Mathematics

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.

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))