Mathematics

I have asked this question before but have never really had a satisfactory answer to it, so I will throw it out here and see what happens. the problem is based on a faulty lightbulb that flashs. However it's flashing is based on the infamous infinite sequence 1 + 1/2 + 1/4 + 1/8 ..... i.e. the light is on for 1 minute and off for 1/2 a minute, goes on for 1/4 of a minute and off for 1/8th of a minute. Now it is well known that this sequence never reaches 2. Therefore at two minutes is the bulb on or off???? Now I'm well aware that this could not physically happen due to the nature of a light bulb, but I want a theoretical answer! i.e. the ideal light bulb, …

nicole, lacey, alec and emilee went to the grocery store to buy some food. If each child picked up one of the foods above, how many combinations could there be, using only these foods? 1. Apple 2. Banana 3. Strawberry 4. carrot 5. ice cream 6. cherry

Half-way through some derivations and I find that I come across an elementary mathematical operation that I embarassingly don't understand. Somehow it seems to have eluded me. The jump from 1 to 2 is: [MATH]z = \sqrt{jA^2}[/MATH] [MATH]z = \sqrt{j}A[/MATH] [MATH]z = \frac{1}{\sqrt{2}} A (1 + j)[/MATH] j indicates the imaginary number. I'm not sure how the square root j was expanded there. Would anybody please explain the idea behind this? Any other generalities to look out for?

I have come across this question while doing my maths homework:- Given that 3^x = 9^(y-1), show that x = 2y - 2 Could anyone give me a hint on how to start. Thank you in advance.

Show that a/c + b/a + c/b > a+b+c, for a, b, c > 0 and a*b*c<1

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?

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

right now we start algebric equations its too difficult to understand the difference between the methods of addition subtraction multiplication and division can any one explain in simple language

Hello This My Problem if anybody can help me to solve it I will so pleased : We have some buildings in fire with some parameter : 1) Fieryness -> that is a number between 1-3 2) Fire Transmission Rate -> that is 1.0 or 1.5 3) Volume of building 4) Area of building and also we have 10 firebrigades who must extinguish buildings. They can pour 1000 litre water per minute. I need a formula or function which tell me : How many Firebrigade will need to extinguish Building X (with it's parameter) ?? And How much time it lasts to extinguish Building X (with it's parameter) by n number of FireBrigad(s)?? Thank You So Much Best Regards Mahdi…

Recently my friend proved theorytically 1=2 using a,b. Like this will one num be equal to another?

Sorry if I put this in the wrong sub-forum (I don't know all the mathematical expressions because I study maths in Estonian). Anyways... Two dices are tossed at the same time. What are the chances that the sum of the points is atleast 4? 31/36?

This is homework-related, so hints should suffice. The text discusses how to negate conjunctions, disjunctions, conditionals, and biconditionals. The examples given are in symbolic logic and English expressions. However, some of the exercises require negating compound statements whose component statements are mathematical expressions. A sample problem is thus [math]3 < 5 \mbox{ or } 7 \geq 8[/math], whose answer at the end of the text is given as [math]3 \geq 5 \mbox{ and } 7 < 8[/math], which happens to be the only answer given. This seems to make some sense if one notes a De Morgan's Law that previously is discussed, which is [math]\neg (P \vee Q ) \Longle…

Hello, i heard from my friend that infinity to the power of infinity is greater than infinity. (e.g opposed to infinity plus 2 would = inifinity). he said there is some mathematical model to prove this. and analogies. i know that the maths is over my head but could some people give me information about this concept

This conjecture states that: Every odd positive integer is the sum of a prime and a power of two. Obviously this conjecture was proved false as a counterexample was found: 509 But, how do I prove that 509 is not the sum of a prime and a power of two? After that, what's the next smallest counterexample after 509?

Use Bertrand's Postulate to show that every positive integer n with n >= 7 is the sum of distinct primes. I know that Bertrand's Postulate states that for every positive integer n with n > 1, there is a prime p such that n < p < 2n. So, in our case since n >= 7 > 1 we can deduce that n < p < 2n That's pretty much all I can say looking at the postulate itself. What else?

Hi all! I'm supposed to prove the following: Suppose that m is a positive real number. Show that Sigma(j^m), j runs from 1 to n is O(n^(m+1)). So we have: Sigma(j^m), j runs from 1 to n = 1^m + 2^m + 3^m + . . . + n^m I think we should use induction on m here to prove this. Basis Step: m = 1 This is definitely true for m = 1 because we have Sigma(j^1), j runs from 1 to n = n(n+1)/2 which is O(n^2) Now, O(n^2) = O(n^(1+1) = O(n^(m+1) Inductive Step: Assume Sigma(j^m), j runs from 1 to n is O(n^(m+1)) to be true. That is, it is true for m = n. (Inductive Hypothesis) Then must show it is also true for m = n + 1: …

Hi all! I'm supposed to use Euclid's proof that there are infinitely many primes to show that the nth prime p_n does not exceed 2^(2^(n-1)) whenever n is a positive integer. Conclude that when n is a positive integer, there are at least n+1 primes less than 2^(2^n). Any help will be greatly appreciated. Thanks!

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))

I'm just wondering if anyone knows any decent books (not magazines) for puzzles. I am not interested in sudoku, word searches, crosswords etc... I prefer maths, geometry, logic and science puzzles. Especially ones that are challenging (but not impossible i.e. PhD standard!!!!) Websites are good, but I'd prefer books... Thanks

This is my first assignment of my first math class or my first year of univercity and they said i should have learned this in grade 11, (too long ago to recall really) so i want to make sure i got them right (which i doubt!) here's how it is, i will give the question and my answer and if i am wrong please tell me. 1) [math]\frac{5x^4}{\sqrt{x^3-6}}+x\sqrt{x^3-6}[/math] solution: [math]\frac{6x^4-6x}{\sqrt{x^3-6}}[/math] 2) [math]\frac{\frac{x^2-x-6}{4x-12}}{\frac{2x+6}{x^2+5x+6}}[/math] solution: [math]\frac{(x+2)^2}{8}[/math]

Today my maths teacher showed us how we can expand [math](x+1)^n[/math] using pascals triangle. For instance, to find [math](x+1)^4[/math], we know that the fourth layer of pascals triangle is 1,4,6,4,1 and these numbers come into the awnser:[math]x^{4}+4x^{3}+6x^{2}+4x+1[/math], the other bits to be put in are fairly simple. This was pretty impressive but if the exponent were 15 I wouldn't really want to draw up a 15 layered pascal triangle, I'm to lazy. So my question is: is there a way I can work out the [math]n^{th}[/math] layer of Pascals triangle without working down the whole thing?

Finding limits of infinite series is possible but I don't know how to calculate the limit of a multiplicative series. I put the problem I have on a website including the background to the problem, would be interested in any insights or alternative ways of doing the sum.... http://www.geocities.com/mobiusmaths/infpoly.htm

This is a question from my school text book:- The line y = 3x - 5 meets the x-axis at the point M. The line y = -2/3x + 2/3 meets the y axis at the point N. Find the equation of the line joining the points M and N. Write your answer in the form ax + by + c = 0. For point M i got the coordinate (5/3, 0) and for point N (0, 2/3) I next worked out the gradient of the line connecting M and N to be -2/5 and tried using y - y1 = m(x - x1) to get the equation for the line eventually getting to 6x - 15y - 3 = 0, however the book lists the answer as 6x + 15y - 10 = 0. Is my answer the correct answer and the book's answer wrong, or did i mess up in my working out …

a vector is given by [math]\vec{v}=\sum_{j=1}^{n}a_j{\vec{i_j}}[/math] where i is the unit vector for a given dimension and n is the number of dimensions of the space in which the vector exists. the magnitude ([math]|\vec{v}|[/math]) is given by [math]|\vec{v}|^2=\sum_{j=1}^{n}a_j^2[/math]. the unit vector in the direction of the vector v is given by [math]\vec{u}=\frac{\vec{v}}{|\vec{v}|}[/math]. if theta is the angle between vectors A and B, then [math]{\vec{A}}*{\vec{B}}={|\vec{A}|}{|\vec{B}|}{\cos{{\theta}}}=\sum_{j=1}^{n}a_jb_j[/math]. [math]\cos{\theta}=\sum_{j=1}^{n}\frac{a_jb_j}{|\vec{A}||\vec{B}|}[/math]. the projection of A on B is [math]Proj_{\vec{B}}{\vec{A}}…

This is from a 6 part physics homework problem, I got part a-e, but part f (likely to be my grade ) is what I'm having some trouble with: A mass m slides down a frictionless incline and sticks to a spring (spring constant k ), initiating simple harmonic motion. f) What is the angular frequency of the SHM? I got [math](k/m)^{1/2}[/math] as the solution (someone please tell me how to get the Latex radical )