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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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