Mathematics

Hi there! I have this question and despite my best efforts I have failed to answer it. I've guessed that is it 5,050 I have no idea how to solve this - any help appreciated! Cheers, Ryan Jones

Sometimes, we may draw a tree diagram with domains (the columns) as (1st, 2nd,3rd) with the rows having "Yes" or "No". For instance, find the P that both of the two children in your home have done their homework. Then, we can apply the above case. Now, consider a case that seven balls are in a bag. One ball will be taken out. There are four red balls, 2 blue balls, and 1 green balls. Find P(G). Obviously, it is 1/7 if we set domains as Type of ball. What about we set the domains as Red ball, Green Ball, Blue ball ,with the rows of "Yes" or "No"? We can find that P(Red yes)=4/7. while P(Red NO)=3/7, Similarly we can find out the other P. Now when doing the qu…

Hi, I've just picked up the following problem and got stuck...although seems easy. You have 100 positive real numbers. The product of each 11 of them (11 different) is greater than 1. Show that the product of all hundred numbers is greater than 1. Please, give me a hint first. Thanks

proove that between any two points a and b, a!=b, on the x axis, there are infinitely many rational points. How do you solve the above? I know it's simple, but I just cant put down mathematically. please help thanks

Hi everyone, Just started my computer science studies and don't have any advanced foundations in math (studied litterature in school). I'm faced with a story driven logical problem which i've translated into the following equasions. if A false and B true => C is False if D true => A is true if E true and A true => B is true if I true => E false or D false if E true and I false => D false and A false if E false => F true and B false if C true => H false if D false and C true => I true I then need to answer if E is true, if D is true , if I is true , (...) if when C true => A true? if when C false => A false? (b…

What is the difference between mathematical laws, such as the law of sines/cosines/tangents, exponents. logarithms, etc. and mathematical theorems (the binomial theorem, fundamental theorem of calculus, and pythagorean theorem). Do theorems ever eventually become laws or how is it decided if something is a law or theorem?

Sorry for cross posting here and in the astronomy forum but the problem falls under both categories. Imagine if you have a gigantic circular space station that is tethered with numerous space elevators, is concentric with the earth and spans the entire geostationary orbit (I think A.C.Clarke played with this idea in one of his early works). My question is, at what altitude would it need to be tethered to provide 1g of centrifugal force in the "roof" of the space station, so that people can walk around up there in a normal way? Some numbers that might help, which i found from a NASA study but the interconnection of which I do not understand since I do not know the …

I need an algorithm for reducing fractions. There is a little twist to the problem. I am not viewing the problem as a fraction. For example: a = 2 b = 4 I know that a and b will eventually be combined to produce a a/b string. But I need to keep them seperate for this particular problem. So knowing the values for a and b I need an algorithm that will reduce it. Something like a = 2 / 2 = 1 and b = 4 / 2 = 2 I understand the prime factors plays a roll in the reduction of fractions but is the only way to find the prime numbers of a given number by looking it up in a table? Is there an equation for obtaining the prime numbers of a given number? This …

Hey, I have sort of an ethical problem here... I really want a math software toolkit such as Mathematica, Matlab, or Maple, but they are very expensive (drop at least 100 bucks easy, 130 for Mathematica). I hate to take things without a liscence, I appreciate the work of the creators of the projects and think they should be payed reasonably for their work. But those prices are insane (and yes I know other software reaches into hundreds, even thousands of dollars, and that is insane too). I just can't afford it. I checked what liscences my school has, and they can run 50 copies of Matlab at any given time on one of the computers in the department building. I would have to…

Would the inverse function of [math] \displaystyle\frac{1 + e^x}{1 - e^x}[/math] be [math]\displaystyle\frac{e^x - 1}{e^x + 1}[/math] ? Just been working through Stewarts calculus, the book only gives answers to the odd numbered questions. Most of the concepts in the book are pretty new to me, having only just started my Alevels, so i thought it would be best to get as much practice at it as i could. Cheers, Rob

lim (sin(2x)cos(3x)sin(4x))/(x*cos(5x)sin(6x)) x->0 I think I'm missing one key trigonometric property to solve this... it seems too tedious to do all by double angle formulas

The Largest prime number, with over 2 million digits, was found on a Michigan State student's PC. Just shows you what PCs can do now days! Read the article now: Largest Prime Number Found (Updated Link)

Are there any numbers with 2, 3, 7 or 8 in the units place that have rational square roots?

I came across a formula by Euler which was a derivation of (IIRC) pi^2 which used an infinite series consisting of the prime numbers. Does anyone know about this or can anyone point me to a useful site?

As some of you might remember, I used to post a few problems every week for people to solve and reply to. This forum was originally used for the purpose, but obviously that's gone to pot a bit I'd quite like to do the same thing again now we have more visitors around. I plan on holding a small competition every 2 weeks. There will be 3 questions at different levels of mathematics: high school, college and university for those interested in some of the higher maths. What I'm really looking for is some help in gathering possible questions. I'll try and do my best to make up questions where appropriate, but sometimes I won't have the time. I'll probably use the foru…

Hello, I wonder if any of you could explain the answer to a question that has left me rather stumped. It's a past question from the UKMT Senior Challenge and I know I should be able to do it, but I don't even understand what it wants me to do Anyway, enough waffling... "The graph of y= l f(x) l is shown ( f(x)= x^2). Given that the graph of y= f(x) is a continuous curve, how many different possibilities are there for the graph of y=f(x)?" What does it want me to do?! Cheers, Michael

[math]L(\theta)=[\frac{1}{4}(1+\theta)]^{112} \times [\frac{1}{4}(2-\theta)]^{94} \times (\frac{1}{4}\theta)^{53} \times [\frac{1}{4}(1-\theta)]^{31}[/math] For the function above, simplify, take logs, derive with respects to theta, and then equate with zero to find the the value of theta that maximizes L(theta). My working out is below. I think I have made a mistake beacuse I'm not sure if I'm supposed to get a negative number. Have I done it right?

Ive just formaly started geometry in school im wondering what do you all prefer algebra or Geometry and what would you guess effects this decision

Picture this, you have an array of 1,000,000 light bulbs, numbered 1 to 1,000,000, all of which are off (and all of which work). The following task involves these light bulbs and an action we'll call "flipping". Flipping simply means changing the state of a light bulb. If the bulb is off, flipping will turn it on. If the bulb is on, flipping it will turn it off. Starting with all the light bulbs off, you start at bulb #1, and flip the state of every bulb. Once you've done that, you go back and start with bulb #2, flipping the state of every second bulb. Next, you go back, start with bulb #3, and flip the state of every third bulb. This continues all the way up…

I just took the SAT Math 2 subject test Saturday, and the very last question was the only that I couldn't figure out, so I'm kind of curious how to do it. The question read if [math]\sin{\theta}=x^2[/math], then what does [math]\sin{2\theta}[/math] equal in terms of x? I've never been very good at trig, so I'm kind of interested in how to do it (and if it's something glaringly obvious I'm gonna feel like an idiot).

Hi!As in the subject, we're doing that in math but I'm having a hard time to understand the concept of what's going on especially when it comes to interest, half-life, most of the questions regarding to what this topic is about. We have this formula T=S®^P I'm confused on how to use this formula. Can anyone please explain?

Let C* be a set of edges of a graph G. Show that, if C* has an edge in common with each spanning forest of G, then C* contains a cutset. Obtain a corresponding result for cycles.

Hi folks I'm not a mathematician but I'd like to ask some simpleminded question about Riemann's hypothesis. It seems to me that the only way the hypothesis can be proved is by showing that the mathematical mechanism that generates the primes is exactly the same mechanism that generates the non-trivial zeros. Am I right about this? If I am then, bearing in mind the origins of the zeta function, would I also be right in thinking that a proof would require showing that the primes are generated or determined by an interaction of interacting sine waves akin to the process that generates the harmonics of a vibrating string? Thanks.

tan(θ°) = (viv) / (vih) = (1.28 ± 0.0676m/s) / (0.514 ± 0.0676m/s) = 2.55 ± 0.467 m/s θ° = 68.0 ± 3.65° This answer may not be correct to the decimal place but it shud b relatively close. Could someone plz explain to me how 3.65° becomes the uncertainty for the angle? Plz. explain very clearly and simply. Im in a hurry. THanks in advance

How do you solve this problem? The parabola y=ax^2 + 6 is tangent to the line y=x. Find a.