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Mathematical Analysis
Mathematical analysis is, simply put, the study of limits and how they can be manipulated. Starting with an exhaustive study of sets, mathematical analysis then continues on to the rigorous development of calculus, differential equations, model theory, and topology. Topics including real and complex analysis, differential equations and vector calculus can be discussed in this category.
2,575 Questions
How many 600mm x 600mm slabs do you need to cover 55 sq meters?
You will need a minimum of 153 slabs. However, that answer assumes that the area to be covered is "well behaved" and that you are happy to use offcuts and chippings so that part of the area will look like a mosaic. If these conditions are not met, you should consider getting 5% extra slabs.
If, for example, the 55 sq metre area is in the form of a rectangle which is 550 mm wide and 100 metres long it may be easier to cover it using 167 trimmed slabs in a long line rather than use offcuts which are 5 mm wide.
How many smarties can fit in a jar?
The diameter of a Smartie is 1cm so so r = .005, and its height is 4mm. With negligibly concave ends, the volume of a smartie is pi (5E-3)^2*4E-3 = pi*1E-7 m^3. A 16 oz jar where 1 oz ~ 30 ml, 1 jar ~ 0.5 L = 10cm x 10cm x 4.8cm = 4.8E-4 m^3. Circles pack hexogonally into a square area with an optimal density 1/6 pi root 3 which is approx 0.9069. Figure a random packing is about 10% less than optimal, shaken and settled gives a density more like .82 of the volume. If this is a good assumption, then 0.82 * 4.8E-4 / pi*1E-7 = 1253 smarties / 16 oz jar.
In what time will 2700 yield the same interest at 4 per annum as 2250 in 4 years at 3 per annum?
Oh, what a lovely question we have here! To find the time it takes for 2700 to yield the same interest as 2250 in 4 years, we simply need to compare the interest rates. Since the interest rates are different, we can use a formula called the "interest formula" to solve for the time needed. Let's embrace the joy of solving this together!
When does the mass of an object affect the time of its free fall?
Without air, it doesn't. All objects accelerate in free fall with the same acceleration.
If they're dropped from the same height above the surface of the same planet at the same time, they hit the ground at the same time. If any difference is noticed,
it's strictly the effect of air resistance. Try it in a tube from which the air has been
pumped out, and a feather and a bowling ball really do fall together.
If there is an atmosphere thick enough to produce aerodynamic drag on the object in free fall, then a frictional force will develop in the opposite direction of the objects movement. Terminal velocity occurs when the reactionary drag force and the force due to gravity are in equilibrium. Since a more massive object with the same aerodynamic properties is driven by a greater force due to gravity, it will need to travel faster than a lighter object to acheive an equilibrium in the reactionary drag force. This means the more massive object achieves a higher terminal velocity and reaches the ground faster.
If there is no air resistance, it doesn't. However, the size can alter the aerodynamics, providing more or less air resistance.
How do you turn a thousand to one million by trading?
There are A WHOLE LOT of books abuot trading. You can do a google search to find out what the titles are and where to buy them. As far as getting an answwer in this forum is concerned, the chances of having someone provide you with THE answer YOU are looking for is very remote. I'll give you my opinion and what I'm doing - along with hundreds of thosands of others. You'll have to come to your own conclusions. In the beginning "newbie" traders & investors DO NOT INVEST any money. It probably won't be long when you'll feel you're ready to invest your hard-earned money. Before taking that step, you really should do research about what you are investing in. You should LEARN HOW: A] the stock market works. B] to invest in many, many various ways. C] to properly trade D] Properly manage the money in your trading account. "Newbie" investors & traders ALWAYS make mistakes. In fact, throughout a person's trading hobby, avocation or career, he/she makes mistakes. In the beginning, you READ & LEARN about the market & how it works: Read "Investing for Dummies" As you read & do research about the investments you are interested in, sometimes you'll come across a financial or investment term you never heard before. Use an on-line investing site or an investment dictionary. There are also free sites where you can set up a virtual account & almost trade as though you were trading with real money. Since Google is providing the ads for this site, you can do a google search for those. There are quite a few of them. You might want to try a few different virtual trading sites, THEN make your selection. A SIMPLER WAY TO TRADE:
This is what I learned about the stock market and trading:
1] I read a little about the overall market and how it works. I read about different aspects: mutual funds, currency, commodities, stocks and options.
2] I asked Qs of my coaches and mentors; suggestions were made to me.
3] THEN I read and studied about those areas which interested me.
4] I concentrated on those areas which interested me and which fit the amount we had to work with.
5A] For those strategies I felt comfortable with, I developed trading rules. For those strategies I didn't know anything about, I developed some trading rules.
5B] I discovered I only needed trading rules for 4 to 6 trading strategies.
6] Using those rules, I paper traded.
7] When trades went against me - when I lost money - I adjusted or "tweaked" those rules for that strategy.
8] I paper traded - again and some more.
9] I made further adjustments.
10] I'll admit I didn't do enough research for the right broker for our trading needs, wants or desires. However, the one we decided to go with is OK - but not the greatest AND definitely not the least expensive. Yet, the actual trading account was opened:
As a speculator, with margin, with the approval to trade options.
11] Yes, it was VERY scary AND I was VERY apprehensive: BUT, I MADE THE BIG JUMP: Going "live" - in-the-market - with real money. I lost some money. NO ONE ever succeeds in each and every trade 100% of the time.
BUT I didn't use the entire amount of the account's money on one trade. I learned AND I lived to trade another day. AND I continue learning and living to trade other days.
AND YES, I STILL have some losing trades. BUT my winning trades are A WHOLE LOT more than the losers.
What are the multiples of 6 from 1 to 5733?
6, 12, 18, 24, 30 and keep adding 6 nine hundred fifty more times till you get to 5730.
It's money. The eurodollar, usually called the euro, is the standard currency in most of Europe. Seventy euro is, well, seventy euros.
What is the formula of exponegtial decay?
The general form is y(t) = a + y(0)*exp(-bt)where y(t) is value of the variable at time t.
the starting value is a + y(0) and the asymptotic value (as t -> infinity) is a.
Why do we find the limit of a function?
Typically, it's to give you an idea of a function graphically. Sometimes you deal with functions that are really hectic in design and they don't really have all the points smoothly in place (for example, a graph with an empty point or ^, a peak). A limit gives you an idea of what's happening with the graph as you get close to that point or area (as with infinity not being an actual point), hence the "as x approaches N," N being either some number, or negative or positive infinity.
The decimal shows a repeating pattern. Repeating decimals are rational.
What is the roles of roman numerals?
Roman numerals were fully developed during the Roman Empire, as the Roman Empire had a large amount of territory; numbers was required to measure and control the immense and vast territory. The Romans made use of Roman numerals, which was based primarily 7 letters which composed the Roman numeration, the Romans assigned values to each letter corresponding to each of the following values: I is 1, V is 5, X is 10, L is 50, C is 100, and D is 500and M is 1,000.
