Virtual-Weltanschauung-PmWiki

May 08, 2006, at 01:17 AM by zeppo -

Changed lines 3-4 from:

http://www.virtual-weltanschauung.com/img_wiki/formula1.jpg

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http://www.virtual-weltanschauung.com/img_wiki/formula2.jpg

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http://www.virtual-weltanschauung.com/img_wiki/quadratic2.jpg

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The general quadratic equation is given by http://www.virtual-weltanschauung.com/img_wiki/quadratic2.jpg.

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The general quadratic equation is given by .

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http://www.virtual-weltanschauung.com/img_wiki/quadratic.jpg

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http://www.virtual-weltanschauung.com/img_wiki/excel_3.jpg

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http://www.virtual-weltanschauung.com/img_wiki/formula2.jpg

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May 03, 2006, at 03:26 AM by zeppo -

Changed lines 59-60 from:

So in this case a = 0.1285, b = 11.232, c = (7758.2-y), and follow the directions from the information above.

to:

So in this case a = 0.003, b = 10.2, c = (4000-y), and follow the directions from the information above.

May 03, 2006, at 03:24 AM by zeppo -

Changed lines 35-37 from:

Looking at y=0.0285x² + 11.232x+ 7758.2 you can see that by subtracting y from each side you get
0 = 0.0285x² + 11.232x+ 7758.2 - y

to:

Looking at y=0.003x² + 10.2x+ 4000 you can see that by subtracting y from each side you get
0 = 0.003x² + 10.2x+ 4000 - y

May 03, 2006, at 03:23 AM by zeppo -

Changed lines 28-29 from:

Formula #2 and Inverse: y=0.0285x² + 11.232x+ 7758.2

to:

Formula #2 and Inverse: y=0.003x² + 10.2x+ 4000

May 03, 2006, at 03:21 AM by zeppo -

Changed lines 19-20 from:

(since ln e^0.00097763x means e must be raised to the power of 0.00097763x in order to equal e^0.00097763x )

to:

(since ln e^0.001x means e must be raised to the power of 0.001x in order to equal e^0.001x )

May 03, 2006, at 03:21 AM by zeppo -

Changed lines 1-2 from:

Formula #1: y=18700e^0.001x

to:

Formula #1: y=12000e^0.001x

Changed lines 13-15 from:

y = 18699.88e^0.001x
y/18699.88 = (18699.88e^0.001x)/ 18699.88 or y/18699.88 = e0.00097763x

to:

y = 12000e^0.001x
y/12000 = (12000e^0.001x)/ 12000 or y/12000 = e0.001x

Changed line 18 from:

LN(y/18699.88) = 0.00097763x\\

to:

LN(y/12000) = 0.001x\\

Changed lines 21-23 from:

Then we divide by 0.00097763 on each side
LN(y/18699.88) 0.00097763 = x

to:

Then we divide by 0.001 on each side
LN(y/12000) 0.001 = x

May 03, 2006, at 03:18 AM by zeppo -

Changed lines 30-33 from:

http://www.virtual-weltanschauung.com/img_wiki/excel_2.jpg

(these cell numbers are a little off from multiple paste-ings)

to:

http://www.virtual-weltanschauung.com/img_wiki/formula2.jpg

May 03, 2006, at 02:58 AM by zeppo -

Changed lines 3-4 from:

http://www.virtual-weltanschauung.com/img_wiki/excel_1.jpg

to:

http://www.virtual-weltanschauung.com/img_wiki/formula1.jpg

Changed lines 60-63 from:

http://www.virtual-weltanschauung.com/img_wiki/excel_4.jpg

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http://www.virtual-weltanschauung.com/img_wiki/formula2.jpg

April 24, 2006, at 04:59 AM by zeppo -

Changed lines 54-55 from:

Say we are given the quadratic equation, , and we wish to find both of its solutions. We can use Excel to help us do this and the screen shot below shows how that is done. (The spaces within the formula were added to make the formula easier to read.)

to:

Say we are given the quadratic equation and we wish to find both of its solutions. There are always a possible minus and plus when using the quadratic equation, although in our case only one will apply. We can use Excel to help us do this and the screen shot below shows how that is done. (The spaces within the formula were added to make the formula easier to read.)

April 23, 2006, at 04:55 PM by zeppo -

Changed lines 47-49 from:

Aslo at the sit e we find http://phoenix.phys.clemson.edu/tutorials/excel/algebra.html an example.

to:

Aslo at the site we find http://phoenix.phys.clemson.edu/tutorials/excel/algebra.html an example.

April 23, 2006, at 04:53 PM by zeppo -

Changed lines 52-53 from:

Its solution is, of course, the quadratic formula, or\\ http://www.virtual-weltanschauung.com/img_wiki/quadratic.jpg\\

to:

Its solution is, of course, the quadratic formula, or http://www.virtual-weltanschauung.com/img_wiki/quadratic.jpg

April 23, 2006, at 04:53 PM by zeppo -

Changed lines 50-51 from:

The general quadratic equation is given by http://www.virtual-weltanschauung.com/img_wiki/quadratic.jpg . Its solution is, of course, the quadratic formula, or

to:

The general quadratic equation is given by http://www.virtual-weltanschauung.com/img_wiki/quadratic2.jpg.

Its solution is, of course, the quadratic formula, or\\ http://www.virtual-weltanschauung.com/img_wiki/quadratic.jpg\\

April 23, 2006, at 04:52 PM by zeppo -

Changed lines 47-48 from:

Aslo at the sit e we find http://phoenix.phys.clemson.edu/tutorials/excel/algebra.html an example. The general quadratic equation is given by . Its solution is, of course, the quadratic formula, or http://www.virtual-weltanschauung.com/img_wiki/quadratic.jpg

to:

Aslo at the sit e we find http://phoenix.phys.clemson.edu/tutorials/excel/algebra.html an example.

The general quadratic equation is given by http://www.virtual-weltanschauung.com/img_wiki/quadratic.jpg . Its solution is, of course, the quadratic formula, or

April 23, 2006, at 04:50 PM by zeppo -

Changed lines 45-48 from:

http://phoenix.phys.clemson.edu/tutorials/excel/algebra.html

From http://phoenix.phys.clemson.edu/tutorials/excel/algebra.html Here is another example. The general quadratic equation is given by . Its solution is, of course, the quadratic formula, or

to:

http://phoenix.phys.clemson.edu/tutorials/excel/algebra.html to remember what we forgot in college Algegra.

Aslo at the sit e we find http://phoenix.phys.clemson.edu/tutorials/excel/algebra.html an example. The general quadratic equation is given by . Its solution is, of course, the quadratic formula, or

April 23, 2006, at 04:48 PM by zeppo -

Changed lines 34-35 from:

To get the inverse of the first formula this is how to proceed.

to:

To get the inverse of the formula this is how to proceed.

April 22, 2006, at 03:35 PM by 70.254.84.166 -

Changed lines 24-25 from:

This is what the formula � =LN(C8/C2)/D2� does for us were C2 and D2 are our constants and C8 is our changeable value of y.

to:

This is what the formula � =LN(C8/C2)/D2� does for us where C2 and D2 are our constants and C8 is our changeable value of y.

April 22, 2006, at 01:51 PM by zeppo -

Changed lines 11-12 from:

All we have to do now is deal with the constants associated with the formula (the 18699.88 and the 0.00097763 0.001 was just an approx.).

to:

All we have to do now is deal with the constants associated with the formula (the 18699.88 and the 0.00097763 - 0.001 was just an approx).

April 22, 2006, at 01:51 PM by zeppo -

Changed lines 11-12 from:

All we have to do now is deal with the constants associated with the formula (the 18699.88 and the 0.00097763).

to:

All we have to do now is deal with the constants associated with the formula (the 18699.88 and the 0.00097763 0.001 was just an approx.).

April 22, 2006, at 01:49 PM by zeppo -

Changed lines 14-15 from:

y/18699.88 = (18699.88e0.001x)/ 18699.88 or y/18699.88 = e'''0.00097763x

to:

y/18699.88 = (18699.88e^0.001x)/ 18699.88 or y/18699.88 = e'''0.00097763x

April 22, 2006, at 01:48 PM by zeppo -

Changed line 13 from:

'''y = 18699.88^e0.001x\\

to:

'''y = 18699.88e^0.001x\\

April 22, 2006, at 01:47 PM by zeppo -

Changed line 13 from:

'''y = 18699.88e0.001x\\

to:

'''y = 18699.88^e0.001x\\

April 22, 2006, at 01:45 PM by zeppo -

Changed lines 19-20 from:

(since ln e0.00097763x means e must be raised to the power of 0.00097763x in order to equal e0.00097763x )

to:

(since ln e^0.00097763x means e must be raised to the power of 0.00097763x in order to equal e^0.00097763x )

April 22, 2006, at 01:43 PM by zeppo -

Changed lines 9-10 from:

To simplify for explanation purposes; if the formula was y = e^x then by taking the ln of each side we see ln(y) = ln(e^x), the second part we can solve since we�re actually asking what power must e be raised to in order to equal ex. Obviously it is x. Then, we can solve for x by changing the value of y since now x = ln(y) which is an algebraic function we can plug into Excel.

to:

To simplify for explanation purposes; if the formula was y = e^x then by taking the ln of each side we see ln(y) = ln(e^x), the second part we can solve since we�re actually asking what power must e be raised to in order to equal e^x. Obviously it is x. Then, we can solve for x by changing the value of y since now x = ln(y) which is an algebraic function we can plug into Excel.

April 22, 2006, at 01:42 PM by zeppo -

Changed lines 9-10 from:

To simplify for explanation purposes; if the formula was y = e_x then by taking the ln of each side we see ln(y) = ln(e_x), the second part we can solve since we�re actually asking what power must e be raised to in order to equal ex. Obviously it is x. Then, we can solve for x by changing the value of y since now x = ln(y) which is an algebraic function we can plug into Excel.

to:

To simplify for explanation purposes; if the formula was y = e^x then by taking the ln of each side we see ln(y) = ln(e^x), the second part we can solve since we�re actually asking what power must e be raised to in order to equal ex. Obviously it is x. Then, we can solve for x by changing the value of y since now x = ln(y) which is an algebraic function we can plug into Excel.

April 22, 2006, at 01:41 PM by zeppo -

Changed lines 9-10 from:

To simplify for explanation purposes; if the formula was y = ex then by taking the ln of each side we see ln(y) = ln(ex), the second part we can solve since we�re actually asking what power must e be raised to in order to equal ex. Obviously it is x. Then, we can solve for x by changing the value of y since now x = ln(y) which is an algebraic function we can plug into Excel.

to:

To simplify for explanation purposes; if the formula was y = e_x then by taking the ln of each side we see ln(y) = ln(e_x), the second part we can solve since we�re actually asking what power must e be raised to in order to equal ex. Obviously it is x. Then, we can solve for x by changing the value of y since now x = ln(y) which is an algebraic function we can plug into Excel.

April 22, 2006, at 01:41 AM by zeppo -

Changed line 48 from:

Here is another example. The general quadratic equation is given by . Its solution is, of course, the quadratic formula, or

to:

Here is another example. The general quadratic equation is given by . Its solution is, of course, the quadratic formula, or

April 22, 2006, at 01:39 AM by zeppo -

Changed line 36 from:

Looking at y=0.0285x² + 11.232x+ 7758.2 you can see that by subtracting y from each side you get

to:

Looking at y=0.0285x² + 11.232x+ 7758.2 you can see that by subtracting y from each side you get\\

April 22, 2006, at 01:39 AM by zeppo -

Changed lines 28-29 from:

Formula #2 and Inverse: y=0.0285x^2t + 11.232x+ 7758.2

to:

Formula #2 and Inverse: y=0.0285x² + 11.232x+ 7758.2

Changed lines 36-38 from:

Looking at y=0.0285x² + 11.232x+ 7758.2 you can see that by subtracting y from each side you get 0 = 0.0285x² + 11.232x+ 7758.2 - y

to:

Looking at y=0.0285x² + 11.232x+ 7758.2 you can see that by subtracting y from each side you get 0 = 0.0285x² + 11.232x+ 7758.2 - y

April 22, 2006, at 01:38 AM by zeppo -

Changed lines 28-29 from:

Formula #2 and Inverse: y=0.0285x'^2t^ + 11.232x+ 7758.2

to:

Formula #2 and Inverse: y=0.0285x^2t + 11.232x+ 7758.2

April 22, 2006, at 01:38 AM by zeppo -

Changed lines 28-29 from:

Formula #2 and Inverse: y=0.0285x2 + 11.232x+ 7758.2

to:

Formula #2 and Inverse: y=0.0285x'^2t^ + 11.232x+ 7758.2

April 22, 2006, at 01:36 AM by zeppo -

Changed line 55 from:

So in this case a = 0.1285, b = 11.232, c = (7758.2-y), and follow the directions from the information above.

to:

So in this case a = 0.1285, b = 11.232, c = (7758.2-y), and follow the directions from the information above.

April 22, 2006, at 01:35 AM by zeppo -

Changed lines 42-43 from:

http://www.virtual-weltanschauung.com/img_wiki/quadratic21.jpg

to:

http://www.virtual-weltanschauung.com/img_wiki/quadratic2.jpg

April 22, 2006, at 01:33 AM by zeppo -

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image

to:

http://www.virtual-weltanschauung.com/img_wiki/quadratic21.jpg

April 22, 2006, at 01:31 AM by zeppo -

Changed lines 36-38 from:

Looking at y=0.0285x2 + 11.232x+ 7758.2 you can see that by subtracting y from each side you get 0 = 0.0285x2 + 11.232x+ 7758.2 - y

to:

Looking at y=0.0285x² + 11.232x+ 7758.2 you can see that by subtracting y from each side you get 0 = 0.0285x² + 11.232x+ 7758.2 - y

April 22, 2006, at 01:30 AM by zeppo -

Added lines 26-27:

April 22, 2006, at 01:28 AM by zeppo -

Changed lines 14-15 from:

y/18699.88 = (18699.88e0.001x)/ 18699.88 or y/18699.88 = e0.00097763x

to:

y/18699.88 = (18699.88e0.001x)/ 18699.88 or y/18699.88 = e'''0.00097763x

April 22, 2006, at 01:27 AM by zeppo -

Changed line 18 from:

LN(y/18699.88) = 0.00097763x'''_\\

to:

LN(y/18699.88) = 0.00097763x\\

April 22, 2006, at 01:27 AM by zeppo -

Changed line 18 from:

LN(y/18699.88) = 0.00097763x\\

to:

LN(y/18699.88) = 0.00097763x'''_\\

April 22, 2006, at 01:26 AM by zeppo -

Changed lines 19-20 from:

[ since ln e0.00097763x means e must be raised to the power of 0.00097763x in order to equal e0.00097763x ]

to:

(since ln e0.00097763x means e must be raised to the power of 0.00097763x in order to equal e0.00097763x )

April 22, 2006, at 01:26 AM by zeppo -

Changed line 18 from:

LN(y/18699.88) = 0.00097763x \\

to:

LN(y/18699.88) = 0.00097763x\\

April 22, 2006, at 01:25 AM by zeppo -

April 22, 2006, at 01:23 AM by zeppo -

Changed lines 1-2 from:

Formula #1: y=18700e^0.001x

to:

Formula #1: y=18700e^0.001x

April 22, 2006, at 01:23 AM by zeppo -

Changed lines 1-2 from:

Formula #1: y=18700e0.001x

to:

Formula #1: y=18700e^0.001x

Changed lines 7-8 from:

To input values for y and get an output for x we need to use logarithms, or more specifically the natural logarithm for e.

to:

To input values for y and get an output for x we need to use logarithms, or more specifically the natural logarithm for e.

Changed lines 11-15 from:

All we have to do now is deal with the constants associated with the formula (the 18699.88 and the 0.00097763).

y = 18699.88e0.001x
y/18699.88 = (18699.88e0.001x)/ 18699.88 or y/18699.88 = e0.00097763x

to:

All we have to do now is deal with the constants associated with the formula (the 18699.88 and the 0.00097763).

y = 18699.88e0.001x
y/18699.88 = (18699.88e0.001x)/ 18699.88 or y/18699.88 = e'''0.00097763x

Changed line 18 from:

LN(y/18699.88) = 0.00097763x \\

to:

LN(y/18699.88) = 0.00097763x \\

April 22, 2006, at 01:20 AM by zeppo -

Changed lines 26-27 from:

to:

Formula #2 and Inverse: y=0.0285x2 + 11.232x+ 7758.2

Changed lines 30-31 from:

http://www.virtual-weltanschauung.com/img_wiki/excel_3.jpg

to:

(these cell numbers are a little off from multiple paste-ings)

To get the inverse of the first formula this is how to proceed.

Looking at y=0.0285x2 + 11.232x+ 7758.2 you can see that by subtracting y from each side you get 0 = 0.0285x2 + 11.232x+ 7758.2 - y

From http://mathworld.wolfram.com/QuadraticEquation.html A quadratic equation is a second-order polynomial equation in a single variable

image

So we see that our formula is now in classic quadratic equation form. THEN we do a quick search of the web to find http://phoenix.phys.clemson.edu/tutorials/excel/algebra.html

From http://phoenix.phys.clemson.edu/tutorials/excel/algebra.html Here is another example. The general quadratic equation is given by . Its solution is, of course, the quadratic formula, or

Changed lines 48-53 from:

to:

Say we are given the quadratic equation, , and we wish to find both of its solutions. We can use Excel to help us do this and the screen shot below shows how that is done. (The spaces within the formula were added to make the formula easier to read.)

http://www.virtual-weltanschauung.com/img_wiki/excel_3.jpg Of course, to solve another quadratic equation, all one needs to do is change the values of the constants a, b and c in cells A1, B1 and C1. There is no need to alter the formula and the new result is given immediately after the new values are entered!

So in this case a = 0.1285, b = 11.232, c = (7758.2-y), and follow the directions from the information above.

April 22, 2006, at 01:17 AM by zeppo -

Added lines 1-2:

Formula #1: y=18700e0.001x

Added lines 5-26:

The first part is straight forward, but how to solve for x when you know y?

To input values for y and get an output for x we need to use logarithms, or more specifically the natural logarithm for e.

To simplify for explanation purposes; if the formula was y = ex then by taking the ln of each side we see ln(y) = ln(ex), the second part we can solve since we�re actually asking what power must e be raised to in order to equal ex. Obviously it is x. Then, we can solve for x by changing the value of y since now x = ln(y) which is an algebraic function we can plug into Excel.

All we have to do now is deal with the constants associated with the formula (the 18699.88 and the 0.00097763).

y = 18699.88e0.001x
y/18699.88 = (18699.88e0.001x)/ 18699.88 or y/18699.88 = e0.00097763x

Now take the natural log of each side and get this:

LN(y/18699.88) = 0.00097763x \\ [ since ln e0.00097763x means e must be raised to the power of 0.00097763x in order to equal e0.00097763x ]

Then we divide by 0.00097763 on each side
LN(y/18699.88) 0.00097763 = x

This is what the formula � =LN(C8/C2)/D2� does for us were C2 and D2 are our constants and C8 is our changeable value of y.

April 22, 2006, at 01:13 AM by zeppo -

Added lines 3-12:

http://www.virtual-weltanschauung.com/img_wiki/excel_2.jpg

http://www.virtual-weltanschauung.com/img_wiki/excel_3.jpg

http://www.virtual-weltanschauung.com/img_wiki/quadratic.jpg

http://www.virtual-weltanschauung.com/img_wiki/excel_4.jpg

April 22, 2006, at 12:59 AM by zeppo -

Changed lines 2-3 from:

one <img src="gifs/barArt2.gif" width="133" height="24">

to:

April 22, 2006, at 12:59 AM by zeppo -

Changed line 1 from:

to:

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April 22, 2006, at 12:49 AM by zeppo -

Changed line 1 from:

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April 22, 2006, at 12:48 AM by zeppo -

Changed line 1 from:

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Added line 3:

April 22, 2006, at 12:45 AM by zeppo -

Changed lines 1-2 from:

http://www.virtual-weltanschauung.com/img/excel_1.jpg one

to:

<img src='http://www.virtual-weltanschauung.com/img/excel_1.jpg' alt='excel_i title ='excel_1' /> one

April 22, 2006, at 12:42 AM by zeppo -

Changed lines 1-2 from:

http://www.virtual-weltanschauung.com/img/excel_1.jpg"Excel_1"

to:

http://www.virtual-weltanschauung.com/img/excel_1.jpg one

April 22, 2006, at 12:41 AM by zeppo -

Changed line 1 from:

http://www.virtual-weltanschauung.com/img/excel_1.jpg

to:

http://www.virtual-weltanschauung.com/img/excel_1.jpg"Excel_1"

April 22, 2006, at 12:39 AM by zeppo -

April 22, 2006, at 12:37 AM by zeppo -

Added line 1:

http://www.virtual-weltanschauung.com/img/excel_1.jpg

AFormula

Main.AFormula History