Search Results for: power

Powers

Powers Date: 10/7/96 at 4:34:52 From: Daniel Johansson Subject: Number to a Power Hello! What do you call it when you have a number raised to a number, like... 3 2 Daniel Johansson Date: 10/17/96 at 11:36:10 From: Doctor Jack Subject:............

Powers

Question : Does or ? Same with a negative fraction. Any tips? Answer 1 : anything to the power of 1/2 is the square root of that base. 8^1/2 = square root of 8 anyting to the power of............

Power

Question : Part 1: At what rate is the spring doing work on the mass as the mass passes through its equilibrium position? I know the answer to this is 0W, but I have no idea how............

power

Question : How much power is wasted in supplying 30000 watts to a small factory at a potential difference of 240 volts if the transmission lines have a resistance of 0.2 ohms in each direction? Answer 1 : Hidden TextP=I^2R............

Powers

Question : Please could someone tell me what 3.2222222 x10 to the power of -5 equals please. left school 10 years ago and have no idea how to do it thankyou! Answer 1 : 0.000032222222 (move the decimal 5 places to the............

power

Question : let a and b be positive integers such that a^n-1 is divisible by b^n-1 for all the positive integer n Prove that a is a power of b Answer 1 : comet_vn wrote:let a and b be positive integers such that a^n-1 is divisible by b^n-1 for all the............

Third power

Question : Prove The sum of the 3rd powers of three consecutive numbers from Z is divisible by 9. Answer 1 : Let´s expand this cubics: (a-1)^3+a^3+(a+1)^3=a^3-3a^2+3a-1+a^3+a^3+3a^2+3a+1=3a^3+6a=3a(a^2+2). And now we have to prove that 3/a(a^2+2). 1)a=0(mod3) and so is proved 2)a=1(mod3) -> a^2=1(mod3) -> a^2+2=3(mod3) and so is proved 3)a=2(mod3) -> a^2=4=1(mod3) and so is............

power

Question : find all natural numbers such that is the power of natural number. Answer 1 : The only solution is 2^3+1=3^2. Assume 2^n+1=x^a where a>1. Then 2^n=(x-1)(x^(a-1)+x^(a-2)+...+x+1) Then x=2^k+1. As a result a must be even for otherwise the second expression would be a sum of an odd............

Powers

Question : I figured out a formula for the sum of 2^0 to 2^n but is there a general formula for x^0+x^1+x^2+.......x^n? Also, I know the formula for 1+2+3+4+5....+n, 1 :^2: +2 :^2: +3 :^2: +......n :^2: , and i know the formula for 1 :^3: +2 :^3: +3 :^3: +.....n............

powers

Question : Very quickly, if your taking powers across the other side eg deifferential equations, how does it work again, im having a blank!!! eg solving for y -y^-5 = 6x+C becomes y = (6x+C)-1/5 IS this right?? If it is can anyone explain the thoery behind............

Power

Question : Find the maximum value of where and Answer 1 : So are you thinking of doing a series of related problems for this, like A&M and Rice usually are, or are you thinking of more of a NOML Vertical type thing with unrelated questions? Answer............

Powers of i

Question : Just going through The Art of Problem Solving: The Basics and came across the following: Why is i^-1 = i^3? Thanks in advance for deigning to answer such a simple question! Answer 1 : Hidden TextTherefore Any number divided by a number equal to itself is equal............

power

Question : , Find min{n} . Answer 1 : Are you sre about the ? In that case, I think the problem follows easily from the greedy algorithm. But according to your other recent post, I think the problem deals with , and in that case, it............

Powers

Question : Prove, that there are no natural numbers m, n satisfying equation: m^3 + 13 = 2^n Answer 1 : It's obvious that n can't be 1. So say . Now we get that . But that's impossible Answer 2 : No, it's not. Answer 3 : The problem............

Powers

Question : Find all natural numbers such that (a) is not a power of two (b) for some prime number and natural number Answer 1 : Only works. This is what is needed for http://www.artofproblemsolving.com/Forum/viewtopic.php?t=82146 and can e.g. be proven by seeing that , setting in and............

powers

Question : Express in and notation Answer 1 : Answer 2 : Altheman wrote:I dont think thats right. But I do not have one either. Answer 3 : there just should not have the k there, but it seems pretty trivial, and the product notation is............

Powers

Question : Find all positive integers x,y,z such that . Bomb Edited by moderator. Bomb, please learn LaTeX Answer 1 : http://www.artofproblemsolving.com/Forum/viewtopic.php?t=32353 Answer 2 : I would appreciate whole soln, thanks. Bomb............

Power

Question : If and , then Answer 1 : Hidden TextFrom we obtain . Thus . Cancelling from both sides and multiplying both sides by , . As we can cancel from both sides, obtaining . Thus and the answer is . Answer............

Powers

Question : Let a be a positive real, and n a postive integer. Depending on the values of a, what is the number of solutions of the equation a^a^...^a^x=x , where a is written n times ? Good luck Answer 1 : This problem does not semm to interest people............

Powers

Question : Prove that for all natural one can find consecutive natural numbers, such that neither of them has the form , , Answer 1 : Chinese Remainder Theorem is what you need: Take an with ( any primes), then is divisible by but............

Powers

Question : Let [tex]n>1[/tex]. Let's shuffle the digits of [tex]n^m[/tex] ([tex]minmathbb{N}[/tex]), and let's denote the new number by [tex]l[/tex]. Prove that for any [tex]kneq m[/tex] we have [tex]n^k neq l[/tex]. P.S. In original problem we had n=2. Answer 1 : consider residue mod 3... it is clear the only case is............

Powers

Question : Find all n such that 2^n-1 is divisble by 3 and this quotient divides m^2+1 for some even m. Bomb Answer 1 : Have a look here : http://www.kalva.demon.co.uk/short/soln/sh98n5.htmlPierre.............

powers

Question : Find integers which satisfy: , where and Answer 1 : Skyward_Sea wrote:Find integers which satisfy:, where and Let , then and . We have , therefore . We have . It give . Et.c. I think it had not solution. Answer 2 : what does mean? I don't............

powers

Question : If , prove that: . Answer 1 : dina013 wrote:If , prove that:.I have two solutions. Solution 1Take of both sides. Then the inequality becomes Let's consider function . It is convex () and is concave, so from Jensen we have which ends the proof. Solution 2Also............

Powers

Question : Hi.. I have the following problem... 2.1604*s^2.513 +0.9921*s^0.512 - 15.95 = 0 I have an answer of s = 2.13 from my text book but i can't seem to calculate it myself.. Can anyone show me the steps leading to the solution ?? Thanks in............

Powers of three

Question : Find such that Answer 1 : t0rajir0u wrote:Find such thatanswer3x-1, 2x, and x obviously have to be less than 6. Testing x = 0 gives the wrong answer, testing x = 1 gives the wrong answer, but testing doesn't. Answer 2 : Hidden TextThis is............

third power

Question : Let , show that Answer 1 : Jumbler, I think etc. gives your inequality. Answer 2 : cause 2 we have : ( with note :) hence : ( note :) where ineq's............

third power

Question : Let be a positive reals. Prove that Answer 1 : By MA-MG inequality: The desired inequality follows from: ............

Power

Question : Please help me! Answer 1 : still no one ? Answer 2 : [No one？ ............

POWER

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