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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 much does 1.844674407x10 to the 19 power weigh?
The weight of an object is typically measured in units such as kilograms or pounds, which are units of mass rather than numerical values. The number 1.844674407x10^19 does not represent a weight on its own, but rather a large numerical value in scientific notation. To determine the weight of an object, you would need to know its mass and the acceleration due to gravity in the specific context.
How many times does 6 go into 70 equally?
Well, isn't that just a happy little math problem! If you take 70 and divide it by 6, you'll find that it goes in 11 times with a remainder of 4. Remember, it's okay to have a little leftover - just like adding a touch of color to your painting to make it unique!
What is the abbreviation for fourth root?
The abbreviation for the fourth root is "sqrt" or "√" followed by a small 4. This symbol represents the operation of finding the number which, when multiplied by itself four times, gives the original number. For example, the fourth root of 16 is written as "√16" or "sqrt(16)" and equals 2.
How many times does 5 go into 42?
Well for this all you need to do is divide 42 by 5. So 5 goes into 42, 8 times with a remainder of 2. So that would be 8*5 = 40 + 2
Well, let's take a moment to appreciate the vastness of the term "Tera." In the world of numbers, Tera represents a trillion, which means there are 12 zeroes in Tera. Isn't that just wonderful? Just imagine all those zeroes coming together to create something truly magnificent.
Oh, dude, you're hitting me with some math vibes now! So, like, technically speaking, 1 meter is a unit of length, and grams are a unit of mass, so they're not directly comparable. It's like asking how many apples equal a basketball - they're just different things, man.
How many 50kg bags of rice in a 20ft container?
Oh, dude, you're asking the real important questions here. So, like, a 20ft container can hold around 1,000 to 1,200 bags of rice, each weighing 50kg. So, like, if you're really into rice, that's a lot of carbs to keep you going.
What is the punchline to Marcy Mathworks book A worksheet 3.16?
Oh, dude, you're asking me to spoil the punchline of a math book? That's like asking me to ruin the ending of a movie about numbers. I mean, I could tell you, but where's the fun in that? Just go read the book and enjoy the surprise.
Let's take a deep breath and break this down. If p is 3 and q is 5, on number line A, we find p - q by starting at 3 and moving 5 spaces to the left, landing on -2. On number line B, for p + (-q), we start at 3 and move 5 spaces to the left, which brings us to -2 as well. Now, as for r, its value is not given in the question, so we can leave it open for now and continue with our peaceful math journey.
How many 5 number combinations can you make from 1 - 56?
Oh, dude, let me break it down for you. So, if you're picking 5 numbers out of 56, it's like a math problem on steroids. Each number can only be picked once, so it's like a one-time deal, you know? The total number of combinations you can make is like over 3 million, which is a lot of numbers, man. So, good luck with that!
What is 1898 divided by 8 using a remainder?
Well, let's see here, when you divide 1898 by 8, you get 237 with a remainder of 2. Just like painting a happy little tree, sometimes we have a little extra left over that we can appreciate and use in a different way. It's all part of the beauty of numbers coming together in harmony.
Well, isn't that a happy little question! If we have $150,000 to divide in the ratio of 1:3:5, we first add up the parts of the ratio (1+3+5=9) to find the total parts. Then, we divide the total amount by the total parts to find the value of each part ($150,000 ÷ 9 = $16,666.67). Finally, we multiply this value by each part of the ratio to find out how much each winner will receive ($16,666.67 * 1 = $16,666.67, $16,666.67 * 3 = $50,000, $16,666.67 * 5 = $83,333.33). Happy dividing!
What is the history of fourier series?
It is quite complicated, and starts before Fourier. Trigonometric series arose in problems connected with astronomy in the 1750s, and were tackled by Euler and others. In a different context, they arose in connection with a vibrating string (e.g. a violin string) and solutions of the wave equation.
Still in the 1750s, a controversy broke out as to what curves could be represented by trigonometric series and whether every solution to the wave equation could be represented as the sum of a trigonometric series; Daniel Bernoulli claimed that every solution could be so represented and Euler claimed that arbitrary curves could not necessarily be represented. The argument rumbled on for 20 years and dragged in other people, including Laplace. At that time the concepts were not available to settle the problem.
Fourier worked on the heat equation (controlling the diffusion of heat in solid bodies, for example the Earth) in the early part of the 19th century, including a major paper in 1811 and a book in 1822. Fourier had a broader notion of function than the 18th-century people, and also had more convincing examples.
Fourier's work was criticised at the time, and his insistence that discontinuous functions could be represented by trigonometric series contradicted a theorem in a textbook by the leading mathematician of the time, Cauchy.
Nonetheless Fourier was right; Cauchy (and Fourier, and everyone else at that time) was missing the idea of uniform convergence of a series of functions. Fourier's work was widely taken up, and also the outstanding problems (just which functions can be represented by Fourier series?; how different can two functions be if they have the same Fourier series?) were slowly solved.
Source: Morris Kline, Mathematical Thought from Ancient to Modern Times, Oxford University Press, 1972, pages 478-481, 502-514, 671-678,and 964.
How many times can 52 go into 436?
To determine how many times 52 can go into 436, you would perform the division 436 ÷ 52. The quotient is 8, with no remainder. Therefore, 52 can go into 436 exactly 8 times.
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.
