Mathematics

The integers 1,2,3,...,100 are written on the board. What is the smallest number of these integers that can be wiped off so that the product of the remaining integers ends in 2?

How would one measure the length of a spiral? I tried figuring it out with nothing but a piece of paper and a pencil, but could figure nothing. I have a feeling it might have something to do with log, cos, sin, and/or tan. Thank's in advance for your help, and I'm sorry if I sound stupid.

I can't remember how to solve this, any help would be appreciated, thank you.

Can anybody explain to me what is the difference between parameter and arbitrary?

I wrote a script that is designed to aid the process of trying to memorise 100 digits of pi. I played with it for an hour last night and this morning I still remember them, I will play it every now and again until the numbers are off by heart. Here is the page you can test it out on: http://www.random.abrahamjoffe.com.au/public/JavaScripts/pi.htm Let me know what you think and if you can imagine perhaps a more effective method I might try. 3. 14159 26535 89793 23846 26433 83279 50288 41971 69399 37510 58209 74944 59230 78164 06286 20899 86280 34825 34211 70679

Go to this thread http://antipsykopat.org/miniBB/index.php? action=vthread&forum=9&topic=12012 and proof that 0.9999....=1 You can of course write in English even though most of it is already written in another language, but everyone there understands English. Why have the Norwegian philosopher Alpha offered this kind of money? It is needed to proof that it can't be 1, because the universe is virtual reality and humans have non-physical soul. It has been showed that the world is not mehanical in amongst other things the Aspect-experiment, and there is something that lies beneath it all, like a computer that controls what is going on on a monito…

I don't know how to isolate an exponent with a variable and a known number, e.g. [math]2 = 3^{0.01t}[/math]. How do I isolate the term 't'? I know that you can square root the opposite side to remove the exponential, like this: [math]\sqrt[0.01t]{2}=3[/math]. But that still doesn't solve the isolation of the term 't'. Any help??

I have a problem with the following: a and b are non-parallel vectors. Choose two numbers x and y so that 3r_1 = 2r_2 can be applied to the following vectors r_1 := (x + 4y) a + (2x + y + 1) b r_2 := (y - 2x + 2) a + (2x - 3y - 1)b Now, I have no idea what to do with the vectors. I could solve it if it were just for x and y without a, b and r, but I don't know whether to just drop the vectors, use some vectors i choose myself or if I have to calculate it with a and b left there as a variable. The solution is x = 2 and y = -1 btw, but even with that information I can't deduce the proper way of calculating it. Can someone give me a hint as to ho…

Is there any type of equation that would represent the total possible amount of sudoku games there are possible to make?

Hi everyone! Here's the ongoing challenge: Using any mathematical operations you want, but only four 4s (Or less) for the numbers, create equations to equal as many numbers as possible. Here are the rules: 1. All four "4"s must be used in each equation. 2. No other numbers can be used in the equations. 3. You may use any mathematical operations and symbols (not including symbols for other numbers, like Pi, e, etc.) you wish. 4. The answers in this thread will start with trying to find an answer resulting in 1, then the next person must find a solution resulting in 2, the next person 3, and so on. 5. This is to continue as long as answers can be found. 6. …

As the following: Find the maximum value of: (a^2/sinb)*[cos(b-2n)-cosb] express in terms of a and b; where n is varied (find a formula in a and b that is the greatest) In fact, this question is derived from a figure, the topic is compound angles, and I would like to know if there is any way to get the answer more faster and make less error, if yes, how to do so.

What are we all reading, maths-wise? Mention your second year complex analysis textbook if you really want to, but I'm interested in hearing about what people (especially postgrads, postdocs, whatever category Matt Grime falls into, and PeopleWhoOnceWereMathmosButThenTurnedTraitor - like me) are reading about maths in their spare time. I'll start off with my current - Modular Forms and Fermat's Last Theorem. It's not easy by any stretch, but it's interesting. What about you?

Here is an extradiotary cool math trick. Try it yourself! 1. Grab a calculator (You won't be able to do this one in your head) 2. Key in the first three digits of your phone number (NOT the area code) 3. Multiply by 80 4. Add 1 5. Multiply by 250 6. Add the last 4 digits of your phone number 7. Add the last 4 digits of your phone number again 8. Subtract 250 9. Divide number by 2 Do you recognize the answer? It's like magic, eh?

Hey all SFNers... Um just to let you know that in support of giving InternationalDiscussionForums.net some special content, I have been posting there exclusively some of the interesting math problems what I would be posting here. I mean, IDF is a pretty cool place, and its run by some of your fellow SFNers, so you'll probably feel comfortable there, and I've been posting interesting math problems there. This isn't meant to be an advertisement, just an announcement of where I've put some math problems that people who enjoy this forum would probably enjoy. But I mean, don't go if you don't want to, because this isn't an advertisement.

i hope that someone could help me with my q's here: http://www.physicsforums.com/showthread.php?t=97985

How anyone help me solve this? A druggist haspure alcohol and a 20% solution. How many gallons of each should be used in forming 4 gallons of a 30% solution?

I know that to find the sum of an arithmetic series I'd use [math]S=\frac{n}{2}[2a+(n-1)d][/math] but what do I do if I want the product of an arithmetic series (all the values multiplied together nicely)?

I have a project in biology with many equations (mostly ODE and PDE). I use LaTeX (MikTeX/TeXnicCenter) and Maple for plotting functions. I convert them to PNG so TeXnicCenter can compile my work in PDF. But the quality is not very good. I saw many PDF with mathematical model where you could "zoom in" without lossing much quality, how ? I know you can draw lines, and cercles with LaTeX but ODE are far too complex.

In the attached page http://www.geocities.com/complementarytheory/no1.pdf we can understand that there is a deep connection between our abstract ideas and the ways that they are represented by us. I'll be glad to know your point of view.

OK, I am having a problem with this economic theory by Piero Sraffa. He says that production affects value, that's not the hard part. Here is his first example of a hypothetical economy: 280 qr. wheat + 12 t. iron --> 400 qr. Wheat 120 qr. wheat + 8 t. iron --> 20 t. iron I figured, hey what the heck, just set the value of a ton of iron to x and a qr. of wheat to y. 280y + 12x = 400y 120y + 8x = 20x Then subtract and we get: 12x = 120y 120y = 12x Thus 10 qr. wheat is exchangeable for 1 t. iron. But now he introduces the production with a surplus of 175 qr. wheat. There is a "rate of profit" scalar "r" that is [math]0\geq r\geq1[/math]and then we mult…

I had these questions in my 4 unit maths test yesterday, the red question is the one that I got wrong however I cannot see a problem with my working: a) Find the non real roots of x³ + 1 = 0 [math]x = \frac{1}{2} \pm \frac{\sqrt{3}}{2} i[/math] b) If h is one of those roots prove that h² = h - 1 [math]LHS = h^2 = \frac{1}{4} \pm \frac{\sqrt{3}}{2}i - \frac{3}{4} = \frac{-1}{2} \pm \frac{\sqrt{3}}{2} i = h - 1 = RHS[/math] c) Hence, find the value of (1-h)^6 [math](1-h)^6 = 1 - 6h + 15h^2 - 20h^3 + 15h^4 - 6h^5 + h^6[/math] Considering the roots of unity: [math]= 1 - 6h + 15h^2 - 20 + 15h - 6h^2 + 1[/math] [math]= -18 + 9h + 9h^2[/math] …

Did you know that the more multiple choices (4 choices) questions that you have, the lower percentage you will get all the answers right? 1 question with 4 choices = 25% chance to get the answer right. 2 question with 8 choices = 6.25% chance to get both questions right. Am I correct? I think you do this by 1/(4^n) where n is the number of questions.

During my schooling, i read from an elementary probability book that the probability of an event occuring in a sample space( i donot know if it was a countable set or whatever else is likely), is a number obtained by letting the no of trials tend to infinity and then drawing up a number of success/failure figure out of it, in the end obtaining the probability structure of an event. Well, now i read from apostol that during the course of formation of games-of-chance theory, and thereafter probabilty/measure theory, many mathematicians had suffered in coming up with a convincing(?) definition of probabilty.Now come to think of it I feel disturbingly uncomfortable with t…

I'm trying to get a concept of what low gravity combat would be like. This should come down to a physics problem. A baseball player can throw a baseball at 90 mph. Therefore his hand must be traveling at 90 mph when the ball leaves his hand. So let us assume that in combat the average fist is traveling at just 50 mph, or just 73.3 feet/second (unless someone can reference something more accurate). Bozer weighs in at 200 pounds, or in 0.2G a mere 40 pounds. Gozer weighs in at 300 pounds, or in 0.2G a mere 60 pounds. Bozer throws a punch and connects with Gozer's chin. His fist (roughly a 2 lb object at 1G, or 0.4 lbs at 0.2G) is moving at 73.3 feet/second. Unfortunately…

This is probably really easy for all you guys, but I can't see the answer: Given that log 2 = 0.3, show that log 5 = 0.7 Thanks in advance.