Fraction Definition and 640 Threads

Now this is a pretty straight forward question. And I just want to make sure that I am not doing anything stupid. But when doing partial fraction expansions of the type \frac{K}{s^{2}+2\zeta\omega_{n}s+\omega_{n}^{2}} Shouldnt I always be able to factor the denominator into the following...

\text{We have: }\:\dfrac{1}{89} \;=\;0.01123595\,\,.\,.\,. \text{The decimal is formed like this:} . . 0.0{\bf1} . . 0.00{\bf1} . . 0.000{\bf2} . . 0.0000{\bf3} . . 0.00000{\bf5} . . 0.000000{\bf8} . . 0.000000{\bf{13}} . . 0.0000000{\bf{21}} . . 0.00000000{\bf{34}} . . . . . . \vdots...

Can anyone help with the following question - see attachment. Answer C is correct. I have been told that it can be solved thus: As our compound contains carbon and hydrogen we need to calculate these masses and deduct them from 128 to give us the mass of the chlorine and bromine...

Homework Statement I want the simplify the following equation Homework Equations \frac{x}{{p}^{2}}+\frac{n-x}{{(1-p)}^{2}}, where p=\frac{x}{n}The Attempt at a Solution I got this \frac{{n}^{2}}{x}-\frac{{n}^{2}}{n-x}, I don't think this is the right answer.

As part of a project I have been working on I fin it necessary to manipulate the following expression. e^(icx)/(x^2 + a^2)^2 for a,c > 0 I would like to decomp it into the form A/(x^2 + a^2) + B/(x^2 + a^2) = e^(icx)/(x^2 + a^2)^2 but I am having trouble getting a usable outcome.

\displaystyle\frac{1}{998,001} \;=\;0.\overline{000\,001\,002\,003\,004\,005\, \cdots\,996\,997\,999}\, \cdots The decimal representation contains all the 3-digit numbers except 998 . . and the 2997-digit cycle repeats forever. This is just one of a family of such fractions. Can you determine...

Hi guys I have a question here relating integration by partial praction.. the question said what is the antiderivative of x^2+2x-1/2x^3 +3x^2 - 2x valid only when x > 1/2. anyway i had poor background in math and working hard to catch up... I don't understant why "valid only...

Homework Statement x^2-x-13/(x^2+7)(x-2) hello i am having trouble solving this problem.. could anyone please show me how to do this step by step? i know polynomial long division is required before it can be converted to partial fractions. I also know the answer is 2x+3/x^2+7 - 1/x-2...

Homework Statement I want to check the answer to this question. ⌠ 2 x dx / (x+1) (x+2) ⌡ 1 Homework Equations The Attempt at a Solution For partial fraction I got A= -1 and B = 2 My final answer is -ln 2 + ln4 - ln3 = ln 4/ ln2 * ln 3

One of the major concerns in any Cosmic Microwave Background (CMB) anisotropy analysis is to determine which fraction of the observed signal is due to some foreground contaminant. Two sources of foreground contamination have been firmly identified: the diffuse Galactic emission and unresolved...

Homework Statement \frac{2e^3}{((s^2)-6s+9)*s^3} you can factorize the denominator into s,s,s,(s-3),(s-3) that gives you 5 residuals. the first 3 should all be the same value but that's apparently not correct, so where am I going wrong?

Homework Statement Julie tightened herself fastened a set of bathroom spring scales to a platform and went down a 30 degree slope. No friction was present and the platform supporting the scales was HORIZONTAL. what fraction of her true weight was indicated by the scales? The Attempt...

Homework Statement I'm supposed to decompose 1 / x(x2 + 1)2 Also, we haven't learned matrices yet so I can't use that technique to solve it. Homework Equations None. The Attempt at a Solution 1 / x(x2 + 1)2 = A/x + (Bx + C) / (x2 + 1) + (Dx + E) / (x2 + 1)2 I multiplied...

This program has been assigned in my intro to programming course, which assumes no previous knowledge of programming. Up to this point we've only been required to write functions that accomplish specific tasks within a program. This is the first time we've been asked to design and write a full...

Homework Statement Approximately what fraction of molecules of a gas (assumed ideal) have velocities for which the angle φ lies between 29.5° and 30.5°, while θ lies between 44.5° and 45.5°? Homework Equations The Attempt at a Solution What does the question even mean...

I was wondering what fraction of 3*3 square matrices are singular? I guess if the elements are real then the answer will be vanishingly small. If however, the elements are integers, is there a way to work this number out?

Homework Statement \stackrel{lim}{x\rightarrow}∞ \sqrt{x^2+x}-x I'm taking the limit of a rational function as x approaches ∞. However, within the problem, there is an algebraic arrangement I'm having trouble with. How would I get from the first fraction to the second fraction? Applying...

I know that you cannot view \frac{dy}{dx} as a fraction, with dy and dx meaning infinitesimal changes in their respective variables, but what I do not understand is why not. Can anyone explain to me why you can't (correctly) view the derivative as a fraction?

I want to split the fraction: 2a/((a+1)(a2+4)) I have tried using partial fractions, but came to something that was nonsense, and my question is why that is. Why doesn't partial fractions work in this case, from a mathematical point of view, and is it still possible to split up the fraction...

Homework Statement Carbon 14 has a half-life of 5730 years, what fraction will have decayed in 2300 years? Homework Equations Nf/No =e^-kt The Attempt at a Solution Nf/No =e^-1.21 x 10^-4 x 2300 =0.068585374 However if I use Nf =No(1/2)^2300/5730 I get 0.757125224 I...

Basically i have this code, obviously the fraction is in display maths, but i want BIG products too, with sub/super scripts above and below rather than next to it. Thanks $$ pr(X=k)=\mu\frac{\prod^{k-1}_{i=1}\{1-\mu+(i-1)\theta\}}{\prod^{k}_{i=1}\{1+(i-1)\theta\}}, \quad \mbox{for k$\geq$ 1,} $$

A block slides a distance d down a frictionless plane and then comes to a stop after sliding a distance s across a rough horizontal plane, as shown in the accompanying figure. What fraction of the distance s does the block slide before its speed is reduced to one-third of the maximum speed it...

This is throwing me through so many loops. I have the equation 1/(x^3 + xa^2). I can not for the life of me decompose this equation. I use 1(x^3 + xa^2) = A/x + (Bx + C)/(v^2+a^2) I can get A=1/a^2, but from there progress stops. All examples on the internet and books only have...

Homework Statement I am told this is wrong, but I am convinced it is right. I just need to show how but don't have a clue. Homework Equations (ab)/(2c(d+e))+(ab)/(2c(d-e))=(abd)/(c(d^2-e^2)) The Attempt at a Solution I do not have a clue where to start. I am clueless as...

Homework Statement Use the definition of a derivitive to find f'(x). f(x)=1/(1-4X) Homework Equations Lim as h approaches 0 [f(x+h)-f(x)]/h The Attempt at a Solution I know that the answer is supposed to be -1/(1-4X)2 but I keep getting 4/(1-4X)2. This is what I have done so far (I...

Hello, Is there any general formula for the partial fraction of the following function: \frac{1}{(ax_1+1)(ax_2+1)\cdots (ax_L+1)} I can work for L=3, but it get involved for larger L! Thanks in advance

Homework Statement I came across a problem that I can't solve and it is ∫dx/x(x^2 + 4)^2 Homework Equations None The Attempt at a Solution So I'm pretty sure this is to be solved by partial fraction since I am on a chapter on Integration by partial fraction. so I started with...

Hi Everyone, I am trying to calculate the mass of oxygen and keep running into dead ends and was wondering if anyone could offer any insight. I am trying to find the resulting mass of oxygen in a 6m x 6m x 6m enclosure at standard temperature and pressure when the mole fraction of oxygen...

Homework Statement Simplify \frac{2}{49^{1/3}+7^{1/3}+1}Homework Equations The Attempt at a Solution I can simplify \frac{2}{49^{1/3}+7^{1/3}} but I don't have idea how to do this one.. EDIT: I have found it. No need to reply this. Thanks :)

how would one evaluate this without using trig substitution? Is it possible to make one integral out of this? {int[(y^2 + a1^2)^-1]dy +c1}/{int[(x^2 + a2^2)^-1]dx +c2} +c3 the numbers behind the 'a's and 'c's are supposed to be subscripts. Also, how would one deal with this...

if: arctan[tan(f(x))/tan(g(x))] then, f(x)/tan(g(x)) ? Is this correct or does the tan function at the denominator also vanish? Please advise

Homework Statement ∫(1/(x^2-x+1)dx Homework Equations No idea The Attempt at a Solution I tried this by the subsitution method but that attempt was feeble as it only complicated the integral even further. let t=x^2-x+1 this integral can neither be split into partial...

This problem comes from an engineering exercise (hence the C/R which you can ignore). I want to see if I got it right. http://img51.imageshack.us/img51/3989/mama1h.jpg http://img851.imageshack.us/img851/3401/mam2.jpg

Is it possible to have an solution to this sort of integral? And if not, why not? \int_0^\infty \frac{e^{-ax}}{e^{-bx}+e^{-cx}}dx Is a Taylor expansion the only way forward? Many thanks David

Hi all, am stuck with the integral with fraction in exponential The equation I=∫exp(bz)/(a+iz)*exp[(6*a^2-ik*w^2*z)/(z^2+a^2)]*dz I already tried to partial fraction the 2nd exponential term, then i tried to perform integration by parts but it doesn't work well.i tried substitution too...

Q: Given a fraction A/B when does there exist a finite group G and an automorphism f s.t. exactly A/B elements of G are mapped to their own inverses (f(a) = a-1? If so how can we find the group? Does anything change if we allow infinite groups? I have a friend who was preparing for an intro...

Homework Statement What fraction of the air molecules in a house must be pushed outside while the furnace raises the inside temperature from 17.0° C to 28.0° C? The pressure does not change since the house is not 100% airtight. Homework Equations v2/v1=17+273/28+273 =.963 Why is my...

Homework Statement \frac{\frac{2}{3}x(x^{2}+4)^{1/2}(x^{2}-9)^{-2/3}-x(x^{2}-9)^{1/3}(x^{2}+4)^{-1/2}}{x^{2}+4} The Attempt at a Solution \frac{x(x^{2}+4)^{-1/2}(x^{2}-9)^{-2/3}(\frac{2}{3}(x^{2}+4)-(x-9))}{x^{2}+4} Then: \frac{x(\frac{2}{3}(x^{2}+4)-(x-9))}{(x^{2}+4)^{3/2}(x^{2}-9)^{2/3}}...

Homework Statement Show that n/(n+1)!=(1/n)-(1/(n+1)!) I am totally lost on the algebraic steps taken to come to this conclusion. It is for an Infinite series. Thanks

Homework Statement H(z) = \frac{6-z^{-1}}{1+0.5z^{-1}} + \frac{2}{1-0.4z^{-1}} = k + \frac{A}{1+0.5z^{-1}} + \frac{2}{1-0.4z^{-1}} where A = (6-z^{-1}) is evaluated at z^{-1}=-2. Homework Equations Partial fraction expansion. The Attempt at a Solution Why is z^{-1} set equal to -2? I...

I was reading and came across a formula that didn’t look right so I tried to simplify the left side to match the right side; however, my fraction algebra is a little rusty and could use some guidance. I did get the 2 fractions to a common denominator; however, the best I could do was factor out...

I need help with Iterated Integration. I'm trying to integrate the following equation: ∫ylnx/x from e^y to y for dx, y>0 (sorry about the messy equation; first time user) I know how to integrate ln, but the fraction has me thrown for a loop. I tried U-substitution, but the equation kept...

Homework Statement i need to integrate: \frac{1}{r(u-r)}dr Homework Equations u is a constant The Attempt at a Solution im not sure if i should decompose the fraction. i tried that, but it didnt seem to be of any help.

im studying for my circuits midterm and the proff has handouts with questions and answers but not detailed answers. i can't figure out how he went from a fraction to an answer. (-j2)(2+j2)/-j2+2+j2 the answer on the paper is 2-j2 i do not know what I am allowed to do with the 2 next to...

\lim_{n\rightarrow ∞}\frac{3^n+2*5^n}{2^n+3*5^n} I tried using l'hopitals rule and got \lim_{n\rightarrow ∞}\frac{3^n*ln(3)+2(5^n*ln5)}{2^n*ln(2))+3(5^n*ln5)} I'm not quite sure if that is the right way to approach this. This problem is an early one in the assignment so I assume that...

Hi, I think I have the first part of the question correct but can't seem to get the second so any help would be fantastic. Q: Express \frac{327}{117} as a continued fraction and find the convergents of it. My working: \frac{327}{117}=2 +\frac{93}{117} =2+\frac{1}{\frac{117}{93}}...

Homework Statement Derive y= \sqrt(2x^4) - \frac{5}{3x^2} The Attempt at a Solution I am still at the first part of the function (the root): First I tried to derive inside the root like this: \sqrt(2x^4) = \sqrt(8x^3) = 2 \sqrt(2) \times \sqrt(x^3) = \sqrt(2) \times x^2...

Homework Statement Heat Q flows into a monatomic ideal gas, and the volume increases while the pressure is kept constant. What fraction of the heat energy is used to do the expansion work of the gas? Homework Equations ΔU = Q - W Q = nC_pΔT W = PΔV C_p = C_v + R => C_p = 3R/2 + R => C_p =...

Homework Statement Find the lim of \frac{\sqrt{6-x}-2}{\sqrt{3-x}-1}when x approaches 2, without using L'hopital rule or the definition. Homework Equations The Attempt at a Solution I try to multiply both the numerator and the denominator to get \frac{(\sqrt{6-x}-2)(\sqrt{3-x}-1)}{2-x}, but...

The problem: f(x)=3-3/5x So I'm perfectly fine with finding the derivatives with stuff but I wasn't sure about this one. Would this be 0 because there is a three in the numerator and no x? Or would it be 3-1/51-1=3-1=2?