Mathematics

the number 54321 is multiplied by a five digit number(*****). the product is a 10 digit number ending in 12345. what is the number we are multiplying by? find what is the astericks

Ok for my homework tonight we had to do problems like these: I=?,P=12,000,R=7%,T=2years I=Intrest P=Principal R=rate T=Time I=83.00,P=6000,R=?,T=3years I got how to do those(IChose random numbers) But I need help trying to get I=125,P=?,R=6%,T=6years How do I get the principal? We never learned it in class

A friend and I were recently watching "The Purge", and the topic came up that if everyone in the world killed only 1 person that the world's population would be halved. I thought about this for a minute and realised mostly it would be reduced by more than half and that in the extreme people pairing off and simultaneously killing each other could reduce it to 0, while still fulfilling the criteria. My question is what would a probability distribution of this scenario look like. What would be the most likely percentage remaining alive? What is this kind of maths problem called? Edit: Feel free to use 7 billion as the world population size or go with any smaller…

No number tables...no properties. No axioms change (except) when involving zero. The following projection operators allow for no further axioms...... [math]0 = \left ( \begin{matrix} 0.z_1 \\ 0.z_2 \end{matrix} \right ) [/math] 0.z1 = 0 0.z2 = 1 [math] P_1 0 = (1, 0) ~ \left ( \begin{matrix} 0.z_1 \\ 0.z_2 \end{matrix} \right ) = 1 \cdot 0.z_1 + 0 \cdot 0.z_2 = 0.z_1[/math] [math] P_2 0 = (0, 1) ~ \left ( \begin{matrix} 0.z_1 \\ 0.z_2 \end{matrix} \right ) = 0 \cdot 0.z_1 + 1 \cdot 0z_2 = 0.z_2[/math] The distributive property (all combinations of a, b, and c as zero) a * (b + c) = a *…

Please look at the attached pdf http://www.geocities.com/complementarytheory/Roots-Chain.pdf . By this model we can see that √1 is the "shadow" of √2 and √2 is the "shadow" of √3. I think that we can conclude that √3 is the "shadow" of √4 ... and so on. In short, I am talking about roots which each one of them is the diagonal of its dimension level, where each n_dim diagonal is the "shadow" of n+1_dim diagonal. We have a chain of "shadows" between infinitely many diagonals in |N| dimension levels. Do you think that this "Chain of Shadows" has any mathematical/physical meaning?

Here is a probability mathematical problem that I think it will make quite a few math brain cells to work overtime....... PROBLEM: John and Mary has each one hat filled with numbered balls. The numbers are from 1 to 40 and there are no balls with the same number. Hence, there are 80 balls in total. John will pick two balls and Mary will pick 3 balls. The process is that John pick one ball first. John looks at the number on the picked ball and writes it down. He then reach into the hat and removes the two balls that has the number just below and above the picked ball. Hence, after John picked the first ball and have removed the adjacent numbered balls the hat cont…

Turns out that the sum of squares of the three distances, a2 + b2 + c2, is the same for all points on the circle. It appears as an algebraic "accident." What could be a geometric reason for this fact?

I have a paper that, IMHO, proves the Collatz conjecture. I will be looking at where to get it confirmed. I welcome comments. Abstract: The Collatz tree can be formed naturally, resulting in a good looking tree, but the numbers seem chaotic. By reforming the tree, the tree becomes weird, but the numbers look nice. And it becomes clear that the hailstone algorithm and its inverse can be used to traverse down and up the tree, from the root to all integers and beyond, and back to the root (the number 1). The link is http://dbarc.net/yr2024/collatz1.0.pdf

This is a good collection of links to audio/video courses and lectures on mathematics from colleges/universities. http://www.infocobuild.com/education/audio-video-courses/mathematics/mathematics.html This contains many courses and lectures on math: linear algebra, calculus, differential equations, statistics, probability, and more.

If kx^2 - kx - 6 is divisible by both (x + 1) and (x + m), find the value of m. Given 2/x = y/3 = x/y , find x^3. One way to pack a 100 by 100 square with 10,000 circles, each of diameter 1, is to put them in 100 rows with 100 circles in each row. If the circles are repacked so that the centers of any three tangent circles form an equilateral triangle, what is the maximum number of additional circles that can be packed?

won't be too many more question, got my last maths exam monday but you help would be much appreciated. Solve for [math]0 \leq x <360[/math] [math]2cos(x + 50)^o = sin(x + 40)^o[/math] and [math]2cosx+sinx = 5[/math]

A person at the centre of a circle needs to tarvel to 5 cities on the circumfarance of the circle. Each city has 5 gates that allow him/her to get through to the city. There is a charge involved when going through each gate. Furthermore, after going through a gate, the charge on all the other gates change (ie they are dynamic). The person is aware of the resulting change in charge by going through a gate, BEFORE entering it. I hope I haven't confused you too much!. I'd like to know your thoughts on this problem. How you would approach a problem like this. A possible matrix???? See it differs from the coonventional TSP problem by the fact that the charges…

Here are a few challenge problems to solve (I don't know what the difficulty of this board is so I would appreciate comments) 1. u and w are in degrees. tan(U)=1/2 and tan(w) = 2 find tan(u-w) 2. There are 20 switches in two columns each with 10 in them. Each switch is either on or off. If exactly 5 must be on in each column what is the number of distinct ways the switches can be set? 3. A metal plate of constant thickness is cut into a rt. triangle. The coordinates are (0,0), (2,0) and (2,1). The plate is balanced on a fulcrum on the side which connects (0,0) and (2,0). Find the x coordinate of the balance point of the fulcrum.

I have been doing research on entropy encoding for some time.. I found some interesting relationships between Arithmetic coding and other methods such as Huffman Coding. I made an article to explain them and am presenting here for review: http://siara.cc/arithmetic_coding_new_approach/ I have also attached a PDF version for convenience Arithmetic_Coding_Formula_based_approach.pdf. Please let me know your ideas.

Here is my way of working out the solution, i would appreciate some other methods to give me some ideas of how best to do these kind of questions: Q: the sum of the first 3 terms in a GP is 9 times less than the sum of the first 6 terms, find the ratio. Here is my solution: since: 9(a+ar+ar^2)= a+ar+ar^2+ar^3+ar^4+ar^5 8+8r+8r^2= r^3+r^4+r^5 factorising: 8(r^2+r+1)=r^3(1+r+r^2) canceling: 8= r^3 therefore r=2.

This is not that easy problem but give it a try. Suppose triangle ABC is equilateral, and AF = BD = CE = 1/3*AB (D,E, and F are on BC,AC, and AB respectively). Compute the ratio of the area of the triangle ABC to that of the area of triangle made by drawing liens CF,AD, and BE.

Hi guys, Its my first post here, and I'm setting up some goals, so I was hoping I could get a few mathematics experts set me up with some helpful tips on making this journey in advanced math a success. Allow me a little extra length on my first post here in the maths forums: A while ago I started pursuing one of my larger life goals to learn the more advanced maths. Then I burnt out for perhaps a number of reasons, but lack of motivation was not one...the biggest was simply that I grinded to a hault because of a strange thing I experienced: Thinking I was understanding the rules on the level of algebra, but for some reason, never getting certain problems right a…

1. Taking an exact number of strides I can walk 9.49 metres. What is the length of my stride? 2. Make a copy of a triangle like that shown with four circles along each edge. Use the numbers 1 to 9. Put one number in each circle so that the four numbers along each edge add up to the same total. Find two different ways of doing this. <IMG height=238 src="http://www.rashidschoolforboys.sch.ae/pages/Maths%20Website2/photots%20for%20maths/trianlge.JPG" width=266> 3.If you multiply together all of the factors of 100, how many zeros will there be on the end of the answer? 4.In this multiplication problem: ?? x ? = ??? all of the digits have been replaced by…

Hi, A chap in the pub gave me a problem last night and I cannot solve it. As I really need to get some work done, can anyone throw some light on the matter ? A 6ft by 6ft box is placed against a wall, and a 20 ft ladder is placed such that it touches the wall, the ground and one corner of the box i.e (the ladder makes the hypothenuse). I need to calculate the opposite and the adjacent. Regards, Phil.

I discovered a Law for Prime Numbers. I have for the couple of years searched ways of finding a law which will determine the prime numbers. As we all know, the law which will allow us to predict prime numbers are unknown. Unfortunately, today, I cannot still offer any remarkable law which will determine prime numbers, but I did find another law for prime numbers along the way. The Law States: The sum of all numbers which make up a prime will give you a number which will never be allowed to be a multiple of 3, nor do any digits ever make the sum of 12 to allow 3 to be divided, with the only acception of the the second prime number that is 3. If after you have taken…

hi people, just started following a linear algebra course and i've run into some trouble trying to solve some problems in the book. I've been asked to calculate the projection of (1,2,3,4) unto [(1,0,0,0),(3,4,0,0)] Obviously they are not orthagonal as their in product is 3 and not 0. So you project the in sum of (3,4,0,0) and (1,0,0,0) = (3,0,0,0) (3,0,0,0) - (3,4,0,0) = (0,4,0,0) Now it is orthagonal, I project vector x on (1,0,0,0) = (1,0,0,0) Projection of vector x onto (0,4,0,0) I think is (0,1,0,0) This leads to V = (1,1,0,0) I was just wondering if anyone can do the calculations as well as I'm not able to confirm this. Thanx in advance

How do you solve problems like f=ma? For each variable, you put in a different number, but they are described in different units, like pounds, or pounds per square inch. How does it work?

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

Im working on a little problem for an idea im having. If you stand on earth and look out over the ocean. Your field of vision would be almost 180 degrees. But lets say 150 degrees for this example. Being 6 feet above sea level puts your distance to the horizon 3 miles out. This means that by trigonometry you can draw a triangle with 3 miles on two sides and the angle between them being 150 degrees. This would make the line between them be 5.8 miles. Ive been wondering. By math, how much of earth curvature would be seen on each side of the middle where the curvature from your point of view would be zero ? Earth will curve down to the sides in respect to the di…

Given two spheres touching at one point, would that be a surface? I think not, but I don't know how to begin to search for the proof. I thought maybe proving it isn't Hausdorff, but I'm not clear on how to go about it. Anyone can help? Sorry about the bad English, not my mother tongue...