Tuesday, August 31, 2010

. : Material Science : .

Hi there,

Sorry guys, manage to do chapter 1 and 2 part 1 as the rest are FACTs which need to be understand more.





Warmest regards,
ZaX

statics tutorial
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Switch Adaptable Online Spinner, Calculator and More!

Tripico a site that designs e-Learning content has an eight section spinner or a four section spinner that can be run by a switch set to mouse click when the pointer is over the spin button. You can put any text you wish in the eight sections, if you have less than eight things to spin for you can put in "spin again", "lose a turn", or you can duplicate som! e items. Should be super fun with an LCD Projector on a "Big Screen" or on a SMART Board.

Also completely there is an amazing calculator that works using switches set to tab and enter to enter what you need to solve your math program. Imagine a FREE, ONLINE accessible, scanning calculator! Of course it also works with a mouse, touch screen or on a SMART Board.
< br />Also at Tripico you can find:

Switch Adapted, Touch Screen, SMART Board or Mouse:
Touch Screen, SMART Board or Mouse

special products calculator
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Making the fractions in a proportion

"How do you know how to make the fractions in a proportion?
When making them, how do you know where each number goes making the fraction, like which ones go on top of the fraction?"

Well, actually you can choose which quantity will go on top; the proportion WILL work either way!

But, sometimes people are used to always putting certain quantity on top and certain on the bottom. For example, if the question is about speed and the unit is "miles per hour", that tells you that miles go on top, and hours on bottom, because "per" means division (the fraction line).

However, you could still solve the proportion by putting hours in the numerator of the fractions and miles in the denominator, and the calculation will turn out alright.

Or, if the question is about "dollars per pound", then dollars go to the numerator and pounds in the denominator.

Let's look at this problem for example:

A car drives on constant speed. It can go 80 miles in 90 minutes. How long will it take for it to travel 100 miles?

You can make both fractions to be


miles
-----------
minutes

OR

minutes
------------
miles


Let's try the first way:

80 mi           100 mi
--------  =   ---------
90 min            x

To solve, cross multiply and you get 80x = 100 * 90, and then x = 900/8 = 112.5 minutes.

The other way it will be

90 min         x
--------  =  --------
80 mi         100 mi

To solve, cross multiply and you get 80x = 90 * 100

You see, the final equation ends up being the same, no matter which
quantities were on top of the fractions! .

HOWEVER, one way is wrong: that is if you but "mi! les" on top in one
fraction, and "minutes" on top in the other... then you'll get it wrong:

90 min        100 mi
--------  =  -------
80 mi         x min

=> 90x = 100* 80 (WRONG)


solve proportions
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5.5 Multiply Rational Expressions


simplifying rational expressions calculator
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"Multiple" Pi Challenges for MS and HS

Consider the following table displaying the first four positive integer multiples of π rounded to 4 places:
\begin{matrix}\pi&3.142\\2\pi&6.283\\3\pi&9.425\\4\pi&12.566 \end{matrix}

So what's the challenge here? You will be a π-multiple investigator!

(1) Determine the EIGHT positive integer multiples of π, up to 1000π, which, when rounded to THREE places, produce an integer result. For example, the decimal 17.9996 when rounded to 3 places results in the integer 18.000, which we will regard as an 'integer'. Unfortunately, this decimal is not an integer multiple of π so have fun searching! Do you notice any pattern in your results? Describe it! Can you explain this pattern? [This requires more than a Yes/No response!]
(2) In fact, the "pattern" you may have found in (1) continues beyond 1000π. Show that you can go up to SIXTEEN multiples of π before the pattern breaks down. Why do you think the pattern eventually ends?

(3) Which of your results in (1) would produce an integer when rounded to FOUR places?

(4) Can you think of any practical application for finding multiples of π which are very close to an integer? Be creative! Responses may depend on how advanced your math background is.

Comments:

  • Do your students know how to program their graphing calculator to do the search? OR in Java or C++ or Python or Perl?? This would certainly facilitate the search! I may display the code for the TI-83 or -84. However, students may also find a creative way to use the TABLE feature on their graphing calculators to save time without programming. Have fun!
  • Please post feedback if you use this in your classes. I will not post answers ye! t in case students find this post in their 'searching'!
    • For mo st students, the full significance of this innocent looking search problem will not be apparent. You might want to give them a hint. Perhaps we should call this post:
    IS π ALMOST RATIONAL?


rationalize the denominator calculator
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SymPy 0.6.6 released

SymPy 0.6.6 has been released on December 20, 2009. It is available at

http://sympy.org

The source distribution can be downloaded from:
http://sympy.googlecode.com/files/sympy-0.6.6.tar.gz

You can get the Windows installer here:
http://sympy.googlecode.com/files/sympy-0.6.6.win32.exe

And the html documentation here:
http://sympy.googlecode.com/files/sympy-0.6.6-docs-html.zip

About SymPy

SymPy is a Python library for symbolic mathematics. It aims to become a full-featured computer algebra system (CAS) while keeping the code as simple as possible in order to be comprehensible and easily extensible. SymPy! is written entirely in Python.

Changes since last stable release

  • many documentation improvements, including docstrings and doctests
  • new assumptions system (GSoC) (See assumptions documentation for more information or have a look at Fabian's blog.)
    • Note: This is going to replace the old assumption system. It is encouraged to use it for new code, however it is not completely finished and parts of sympy have yet to be rewritten to use it; this scheduled for the 0.7 release.
  • improvements to test runner
  • printing improvements (especially LaTeX, but also mathml and pretty printing)
  • discriminant of polys
  • block diagonal methods for matrices!
  • vast improvements to solving of ODEs (GSoC) (See ODE documentation for full details or Aaron's blog).
  • logcombine function
  • improvements to sets
  • better trigonometric simplification
  • improvements to piecewise functions
  • improvements to solve() and nsolve()
  • improvements to as_numer_denom()
  • much better quartic and cubic polynomial rootfinding
  • code refactoring and cleanup
  • physics: coupled clusters and wick expansion
  • matrices: symbolic QR solving
  • mpmath updated
  • pyglet updated
  • many, many bug fixes and small improvements

The following 22 people have contributed patches to this release (sorted alphabetically):

  • Aaron Meurer
  • Alan Bromborsky
  • Andy R. Terrel
  • Bill Flynn
  • Chris Smith
  • Eh Tan
  • Fabian Pedregosa
  • Fredr! ik Johansson
  • Jorn Baayen
  • Julio Idichekop Filho
  • Kevin Goodsell
  • Łukasz Pankowski
  • Luke Peterson
  • Øyvind Jensen
  • Ondrej Certik
  • Oscar Benjamin
  • Priit Laes
  • Renato Coutinho
  • Ronan Lamy
  • Ryan Krauss
  • Ted Horst
  • Toon Verstraelen
  • Vinzent Steinberg

The following 10 people helped reviewing patches:

  • Aaron Meurer
  • Andy R. Terrel
  • Chris Smith
  • Fabian Pedregosa
  • Fredrik Johansson
  • Luke Peterson
  • Mateusz Paprocki
  • Ondrej Certik
  • Ronan Lamy
  • Vinzent Steinberg

polynomial simplifier
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Two MIT math graduates bump into each other. They hadn’t seen each

Two MIT math graduates bump into each other. They hadn’t seen each other in over 20 years.
The first grad says to the second: “how have you been?”
Second: “Great! I got married and I have three daughters now”
First: “Really? how old are they?”
Second: “Well, the product of their ages is 72, and the sum of their ages is the same as the number on that building over there..”
First: “Right, ok.. oh wait.. I still don’t know”
second: “Oh sorry, the oldest one just started to play the piano”
First: “Wonderful! my oldest is the same age!” Problem: How old are the daughters?

maths mate 9 answers
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