Mathematics

Hi. I tried these questions however i am unable to do them:embarass: Question1. There are 52 white keys on a piano.The lowest key is A. The keys are designated A,B,C,D,E,F and G in succession, and the sequence of letters repeats, ending with a C for the highest key. a) If five notes are played simultaneously, in how many ways could the notes all be i) As? ii) Gs iii) the same letter? iv) different letters? b) If the five keys are played in order, how would your answers in part a) change? Question2. A basketball team consists of five players-one centre, two forwards, and two guards. The senior squad has two centres, six forwards, and four guar…

A finite number divided by nothing (zero) is infinity. A finite number divided by infinity is nothing (zero). Therefore, nothing multiplied by infinite equals a finite number.

A light is at the top of a pole 20 m high. From a point on the ground 8m from the base of the pole a ball is thrown upwards with an inital velocity of 13 m/s. At what rate is the shadow of the ball moving along the ground 1 second later.

can soem one resolve his equation for me, find the units for k .... T is measured in seconds.... R is measured in meters . thnx

I was reading my Maths textbook for fun when I came across the chapter on combinations and permutations. The textbook states that the number of permutations of n different objects is n! = n(n-1) (n-2) x...x 3 x 2 x 1 Then how should we define 0! so that the above result would stilll hold?? I checked 0! = 1. Hmm... can somebody enlighten me how this works?

IN SUMMARY How do I best go about becoming an amateur mathematician? MORE SPECIFICALLY I've been a computer consultant for a decade now. Math has always intrigued me. My knowledge and understanding is pretty good up through integral calculus. I'm new to differential equations. I'd like very much to become a mathematician. It won't be a career, but I look forward to it becoming one heck of a hobby. My question is: How do I best go about becoming an amateur mathematician? For example, I have studied courses and text in pretty much the following order: - Arithemtic - Algebra - Geometry - Trigonometry - Differential Calculus - Integral Calculus…

Could someone help me with this question? The base of an isosceles triangle is 6 m. The other two sides are both increasing at 4m/s. Find the rate of increase of the area of the triangle when these sides are 5 m.

hey all! I currently use GraphCalc v4.0.1 It supports 3D graphing, and is a pretty interesting program, however I was wondering if there are any graphing programs that support relational graphs? I find having to create graphs as functions only a bit restrictive. an example is z^2 = x^2 + y^2 (a sphere) I can't make one with my current graphing calc because it doesnt do non-function graphing. If anyone knows of a graphing calculator that can do what I'm proposing, please post a link. BTW - It'd have to be a free one too lol Thanks in Advance!

Here's problem I need help on. It relies mainly on one's intuition and intelligence. Can anone hlep me out and give a full, good explanation? Every number can be represented in the standard form such as [math]\frac{100}{3} = 3.33 * 10^1[/math]. In this form the number [math]x = a * 10^N[/math], where [math]1<a<10[/math], while N is an integer exponent. Find the standard form for [math]x = 1234^1234[/math]. Include only three leading decimals in your answer, as in the previous example.

Look at this equation: [math] z(x,y) = (\cos(\sqrt{(x^2 + (y + .913*2\pi)^2}) + \cos(\sqrt{(x^2 + (y - .913*2\pi)^2}) + [/math] [math] (\cos(\sqrt{((x + .913*2pi)^2) + y^2}) + (\cos(sqrt{((x - .913*2pi)^2) + y^2}))*4[/math] Pretty crazy, eh? lol, It's supposed to be some kind of complex wave thing... the graph looks like this: If anyone else has any cool looking graphs, post a screenshot of it (or a link to a screenshot) on this thread, with the equation used to make it.

Í have a problem from chemistry, which translates to the following mathematical problem: Given a (non-square underdetermined) matrix A with integer elements only, find the null-space of it. I.e. determine the space of vectors x, with the property Ax = 0 The space is determined by computing all independent base vectors of the null-space. An example is given below: (1 -2 0 1) (3 -2 1 0) Here the matrix A has two rows, each having 4 elements. The null-space of this matrix A is fully specified by the following two vectors: x1 = (1 1 -1 1)T and x2 = (0 1 2 2)T With (...)T I mean a column vector (the math editor is not very cooperative to me…

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?