified equation is:

g(r)= GM/r^2

g varies with latitude and longitude, altitude and distance from the center of the Earth etc. etc.

It varies according to the type of rock found underground and is even used by geologists to find out what is underground (to help miners and engineers from petrochemical industry).

https://en.wikipedia.org/wiki/Gravity_of_Earth

https://en.wikipedia.org/wiki/Gravity_anomaly

 

https://www.google.com/search?q=gravity+anomaly+map

 

Edited December 13, 2020 by Sensei

[John Cuthber]

8 hours ago, CuriosOne said:

A base is obviously a conversion factor by...

No.

It is not.
Try learning what words mean before trying to use them.

 

https://simple.wikipedia.org/wiki/Base_(mathematics)

8 hours ago, CuriosOne said:

I sure will read and study this...And give it the benifit of a doubt

There isn't any daunt.

He's correct.

[HallsofIvy]

9 hours ago, CuriosOne said:

Neither does anyone else for that matter, as bases seize to exists through the use of pi ratio....

So you posted this whole thread as a joke?  I suspected that from the start.   I didn't think a person would use so many words without having any idea what they mean!

(And the word is "cease", not "seize"!)

[swansont]

9 hours ago, CuriosOne said:

Neither does anyone else for that matter, as bases seize to exists through the use of pi ratio....

So much for your claim that you don't assert things as true. 

Just because you don't understand something doesn't mean others don't, and just because you think you understand something doesn't mean others "understand" it the way you do. You don't understand it - you should investigate and ask questions. This kind of dismissal is lame.

You have quite the fascination with pi, and seemingly have imbued it with certain powers, but despite this, math is not mysticism.

[CuriosOne]

8 hours ago, swansont said:

So much for your claim that you don't assert things as true. 

Just because you don't understand something doesn't mean others don't, and just because you think you understand something doesn't mean others "understand" it the way you do. You don't understand it - you should investigate and ask questions. This kind of dismissal is lame.

You have quite the fascination with pi, and seemingly have imbued it with certain powers, but despite this, math is not mysticism.

I can agree with this.