Mathematics

There are 25 bicyclists and just 5 bicycles. Of all these we need to find best 3 cyclists. How many races should be held to determine top three winners and why? <link removed>

Hi, Does anybody know good math games like 2048? PS, these games should not be for children. Spent a hour on Google but all I found were either boring games or games for children. Regards, Nuur

I downloaded a MS file about maths. I don't know why the symbols and numbers cannot be shown clearly and correctly. Anyone help me>?

I would like an explanation on how to go about solving these two. I am having some trouble. 24. In 1975, the U.S. EPA set a standard of 50 ppb of lead in drinking water. In 1991, a new standard was set that safe water contains less than 15 ppb. a.Write each of these rates as fractions using positive powers of 10 b.Write each rate without fractions, using negative powers of 10

I am trying to expand the following eaquation to plain english. Can anyone help? The magnetic field on the z axis of a solenoid (in Gaussian units) is: B=[2\pi(N/L)I/c][sin A_2-sin A_1], where A_i is the angle between a line perpendicular to the axis of the solenoid at one end and a point on the z axis. If you write this in terms of z and expand, you can use Legendre polyomials to find the field off the axis and the dipole moment of the solenoid. Can someone just make this equation simpler?

This is something my teacher did accidently whilst showing something else. [math]-i = -\sqrt{-1} = \sqrt{(-1)^{2} \times -1} = \sqrt{1\times -1} = \sqrt{-1} = i[/math] He said "that can't be right", rubbed it off the board and started again. Thing is, I can't see where the mistake was. Can you point it out?

Hi all, I was reading an article in new scientistabout physicists suggestion the universe may be fractal, this kind of makes sinceto me since they’re rather good at describing leaves, trees coastlines ..basically anything well.. ‘natural / organic’. I know complex structures likesocial networks can exhibit fractal geometry as well; these structures can alsoexhibit complex and chaotic behaviours like weather patterns, neurons and othergraph structures. Navigating suchstructures could be considered NP-Hard (e.g. what order and how to manipulate proteinsin to fold them optimally). This got methinking about whether fractals could be used to turn the complexit…

Let a,b, and c be positive real numbers. Prove that [math]\sqrt{\frac {a}{a+b}}+ \sqrt{\frac {b}{b+c}}+ \sqrt{\frac {c}{c+a}} \leq 2\sqrt{1+\frac {abc}{(a+b)(b+c)(c+a)}}[/math] I've tried squaring both sides, and that eventually lead me to nothing. Then I tried taking the common denominator of the left side, but I got nothing either... There has to be some trick involved that I'm not seeing... Anyone has any suggestions or input, that will be great!

Hello, Does the Price Equation, when it comes to explain how the altruism trait can spread throughout the population, break down if a group has only one individual who has the trait? In other words, when applying the Price Equation to altruism, is there a lower bound beyond which the Equation doesn't work? If the Equation needs more than one altruistic individual (and actually many individuals) within the group, is it not the case that the Price Equation is a non starter when is comes to explain how altruism can spread within the population? Here's a link to Wikipedia: http://en.wikipedia.org/wiki/Price_equation BTW, I also posted the question in the Biology Sec…

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 am interested in knowing how to find the distance along a function between two values. I am surprised to see that this kind of problem is never encountered in the highest level mathematics in high schools in Australia and decided to research it myself. I would appreciate a term that might be useful to google or perhaps a link to a wiki article or something. Thankyou, BigMoosie

Make L the subject of the equation for [math]\frac{1}{3}pK^{\frac{1}{3}L^{-\frac{2}{3}}}=w[/math]. My friend told me that the answer is [math]L=\left(\frac{p}{3w}\right)^\frac{3}{2}K^2[/math], but I got [math]L=\left(\frac{p}{3w}\right)^\frac{3}{2}K^\frac{1}{2}[/math]. Am I right or is my friend wrong? _____________________ Kettheya Uong

What is the smallest number that is divisible by 13 but when divided by the whole numbers 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12 yields a remainder of 1?

When I read " We work out this example as if it were 3(x - y) - 5(2y - x). We begin by multiplying out using the distributive property" Does "multiplying out using the distributive property" just mean multiplying everything inside the bracket by what's outside it, in this case 3 & 5?

This is a problem faced within another topic and I made this topic separate because I wanted to focus on this specific problem, which would deviate from the other topic. However, if moderators feel otherwise then it will be fine if the topic is moved to the other topic. So the problem(which I still haven't solved) is dealing with finding an equation to predict the amount of matrix solutions for a given Collatz-Matrix equation, which is defined by as the following: [math]C(x)_{k\times d}\begin{Bmatrix} a_{f} &b_{f} \\ u_{f}&v_{f} \end{Bmatrix},s(k_{p},d_{p})[/math] Now, how these work is there could be multiple or just 1 matrix solution for a given Coll…

picture : http://s6907.chomikuj.pl/ChomikImage.aspx?e=BNis-wCuwcNDkpjatdNzsgfVQtxAral5imWMh2pcl5i3we1zEJnLAb22thcIwURy0BZgsnZ7wrNEOE4LLgkqslbSC1Gc0yINw0Y-KxmPKgc&pv=2

Is the answer to this equation correct? I'm unsure if it should 2g in the denominator of the answer. I think it should be just g. (U sinX)^2/g - (U sinX)^2/2g = (U sinX)^2/2g (The g and the 2g are the denominator of (U sinX)^2 respectivley)

Here is a problem which was given in a Norwegian mathematical contest: Suppose [MATH]a[/MATH], [MATH]b[/MATH] and [MATH]c[/MATH] are real numbers such that [MATH]ab + bc + ca > a + b + c > 0[/MATH]. Show that [MATH]a + b + c > 3[/MATH].

how do i work out that if a machine is worth $15000 and if it's price decreases by 20% per annum that it will cost $9600 in two years using Sn=a(r^n-1)/r-1? using this formula it doesn't work.... thanks guys

I have a vague recolection from Pre-Calculus of learning about unit vectors... Vector "i" and "j"... one of which goes from (0,0) to (0,1), the other (0,0) to (1,0). Does any this ring a bell to anyone? and if so, can you tell me which one is which? I can't seem to find it. I think "i" is (0,0) -> (0,1), and "j" is (0,0) -> (1,0). And, is there one of these for the thrid dimention? (eg, from (0,0,0) -> (0,0,1))

what would it be then?

I'm trying to prove that, hopefully this comes out right, [math]\sum_{r=0}^{n}{(-1)}^{r}{_n}C{_r}{(n+1)}^n = n![/math] Can anyone help? The pattern is from 1 4 9 3 5 2 1 8 27 64 7 19 37 12 18 6 1 2 1 etc.

i'm trying to prove that a funtion f(being f injective, and it's inverse are symmetric to the line y=x i can prove that the any segment defined by the points (fx,x) (x,fx) is perpendicular to that line, which also contains the midpoint of the segment. SO the line is the perpendicular bisector to any segment (fx,x)(x,fx) however i realy don't know where to go next? is this enough?whats is the definition of symmetry axe?

Google docs gives the option to draw an orginisation diagram, it shows hyrachy in an orginisation. me parent son1 me son2 me son3 me Drawing this gives you a box at the top entitled parent with a line going down to me and then branching out to 3 sons. Moving on to another expample. 2n n 0 0 2 1 4 2 6 3 The values in the top row are lables, the second column is increased by 1 each row. The first column is double the second column. If we continue this chart up to n=40 and draw it according to the rules this is the result. http://img253.imageshack.us/img253/7651/image1kq7.png This allows you to see th…

Hi, I was wondering where you can find resources and tips on contest math and similar problem solving type questions. I really want to develop my reasoning and problem solving skills. Thanks a bunch.