Tuesday, August 31, 2010

Precalculus help

Introduction of Square Number:

The result of the when a number is multiplied by itself as once, we get square number. This squared number is termed as perfect square. The expression of square number is represented as n2 = M, which is the square number.

For Example:

5 × 5 = 25, →square number

4 × 4 = 16, →square number

7 × 7 = 49, →square number

In this article, we see about the number 36 is perfect square numbers or not.

Square Number:

We get the square number by using the follow formula.

M (square number) = n2 = (n - 1)2 + (2n - 1)

Or formula using square the number

Let us see the number 36 is square number or not by using this formula.

Would you like to improve your Number learning skills...


precalculus help

Make your own globe -- Paper Template











Make Your Own Globe

Template needed for this acti! vity





globe1.png



Flat maps may be easier to carry around, but there is! still a need to make globes so that Earth's geography can be viewed without any directional or spatial distortions. Printing the location of continents and oceans directly onto a round surface would be difficult. Instead, this map of the Earth is printed in flat, roughly triangular sections and then attached to a ball. These sections are called gores.

Make a globe


1. Using a tape measure, determine the circumference of the ball, making sure that the tape measure circles the ball without wandering away from the "equator."


2. On a large piece of paper draw a rectangle the same length as the circumference of the ball. The height of the rectangle should be half the circumference of the ball. Draw an equator line through the center of the rectangle, lengthwise.


3. Cut out the rectangle.


4. Place the rectangle in front of you horizontally. Fold it in half three times. Unfold the rectangle and there are eight equal sections. Draw a line along each fold. Measure the bottom edge of one section to find its midpoint, and mark that point "A." Ma! rk the end of the equator in that end section "B."





globe2.png

Drawing the gores

5. Find the midpoint between A and B as follows: ! Place the compass point on A. Set the compass radius to a leng! th just short of B and draw a semicircle. Maintaining the same radius, place the compass point on B and draw a second semicircle. The two semicircles should intersect at two points. Draw a straight line through the points where the semicircles intersect, extending the line to a point at which it intersects the equator line. Mark this point "C."


The length of the line from A to C is the radius of the gores.


6. Attach extra paper to both ends of the original piece (These extensions should be at least the length of the gore radius) Extend the equat! or line out onto the extra paper at least the distance of the gore radius. This will allow you to move your compass point out along the equator far enough to draw all of the gores.


7. Set the compass to the gore radius (the distance between A and C). Place the compass pencil on A and the compass point on C. Draw an arc from A to the top of the rectangle.


Maintaining the same compass radius, move the compass pencil to the midpoint of the bottom edge of the next section and place the compass point on the equator. Draw another arc in the s! ame manner. Continue moving the compass and drawing arcs for e! ach of t he eight sections.


Turn the paper upside down and repeat the above procedure to draw the opposing arcs and form the gores.


Remove the extra paper from the rectangle.


8. Create grid lines for transposing the map onto the rectangle as follows :


Fold the rectangle as you did in Step 4. Fold once more in the same direction. Unfold the rectangle, and place it in front of you horizontally. Fold it in half, top to bottom, three times. Unfold the rectangle. The rectangle should be divided into 16 sections left to right and 8 sections top to bottom. Cut out the spaces between the gores. Transpose the map from the given to your gores using the gridlines on the diagram and the gridlines (folds) on the gores as a reference.





globe3.png


Taping the gores to the ball, step one

9. Tape the strip of gores at one end of the equator to the ball. Wrap the strip around the ball and tape the loose ends in place, taking care to align the equator line.


Ta! ping the gores to the ball, step two





globe4.png




10. Glue each gore down against the ball so the tips meet to form the north and south poles.

The final globe


globe5.png


Copyright (c) 2000. Gulf of Maine Aquarium.

All rights reserved.


If you got here in solidarity with or curiosity about a certain rather experimental proposal to save the Gulf (and thus our Eath & perhaps our souls) – may I add, the most absorbent card stock might prove best. .... ;)





This is meant to accompany this post .





Be seeing you.



















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point paper template

Algebra Made Easy With Online Tutoring Solution

Math is one subject I'd never had a problem with. In fact, I always enjoy answering every mathematical problems and I even received an outstanding grade of 1.25 in my Algebra subjects. I guess this is also the reason why my kids love their Math subjects too.

But then, Math can be horrible and stressful for most students. Some are already having a hard time understanding their 4th grade math and 5th grade math lessons. This is the reason why some students need tutoring help from their teachers while some others are enrolled in tutorial centers that can assist them in this challenging subject. Luckily, there's an online tutorial site that can assist them with their Math tests and homework problems.

Learning Math becomes easier with TutorVista. It offers free online math tutoring session for any levels from K-12 up to college. Learning the Formula for volume and Adding fractions can be made easy with a guidance from the online tutor. You can even enjoy Graphing linear equations.

College students can benefit from solving intensive Algebra 2 problems - from Quadratic Equations to Quadratic Functions from Linear Equations to Polynomial functions; relations, functions and a lot more.

There's an interactive whiteboard which is like studying face to face with a tutor. A live chat with the qualified tutors can also assists students in Chemistry, Physics, Biology and other subjects as well. Students can make use of this service 24/6, as much as they much and whenever they need it.

With TutorVista, you would surely enjoy your Algebra lessons. Moreover, it will motivate you love learning and get that desired edge in any subject.

online algebra tutor

Do Random Events Happen?

One way to consider random events is by seeing them as events arising where there is no intervention. In the world of mathematical statistics, we have the possibility of a mathematical equation or system of equations that seemingly creates a series or wave forms that one could consider random. People even patent such generators. In the real world, and especially if the cosmos could be considered as a ginormous calculator, we have 'something or somethings' that seemingly generate what appear to be random events. Such random distributions are even said to be normal.

When Being Abnormal is Normal

The science of statistics makes extensive use of the concept of the 'normal' distribution of events that exhibit randomness against which other distributions can be compared. If such a distribution is normal then why or how do we exist? We find that in the normal world, it is perfectly fine to discover events that are not normal. Individually, our very existence is 'not on the chart of cosmic normality." But, then we all realize this.

The Relativity of Normality!

What we find is that normality is relative. W! ithin th e world of human beings that have lived on earth over the past two thousand years, we may think that we are relatively normal, but is that true?

Randomness

To get a random distribution in statistics we collect numbers from some source and we then classify the numbers as somehow meaningful or alternatively is random and without a specific meaning if the pattern or scatter of the numbers against a vector to measure differences produces or does not produce a recognizable 'bell shaped' distribution. When we say something is random, what we usually mean is that we cannot say that there is some relationship between two entities that produced the numbers. This is because we tend to work with associations. We say that there is no relationship between the two entities that is statistically significant. The relationship appears to have no discernible meaning in a statistical sense.

A is associate with B. There appears to be no relationship between A and B as far as a particular characteristic is concerned because we find that the distribution of measures of this characteristic on our frequency number chart is entirely random. We know what random is because we have in mind a statistical formula that produces frequencies that we would consider random.

Fooled by Randomness

The fact is that two things or events might appear to be entirely disassociated and random relative to each other, yet be connected in a meaningful way. We use the world meaningful to describe a relationship of a causal nature whether directly causal or indirectly causal.
The problem is that a relationship can exist between two ! entities that we have not captured because we are not really looking at the true relationship at all. We are blind to the relationship that exists, just as certainly as a blind and deaf person may be unaware of someone sitting on a wooden stool at a bar near them.

To pick up relationships, one needs a lens or something that can detect the waves or relationships between entities.

In our world of sight, sound, smell, taste, feeling, intuition we have an array of tools that measure some but not all of the waves. Our lenses may not detect relationships because we do not see the fields that exist between things or link them. We may not be aware that the relationships come in and out of existence into or within our cosmos following a pattern.

Meaning

We say something has meaning because we know of a relationship. Our next door neighbours may not know of this rel! ationship and would have to admit that the same something has no meaning for them. This is not the same as coincidence, but in coincident events an interpreter or observer might say that several events provide the basis of meaning. Another interpreter may say that the same events have no meaning.

Language of People and the Language of the Universe

For a long while the language of the Egyptians had no meaning to scholars. They tried to understand the hieroglyphs, but could not make sense of them. Suddenly, someone discovered that by using another language found on the Rosetta Stone, it would be possible to gain a meaning of what would otherwise appear to be random scratchings. Well, we knew that the scratchings were not random, but we had no way of interpreting them without the help of the Rosetta Stone.
The Rosetta Stone Puts Meaning into Nonsense or Randomn! ess

In order for one to attain meaning, one needs a Rosetta Stone situation that allows for a translation of seemingly random or nonsense events into patterns that can be read and understood.

Very little is Random

In the Wuh Lax cosmos, there is nothing that is random. What is needed to understand the cosmos are lenses that interpret the waves that exist between things.

normality calculator

STREET LAW: May 26th to June 3rd


This will be the last post for this school year. I have devided it into the final two weeks. I hope you have learned a lot about consumer law and the responsibilities that adulthood bring.

May 26th - 29th: Our focus will be the final chapter of the book, #43, "Working For A Living", pages 542 - 567. We will cover and discuss 8 pages a day as we take time to do our Final Project for this class. You will be given time during class on Tuesday, Wednesday, and Thursday to answer questions on t! he direction sheet. Friday we will have a round table discussion about the information you discovered and your opinions. The final step in the project is a letter to be written for Monday, June 1st. NO LATE PAPERS WILL BE TAKEN AS THEY WILL BE GRADED IMMEDIATELY.
_____________________________________________________________
June 1st - 3rd: FINAL PROJECT IS DUE. In class we will review for our post test on Monday. Tuesday, Post Test and correction. BOOKS WILL BE COLLECTED - DO NOT LEAVE AT HOME!

myskillstutor answers

Frost DW Tank Spec and Glyphs (3.2)

The Case for Dual Wield Tanking
(If you're looking for a rotation, go here)

I've decided to take a small plunge into the world of Death Knight tanking. In fact, this plunge is going to be a very pointed one. We all know that DK's can tank just fine, but I want to dual wield tank. Yes, you heard me, DUAL WIELD. In addition, I want to be a frost dual wield tank. Why? Because it's atypical and fun for me. What more reason does one need?

I want to start by defining the scope of the article. I'm not trying to say DW tanking is better than other tanking, I'm merely making the case that it is equally viable as a form of tanking. Thus, please keep that in mind when reading. I'm not trying to disprove other methods of tanking, only trying to prove mine by association and comparison.

The whole concept of dual wield tanking has been taboo for some time. Ask any seasoned veteran elitist and they'll probably spout off some diatribe about the parry-haste mechanics on bosses. For those of you that don't know, this mechanic is that each time a boss parries one of your attacks, he gains a temporary haste for his attacks, meaning you take more damage. This is why we force melee to the back of bosses (so they don't contribute) and why expertise capping is a must.

Note that I didn't say hit capping there. Hit capping has NOTHING to do with the chance for a boss to parry you. That's all expertise, baby.

Anyways, at first I thought this was going to be an uphill battle, filled with complicated maths to be able to be respected by the otherwise skeptical tanking community. Luckily, Mr. Vick (nothing to do with dogfighting, I'm sure, unless he wants to roll a worgen) commented the other day about a Tankspot discussion that debunks the theory that DW tanking for DK's is completely unviable. I went and found that discussion, read through the whole of it, and what follows now is my interpretation of the data and what it means for DW DK tanks everywhere.

First things first: the spec. 
With the new DW friendly talents that Blizz gave us in 3.2, it's very important to be sure you're specced correctly for any sort of dual wielding. This means basically for DW you must get the following two talents: Nerves of Cold Steel and Threat of Thassarian. You can see if you'd like to click that my 8/53/10 spec reflects these. Additionally, I've taken many of the traditional frost tanking talents.

Now, I mentioned that I thought the DW part was going to be the harder sell. However, I think with the recent nerfs of the frost tree while buffing DW talents, it may in reality end up being the fact that I'm going to be a frost tank and not a blood or unholy tank. Still, while frost may be the least attractive at the moment, there is no obvious taboo on using it as your tank spec. Plenty of people still Frost tank with a 2H. Thus, I'm not going to try to justify the frost part here, this is mainly to address the issue of dual wielding. If you have a problem with frost, that's fine. Just don't give me crap about my DW.

Glyphs
Secondly, it's important to note that I'm going with the following glyphs:
Then, I snatched up two Teldrassil Protectors from the Argent Tournament, because these seemed like a good place to start for 1H tanking weapons. The fact that they have defense and parry is really good for a DK DW tank. Most 1h weapons may waste some points on block, which is obviously useless for us. The rest of my gear is your typical DK tanking fare.

These get me to around 535 defense, which is the heroic defense cap. I'd like to get to 540, which is the raiding defense cap, but I'll need to work on my gear a bit more to get there. I've maxxed out the enchants and such that I can use to help my gear.

Runeforging
Finally, I headed to the runeforge to get my weapons to glow. I was a bit saddened when I learned I couldn't use Stoneskin Gargoyle to bump my defense some more (duh, it's only for 2h weapons), so I slapped one with Swordbreaking and the other with Spellbreaking. It may behoove me later to pick up an enchant for Blade Ward, since from all reports this looks like a good one, especially for DW DK tanks (since we both hit more and rely more on our own parry).

Okay, so now on to the more mathy portion of this post, since I've covered the initial setup.

I mentioned earlier about Expertise and Hit capping. For hit, with the Nerves of Cold Steel talent, we only need to gather a paltry 5% hit. "But wait!" you may say, "I thought DW imposed a penalty that means you need a whopping 27% hit in order not to miss." Yea, I say to you, that is indeed the case for white noise hits. That is most certainly NOT the case for melee based special attacks, where we need 8% (minus the 3% from the talent gives us 5%). Now, we do gain some benefit by going higher, since we rely on spells and they don't cap until 17% (minus 3% gives us 14%)... but you really don't see as much of a threat/dps gain from hit after 8% than you do from stacking other important stats. If you can pick up more, fine, just don't sacrifice better stats for it.

Also, to quote myself from earlier: Hit capping has NOTHING to do with the chance for a boss to parry you.

Like I said, that's expertise. The number we need to shoot for there is 26 "skill" (not rating). This is the so-called Dodge Cap. The prolific Splug from the tankspot forums explained it pretty well and was venerated by his peers, so I'll quote him:

"Getting over the 6.5% dodge cap [26 skill] is very efficient for threat, and by that point the parry-haste contribution becomes overshadowed by the raw avoidance gains from dual wielding tanking weapons [Splug]."

Yes, therein lies our first right hook at the jaw of the DW parry-haste myth. You see, one of the benefits of dual wielding is an increased contribution by your extra weapons to avoidance in the form of more parrying. Thus, it is argued that at the dodge cap, your expertise is enough to minimize the amount the boss is parrying you, while granting you enough avoidance that you reach a tipping point where the boss mechanic is overshadowed by your avoidance. Yes, that is just a restatement of the quote above, but it is an important point not to miss. This is one big feather in our cap for the viability of DW tanking.

Now, we can get more expertise, which will further decrease our chance of being parried as well as help with threat generation, but once we get to this cap, we should again not sacrifice other essential stats. This is just another benchmark similar to hit capping that we want to hit prior to throwing ourselves out in LFG saying "hey, I can haz tank!"

Along this line, we need to remember that we'll be parrying a bit more ourselves with two weapons. The increase in parry for a dual wield tank is significant not only for avoidance, but also for threat generation. Remember, parry doesn't suffer from diminishing returns like many other stats, and DK's start out with more than our fair share of parries anyways.

What does this mean? Well, recall that DK tanks have an ability called Rune Strike. This is the very cornerstone of DK tanking. Check it out via that link if you haven't heard of it. It is important to note that not only is it high threat, but it is also activated every time we parry an incoming attack. Didn't we just say that a DW tank will be parrying a lot more do to having more parry and an extra weapon (more attacks)? Why yes, we did. Quite simply, this means we'll be doing more Rune Strikes than our 2H counterparts.

Let me assure you that Rune Strike seems to proc almost constantly when you DW tank. I just tried it this last weekend in a heroic, and was amazed at how often that button lit up. I basically had to press it between each spell/special cast. If you've read that tooltip or are familiar with the ability, you also know that Rune strike is both UN-parriable AND it replaces parriable white noise attacks. Thus, not only are we increasing threat generation by DW, but we're also decreasing that nasty parry-haste mechanic contribution even further.

If the above is not enough to convince you, lets put this in a little perspective. After all, a DW DK tank is probably still going to be parried more than a 2H DK tank, if we're comparing apples to apples. Let's bust out the oranges though! That is, lets look at another flavor of tanks: Warriors. They have to deal with the same parry-haste mechanic we do.

Again, it was done better in the tankspot forum discussion, so I'll quote the enlightening and math-centric Satorri (2S is two slow weapons, 2F is two fast weapons, 1S is one slow two-handed weapon, just FYI... warrior is your typical warrior tank):

"So let's adjust the table from above [which did not take into account replacing white attacks with Rune Strikes]:
#attacks  #parries(no Exp) #parries(26 Exp) Warrior =     72       10.1             5.4 DK-2S =       58        8.1             4.4 DK-2F =       80       11.2             6.0 DK-1S =       31        4.3             2.3
So, notice now that while you will get more parriable swings, and more parries with dual wielding than a 2-h as a DK, DK's also start way ahead of the curve for parriable attacks, and in fact, dual wielding tank weapons can only marginally increase your risk of parry-haste over that of a warrior with the same Expertise. And after expertise we're nitpicking on half an actual parry (which is only relevant in a giant number statistical average) [Satorri]."

So what's the point here? Well, I haven't noticed any Warrior tanks being shunned from groups for parry-haste mechanics, nor has that mechanic been a particular problem for them. Yet, DW tanking for DK's is on par with warrior tanking when it comes to the same mechanic. Sure, 2H DK tanking may be better from a very selective perspective, but DW tanking has it's own perks as well (more parries, more avoidance, more rune strikes... the threat may end up being a wash since you hit harder with 2H weapons, but more often with two weapons). Also, I'm not trying to answer the question of if DW tanking is better, only if it's viable. I'm trying to debunk the myth that DW tanking suffers from too much parry-haste. Clearly, I think I've shown that it is just that... a myth. So, to answer the question...

Is dual wield Death Knight tanking viable in the 3.2 World of Warcraft?

My answer is an emphatic: Yes.

(Edit: I tried to clean this up a bit to make it easier to browse.  Also, if you're looking for more... I go into detail about my rotation and such things here.)

maths is fun tanks

Factoring the time

I stumbled upon this comic that you might enjoy... factoring the time (from xkcd.com).


math help online

Tutorials: Identifying Quadrilaterals!


In our polygon unit we are learning about four-sided figures called

QUADRILATERALS!

Many people were confused about why some shapes have more than one name. Here are some tutorials to help you learn about quadrilaterals.

*     *     *     *     *
What is a parallelogram?







Here is an interactive parallelogram.


*     *     *     *     *


What is a rectangle?



Here is an interactive rectangle.


*     *     *     *     *


What is a rhombus?




Here is an interactive rhombus.


*     *     *     *     *

What is a square?









Here is an interactive square.



*     *     *     *     *

Have you used our quadrilateral tutorials? 

Which one helped the most?
Please leave a comment by clicking the comment link right below this sentence.

list of quadrilaterals

Trading Creatively: Finding New Niches as a Trader

A while back I wrote six pieces of advice for new traders. One additional piece of advice that I would offer is to be creative in finding markets and strategies to trade.

If you were starting a new business, you wouldn't necessarily select an area that is loaded with competition. You would find a business niche where demand is not fully met; where there is potential opportunity.

Interestingly, new traders often gravitate to the most common and popular strategies and markets, such as the directional trading of stock indexes. Rarely do traders venture outside their national boundaries (especially in the U.S.), and rarely do they look into strategies at different time frames, non-dir! ectional strategies, and strategies across asset classes.

One trader I met recently collected extensive information on world trade and used this (along with other information) to trade calendar spreads in commodities. He has been unusually successful, using reasoning processes that are quite different from the norm.

I encourage traders to never stop exploring markets and strategies. There is always room to grow. Those who develop new opportunities are best positioned for those occasions in which current sources of edge start to go away. It is great to find a niche as a trader; even better is to continually develop fresh niches.
.

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Online math help

Here I found another interesting a site that provide online math help. If you are looking for help on your math lesson, Guaranteach might suit your need.  They have more than 20000 lessons that you can access. The interesting part is, this lesson is in video format. Another interesting fact is that they provide some interesting method to detect your learning style. This of course will be great advantage for you, you can maximize your learning process by learning on your own style. Don't worry about the quality of the tutorial, the lessons is teacher approved and more importantly, you can access it whenever and wherever you want it. Don't ruin your math learning because you're shy to ask a question in the class. With those thousands online tutoring that Guaranteach has, I ! believe you will overcome your difficulties on math lesson.

Did they provide video only? No. This is getting more interesting about Guaranteach service. Like a normal class-teaching, they also has quizzes and progress report. Isn't it great? Now, you can measure your learning progress just like normal without exposing your result to your friend (well, honestly, I, sometimes got bad mark on math that I really really shy on it -- being laughed by my classmates). Before applying for their service, you may try it for free. They provide up to 5 lessons videos that you can watch, so you know how's their lessons quality. The registration is quick and no need for credit card (obviously, most of us -- student -- didn't have any credit card yet). Go try them out!


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Pi-Squared Over 6: The Algebraic Genius of Euler

Yes, Pi Day 2010 is "history" unless of course you celebrate July 22nd! Then again, Ï€ is so universal in our world that "All Ï€, All The Time" seems appropriate to me. That was a long-winded way of motivating a post about one of the most famous formulas in mathematics:

1/12 + 1/22 + 1/32 + 1/42 + ... + 1/n2 + ... = π2/6

The videos below were inspired by one of my most faithful readers, Prof. Jablow. He brilliantly outlined Euler's derivation of the above formula in one of his comments.  I decided to develop it in more detail and provide some background for the younger student. Advanced middle schoolers through undergraduates in college may find this interesting. You might also want to share it with your math team/club.  The 2-part video presumes strong algebraic background and some knowledge of calculus although the latter is not necessary if you simply accept the well-known series expansion for sin(x). You may also find background and details in the excellent Wikipedia article, The Basel Problem.

As always, I add my disclaimer that I am solely responsible for any errors. I know there are a couple of errors in Part II, towards the end. They're pretty obvious and not serious, so I hope they won't ruin it for you! I invite you to comment on these videos both here and on my new YouTube channel, MathNotationsVids.  Of course, as I am finishing this post on 3-25-10 in the AM, YouTubew is down apparently worldwide, so I cannot embed these videos yet!!

Part I of Euler Video



Part II of Euler Video





FURTHER INVESTIGATION
Although the material on infinite series seems quite advanced, middle schoolers can use their graphing or scientific calculators to compute the sum of the first 10, 20, or even 50 terms of the series above. A simple program can also be written on the graphing calculator for summing the first n terms up to, say, n = 500 or 1000. Challenge them to see how "close" they can get to the decimal value of π2/6...
---------------------------------------------------------------------------------------------------------------------

"All Truth passes through Three Stages: First, it is Ridiculed...
Second, it is Violently Opposed...
Third, it is Accepted as being Self-Evident."
- Arthur Schopenhauer (1778-1860)


You've got to be taught
To hate and fear,
You've got to be taught
From year to year,
It's got to be drummed
In your dear little ear
You've got to be carefully taught.
--from South Pacific




factoring quadratic trinomials calculator

Factoring the time

I stumbled upon this comic that you might enjoy... factoring the time (from xkcd.com).


free math help

Free algebra worksheets

Usually algebra textbooks provide lots of problems to practice the algebraic concepts and techniques, but some of you may still benefit from resources for free (or mostly so) printable algebra worksheets. Please see the list below, which I've originally compiled for my HomeschoolMath.net site.

Algebra worksheets

Worksheet Builder
Great and free worksheet maker software with nearly 7,000 built-in algebra and geometry questions.
www.jmap.org/JMAP_WORKSHEET_BUILDER_INSTALLATION_FILES.htm

Free Algebra Worksheets from KUTA Software
Free worksheets (PDF) for equations, exponents, inequalities, polynomials, radical & rational expressions and more.
www.kutasoftware.com/free.html

AlgebraHelp.com worksheets
Interactive worksheets that are checked online for most algebra 1 topics.
www.algebrahelp.com/worksheets/

Math.Com algebra worksheets generator
Generate worksheets for: linear equations, systems of equations, and quadratic equations.
www.math.com/students/worksheet/algebra_sp.htm

LessonCorner worksheets
These free worksheets include a few topics such as calculations with polynomials, factoring, and graphing lines.
www.lessoncorner.com/worksheets/

Algebra Fun Sheets
Worksheets that integrate algebra skills with fun activities including sudoku, word finds, riddles, color patterns, crosswords, games, matching cards, etc. A subscription is required.
www.algebrafunsheets.com

About.com Algebra Worksheets
An assorted collection of free algebra worksheets and answers. These pages are not very well organized, but they have lots of worksheets.
math.about.com/od/algebraworksheets/Algebra_Worksheets.htm

Algebra Worksheets from MathWorksheetCenter
Lots of worksheets for over 100 algebra topics. A few are free; most are accessible only by one-year a subscription.
www.mathworksheetscenter.com/mathskills/algebra/

A few fun algebra worksheets
These are for graphing linear equations and linear inequalities.

Online Math Work
Free multiple-choice worksheets for pre-algebra and algebra 1 topics. You can do them online, or copy to a word processor to print.
www.mathonlinework.com




Lastly... my own algebra worksheet collections, which aren't free but there are many free samples:

Algebra 1-A worksheets cover Algebra 1-B worksheets cover Math Mammoth Algebra 1 Worksheets Collection
A two-part collection (A and B) of 137 quality algebra worksheets covering all the topics in a typical algebra 1 curriculum. These worksheets are hand-crafted and contain lots of word problems and other variable problems. Free samples available. $11.50.
www.mathmammoth.com/worksheets/algebra_1.php


Summer Math Program


free algebra 1 help online

Soy Biodiesel Review

The topic of discussion is Sheehan, J., V. Camobreco et al. (1998) . Life Cycle Inventory of Biodiesel and Petroleum Diesel for Use in an Urban Bus. Golden, National Renewable Energy Laboratory. It's a big, inclusive report (314 pages) on the the energy balance of soy derived biodiesel and fossil diesel.

Energy Return

Let's start on p. V of the executive summary:
Biodiesel yields 3.2 units of fuel product energy for every unit of fossil energy consumed in its life cycle. The production of B20 yields 0.98 units of fuel product energy for every unit of fossil energy consumed.
That first number, 3.2 units of fuel product energy for every unit of fossil energy. What does this mean? It's in a big bold block quote in the executive summary. It looks like the EROEI, rig! ht? Unfortunately it's not. On p. 207 we find that Fossil Energy Ratio = Fuel Energy/Fossil Energy Inputs. In other worlds, any power input that is not a fossil source is not accounted for. For the purposes of this study, this means the hydroelectric and nuclear power share. What we actually want to know is the total process energy required. The energy inputs for biodiesel are predominately electricity (to run machinery) and low grade steam (50 - 70 °C), along with natural gas (to produce methanol) in addition to the standard farm inputs.

Fortunately, the results are not that badly off due to this factor. The study divides the production of biodiesel into five stages:
  1. Agriculture
  2. Transport from farm to processing plant
  3. Soybean crushing and oil separation operations
  4. Conversion of soy oil to methyl ester fuel.
  5. Transport and distribution of biodiesel to consumers.
  6. The study also accounts for transport from the separation p! lant to the conversion plant but this energy input is left out of the end results. I agree with this because it is overly high due to the small number of biodiesel plants in the USA at the time of the study. For large scale biodiesel production the two operations would be naturally collocated.

    I went through the study to attempt to figure out what the difference was between fossil and absolute energy inputs. Annoyingly, for Stage 4 (Conversion), the energy of the soy oil is incorporated as an input. What makes this frustrating is that the authors at no point in the study actually define what they consider the energy content of soy oil to be, which makes deconstructing this part of the study difficult.

    Table 1: Energy Allocation to Biodiesel Production Stages
    !

    Activity

    Energy

    (MJ/kg biodiesel)

    Source

    Agriculture

    3.158

    Table 62, p. 116!

    Transport

    0.162

    Table 63, p. 118

    Separation

    3.471

    Table 83, p. 137

    Conversion

    5.572

    Table 105, p. 166

    Distribution

    0.162

    Table 106, p. 169

    Total

    12.526


    Higher Heating Value

    40.6

    Table 108, p. 173

    Lower Heating Value

    37.0

    Table 108, p. 173

    ERR (HHV)

    3.24



    As it happens, I get a better result (3.24 > 3.2) but that's due to the fact that I employ the Higher Heating Value -- the original authors' calculation uses the LHV. As it happens, this is only a minor bone I have to pick with the study. The big problem is with what's called "Allocation of Lifecycle Flows." Anyone who has read into ethanol studies will know this as 'coproducts'.

    Funny Coproduct Accounting

    The first giant problem associated with 'coproducts' appears in the Separation (or crushing) stage. The oil content of soybeans is rather low − around 18.4 %. For this entire study, allocation of energy consumption between biodiesel and coproducts is done purely on a mass basis. Unfortuna! tely, this leads to a silly assumption. Table 82 (p. 136) allocates 18 % of energy consumption for the Separation stage to soy oil and 82 % to meal. This in turn propagates back through the allocations for transport and agricultural energy consumption. Is this fair? Take a look at Table 64 (p. 121):

    Table 2: Mass composition of soybeans

    Oil

    18.4 %

    Dirt

    0.8 %

    Hulls

    7.4 %

    Water

    16.0 %

    Meal

    57.4 %


    That's right boys and girls, the authors are allocating the same value to oil as dirt and water. Realistically if the mass of dirt, water, and hulls were discarded then the oil would have to assume 24.2 % of energy use for the first three stages. Furthermore, it probably makes more sense to compare the ratio between the wholesale price of soy oil versus soy meal to determine the proper value of the coproducts. Free hint: the oil is worth more per kilogram than the meal.

    This process is repeated for the Co! nversion stage is similar for the allocation between methyl es! ter (bio diesel) and glycerin. For this stage, 82 % of the energy is allocated to biodiesel and 18 % to glycerin. Once again this allocation is propagated back through the previous steps. However, this calculation is actually unfavourable to the biodiesel. Separating the glycerin and excess methanol consumes approximately 65 % of the energy for the Conversion stage (Table 96, p. 159). The reason is distillation. As anyone who has looked at ethanol systems will know, distillation is a killer because it requires so much energy to vapourize water. Also, the NREL numbers come out quite high compared to some European plants also presented in the report.

    From my point of view, I want to know if biodiesel is energy positive, regardless of coproducts. For soy, the answer appears to be no. Going back and removing the coproduct credits appears to give the following results:

    Table 3: Energy Consumption for Biodiesel Production
    with Zero Coproduct Credits

    Activity

    Energy

    (MJ/kg biodiesel)

    Agriculture

    21.40

    Transport

    1.10

    Separation

    23.52

    Conversion

    6.80

    Distribution

    0.20

    Total

    53.01

    ERR (HHV)

    0.766


    Before we all fall into a state! of depr ession, it is fairly clear from the report that there is a lot of promise in reducing the energy inputs for the conversion stage. Methanol inputs constitute approximately half the energy inputs. I have previously hypothesized that anaerobic digestion of the meal could produce methane which in turn could be made into methanol in addition to providing heat energy. The NREL numbers require approximately three times as much energy as some quoted European operations (Table 98, p. 161).

    There are potential improvements to be made to the efficiency of the Conversion stage as well. Research and development on catalysts offers the potential to reduce the reaction temperature. In particular I think a zeolite could be ideal for separating the glycerol from the methyl ester chains. Most of the energy (65 %) is used not for the actual conversion but for distilling out glycerin and excess methanol post-transesterfication − normally an excess of methanol is added to! carry through the reaction to completion. Reducing the amount of water and methanol used will have a direct result on the distillation requirements.

    Like ethanol, biodiesel would benefit significantly from combined heat and power generation. The temperature requirements for most processes is low enough (50 - 70 °C) that the use of solar thermal systems to augment the heat production is feasible.

    To a certain extent glycerin might be the biodiesel analogue to sulfur for petroleum oil. Sulfur is a chemical with its uses, but oil refining produces mountains of the stuff. Will glycerin be a product worth distilling in a biodiesel nation, or should it just go into the anaerobic digester to make more methane?

    Soy versus Rapeseed (Canola)

    Any way you cut it soy is not an ideal crop for biofuel production. Soy does have one significant advantage in that it's a legume and hence fixes atmospheric nitrogen. As su! ch, the energy requirements for fertilizer for soy is very low! compare d to everyone's favourite biomass villain, corn. However, the foremost quantity on my mind is the low oil content of soybeans. It's about 18 % (Table 64, p. 121) versus 40 % for rape and jatropha or 70 % for coconut. Rape appears to be the best temperate crop for biodiesel production. Its oil quality is high as its content, and its moisture content low.

    The NREL study uses an average yield of 36 bushels/acre for soy which works out to 445 kg (oil)/hectare. (Here is a useful webpage for converting agricultural units from US Customary nonsense to more sensible metric units. Oh, and soybeans are 60 lbs./bushel, not 56 or 48 or 25 lbs./bushel but you all knew that, right? Next thing you know they'll be measuring the volume of biodiesel in barrels.) In comparison! Canadian Canola yields about 640 kg (oil)/ha. The same source gives European Rapeseed a much higher yield of approximately 1280 kg (oil)/ha, largely due to the greater use of irrigation.

    Aside from the oil content issue there are a number of other drawbacks for soy. For the most part, soy appears to take a great deal of work to get the oil separated from the meal. Soy has a high moisture content of 16.0 % water by mass (Table 64, p. 121) which necessitates drying.
    In comparison, Canola is about half that if properly sun dried, and hence can be processed without drying. Soy also needs to be flaked into regular sized small pieces, which constitutes about a quarter of the electricity requirements for the Separation stage.

    entropy values table

Strategies to solve simple math equations

What are the strategies for solving simple equations?

I got this question in the mail just today.

I assume the person means LINEAR equations - those where you only have one variable (usually x), and that x is not raised to second or third or any other power, nor is it in the denominator or under square root sign or anything. Just x's multiplied by numbers and numbers by themselves, such as:


2x - 14 = 9x + 5

OR

1/3x - 3 = 2 - 1/2x

OR

2(5x - 4) = 3 + 5(-x + 1)

Here are the strategies for solving these:
* You get rid of paretheses using distributive property
* You may multiply both sides of the equation by the same number
* You may divide both sides of the equation by the same number
* You may add the same number to both sides of the equation
* You may subtract the same number from both sides of the equation

You might think, "W! hich one of those will I use, and in which order?"

That depends. There is no clear cut-n-dried answer.

Whatever you do, you try to transform your equation towards the ultimate goal: where you have x on one side alone. Also whatever you do, your goal is to transform the equation to one that you already know how to solve. It might take several steps.

For example, your first step with these equations, could be to...
1/3x - 3 = 2 - 1/2x... multiply both sides by 6 to get rid of the fractions
2(5x - 4) = 3 + 5(-x + 1)...multiply out the parentheses
2x - 14 = 9x + 5...add 14 to both sides (or subtract 9x)
1/4(2x - 27 + 0.5x) = 2/5(8x + 3)...multiply by 20 to get rid of the fractions

As with most things, practice makes perfect. ! Check also the websites below:

Tutorial on linear equations has a 4-step strategy for solving linear equations which summarizes it real well.

Algebra 1 Review - Solving Simple Equations - a step-by-step slideshow.

Ask Dr. Math ® - Solving simple linear equations - lots of examples to read here.


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distributive property equations

Chemistry and Christianity

Chemistry is a bit of mystery to me. I did fairly well in high school in most subjects even without the discipline of study (a habit I would rue in college) until I met chemistry. I decided to monitor the class during my lunch hour since my schedule was already full of things like calculus, physics, mechanical drawing and other fascinating subjects. I sat there daily for a whole semester trying to grasp the concepts of the atomic chart and what it meant in combining elements to form new exciting compounds that would make the world of tomorrow a better place. I never got it. It was beyond me.

I did realize however that those who do get it go on to become highly paid professionals (as opposed to myself) who specialize in creating formulas that bring exciting new applications to this life. It is the formulas that fascinate me. Someone carefully writes down the exact process and steps that combine this element with that element under these specific conditions leading ! to a new creation. It is so exact that anyone can later upon discovering these notes duplicate the exact same creation. This science is duplicatable and because it is a science, it will guarantee the original results every time.

The results benefit all of us who take prescription, drink from plastic containers, nuke our food, drive our cars, and pretty much engage in everything else in our world. Formulas rule our world, or at least a good portion of it. It is the crowning achievement of the Industrial Revolution and the trademark of our modern enlightened culture.

You might say we are a formula driven society. We engage in the dating world by inputting our personalities into computer data banks that in turn crank out a dream match for our future spouse based on formulas. We have seven habits to being highly successful people. We have a ten step formula to making children mind without losing ours. We have formulas for better marriages, better sex, an! d better sex in marriage. We have formulas for attaining wealt! h, achie ving our goals, and getting the corner office. We have formulas that make government the solution to our problems and formulas that promise us that less government is the solution to our problems. We even have four spiritual laws that formulate how to get to heaven.

Is everything in life a formula? What about the computer matched perfect spouse who turns out to be a wife beater or control freak? What about people who just aren't that gifted to begin with and can't make the seven habits stick? What happens when less government fosters unbridled greed that almost bankrupts a nation? What happens when the government program only adds to an already bloated bureaucracy that moves ever closer to financial Armageddon?

It seems to me that formulas work in science but rarely work in matters of life. Life as God designed it is more complex than the atomic chart and thermo-dynamics. If your formula gets you to where you want to go in life, it probably created a tr! ail of broken pieces and sacrificed people or values along the way.

Perhaps most devastating in all of this is the notion championed by the Christian Community that things relating to God can some how be put into a formula. Sacramentalism when adhered to will repeatedly upon execution produce God's intentions. Liturgical readings and common confessions will repeatedly upon execution produce relationship with God. The Evangelicalsim's sinner's prayer upon recitation will guarantee entrance to heaven. Is this what it has all come down to?

We argue about and base fellowship upon whose formula is correct. The Sacramentalist declares their formula is correct having been discovered by the early Church Fathers through oral tradition. Their formula is 2,000 years old without interruption and if nothing else, longevity must stand for something. If "we are wrong, the masses throughout history are doomed and these consequences cannot even be considered." The Lit! urgist declares their formula correct because the Reformers di! scovered the error in the formula some 500 years ago and fixed the problem. The Evangelical knows that their formula is correct because its "in the Bible." They have 23 verses in scripture to prove it.

But the proof of any formula is always in the product. The most complex formula on a blackboard may be impressive to the uninformed mind, but if it doesn't produce a higher quality of plastic when executed, it is just hieroglyphic arrogance meant to impress. So I ask where is the product...the fruit that our post-modern expressions of the beloved faith are allegedly producing? It is time to ask God to forgive us for our theological arrogance.

God is beyond formula. Relationship with Him cannot be reduced to four spiritual laws or an entrance-level prayer. The passport to heaven cannot be easily stamped and the bus ticket to the Kingdom costs more than prayer. The God who sovereignly chose Abraham for indescribable blessing was also the God who called for him to p! lace his son on an altar of sacrifice. The Jesus who invites all the weary and burdened to come and receive his restful yoke is also the who sits on the throne before whom everyone must stand and give an account. The One who says "Come" also says "Depart". God is beyond formula and our attempts to reduce Him to our formulas are beneath His high calling to be His people showing forth his excellencies to the world around us.

The treasure that we discover in Christ is such that for joy we sell all we have to secure the field wherein the treasure lies. There is no formula for this. It is a matter of heart and soul. It is a matter of devotion and commitment. It is a matter of relationship that is to be sustained through His grace until the end. It is a matter of life with the Creator outside of a labratory in a Kingdom that is permeated by righteousness, peace, and joy in the Holy Spirit. There is no formula for that.

chemistry formula chart

Power Transformer Basics and Important Factors

Power Transformer Basics
By Andrew Peter

Transformer is an electrical machine so as to transfer power commencing one circuit to a different by transformer attractive combination through no affecting parts. Transformer comprise of two or supplementary attached windings otherwise a single tap windy and, in most cases, Transformer a magnet, the category of the magnet cover all method of strategy intended to create, conduct, straight, exchange otherwise defend the abuser from electrical liberation.

Most important produce families contained by electrical and electronic mechanism consist of batteries, connectors, inactive electronic mechanism, electrical allocation and defense gear fuse! , supremacy supplies and conditioners, relay and timers, switches, rush forward suppressors, and wires and lead. Batteries are strategy that exchange power into electrical current Batteries is worn in a broad range of engineering application to power electronic strategy.

In attendance there are two main sequence types - chemical and physical Battery related trimmings and mechanism such as chargers, racks and cabinet are also enclosed in this segment Connectors consist of all method of plug, socket, cap, strips and conductors considered to connect and demeanor electrical energy throughout cords, wires, and appliance, over and above, whole electrical allocation system.

Electrical supply and protection apparatus include items such since circuit breakers, surge suppressors, fuses and safety switches designed to shut-off electrical current when a machine, arrangement or indivi! dual is in danger due to electrical flow or fleeting in excess! of volt age Authority provisions and conditioners cover up an extensive array of electrical as well as electronic mechanism that create, or exchange electrical energy.

Andrew Peter is an author of CustomPowerTransformer.com ,one of the worlds
MOST popular company for selling power transformer inductor, current transformer
electric transformer and voltage transformer on the
web. He writtern many articles about step up transformer,electrical
transformer, toroidal transformer etc. Contact him at andrew.seocopywriter@gmail.com

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Important Factors That Determine Power Transformers
By Nisha Sabbik

A transformer is an electrical device designed to transfer alternating current or voltage from one electric circuit to another by means of electromagnetic induction. It is designed based on step up and step down voltages. To select the right transformer you should remember certain things like the primary voltage and secondary voltage that is required, the capacity that is required in volt amperes. Other things include seismic requirement, impedance, secondary voltage or delta-wy! e, location and space requirement, case style etc.

< span style="font-family: arial;">Voltage is different in every country like in U.S.A and Canada it runs on 110/120 and rest of the world runs on 220/240 and industrial plant may use 440 to 480. Most utilities will provide a customer with one service or electrical system. You may wonder why anyone would need a transformer. Let's say a new industrial plat comes in town. They have many motors in use at their company so they requested a 480Y/277 volts three phase system. This takes care of their motor load at 480 volts and their office and plant lighting loads at 277 volts. However to operate their office machinery and incandescent lighting they require 120 volts. They also have some small horsepower motors they want to operate at 208 volts. Since the utility will only provide them with 480Y/277 volt three phase system, they require a transformer to provide the rest of there needs. A buck boost transformer is the ideal solution for changing line voltage by small amounts. Single ! phase transformer is mostly used in rural areas. These are used in rural areas because the cost of three phase transformer is high and motor loads are small. In shopping centers, factories, large buildings three phase transformers are used. The incoming electric transformers voltage is an important factor. The three important frequencies are 50 Hz, 60 Hz and 400 Hz. 400 Hz is reserved for high-powered applications such as aerospace technologies.

Transformers are highly efficient. A large power transformer has efficiency as high as 99.75% and small transformers have less than 85% efficiency. When you overload a transformer excessive temperature can cause overheating which result in rapid deterioration of the insulation and cause complete failure of the transformer coils. Thermometers are the best way to determine the temperature. Touch is a poor indicator of proper operating temperature for transformers. Properly designed t! ransformers can reach 50 degree Celsius above ambient temperat! ure. In an ambient temperature of 20 degree Celsius, the total temperature can reach 70 degree Celsius, which is too hot to touch.

For harsh environments, whether indoor or outdoor, it's critical that a transformer's core/coil, leads, and accessories be adequately protected. Dry-type transformers are available for either indoor or outdoor installation.

Nisha is a Copywriter of electronic transformer. She written many articles in various topics.For more information visit: power transformer. contact she at currenttransformer@gmail.com.

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basics of factors