Fraction Definition and 653 Threads

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?

Homework Statement Evaluate ∫1/x(x-1)2, by using the partial fraction method2. The attempt at a solution Stating in partial fraction form: 1/(x(x-1)2 = A/x + B/(x-1) + C/(x-1)2 1 = Ax(x-1)2/x + Bx(x-1)2/(x-1) + Cx(x-1)2/(x-1)2 1 = A(x-1)2 + Bx(x-1) + Cx and this is where I am stuck...

It looks like my first post on this did not make it on this forum some how. I came across this statement. Even though \frac{N_i}{N}=X_i, \frac{dN_i}{N}\neq dX_i How does this work? The book offered no help as well as searches on the internet.

I am a bit confused over the use of the derivative operator dy/dx. I realize dy is a very small change in y and dx is a very small change in x. When combined into dy/dx it is an operator which means take the derivative of y with respect to x. However I notice many authors still treat it as a...

Homework Statement I'm trying to expand the following with partial fractions: H(z) = \frac{z^2 + 1.5932z + 1}{z^2 + 0.9214z + 0.5857} Homework Equations The Attempt at a Solution Just going through my normal procedure, I end up with the following: H(z) =...

I don't understand how to evaluate a fraction in a definite integral, could anyone please explain this problem to me? int. between 3 (lower integral) and 4 (upper integral) of 3x^2+2/x^2 I thought of using the substitution law, and got as far as 1/6 u * du/x ...I don't quite know how to...

Yes, another of these. How do you decompose (z3+1)/(z(1-z)2) ? I've tried A/z + B/(1-z) + (Cz+D)/(1-z)2 and a slew of others that don't work. Thanks a bunch!

I hope its not a problem if I don't have an actual problem. I have a question about partial fractions. When I spilt it into two, the numerator of the original is equal to unknown constant A times secondimerator, plus unknown constant b times first denominator. What if it is spilt into three...

Homework Statement Simplify the following expression by rewriting it as a single simple fraction in simplest form: Homework Equations not much just factoring and solving for P The Attempt at a Solution I tried to factor the fractions by multiplying the denominators with the numerators and...

It's been two years since Algebra I, and I forgot a lot. I'm doing a review of solving equations, and every single one includes fractions. I don't like fractions. The easiest one is as follows (simplified to an improper fraction): 4/3x = 5. If I remember anything about solving equations with...

Homework Statement Solve the following Cauchy problem . y' = (3y2 + t2)/ 2ty y(1) = 1 Homework Equations The Attempt at a Solution I know that the equation is not separable or linear from the get-go. I spoke with my professor and he said it is related to the squared...

Lets say we have a frame of reference moving at, say, 10% speed of light. In it is a nuclear reactor (fusion or fission etc) that can be used to convert tiny amounts of mass into energy. Since the reactor is moving at, say, 10% the speed of light, the mass of the nuclear material would...

Supposedly this proof answers my question. 8 / 16 = .5 8 / 8 = 1 8 / 4 = 2 8 / 2 = 4 8 / 1 = 8 8 / .5 = 16 8 * 2/1 = 8 / .5 I'm just wondering how this proof answers my question?

I've been playing with a computational system that represents numbers in their simple continued fraction form. That is, CF([a0,a1, ... , an]) =a0 + \frac{1}{ a_{1}+\frac{1}{a_{2}+\ddots\frac{1}{a_{n}}} }Considering what types of numbers such a system can represent, the finite CF's correspond to...

I am interested in calculating a a partial sum of harmonic series as an improper fraction. I added 1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10 with my calculator by finding a common denominator and got the fraction 6 999 840/3 628 800. It would take some time to do it for 1/2+1/3+...1/100. Is...

Dear all, It's late in the night and I have some trouble in deriving the expression of the ratio of the illuminated disk to the whole disk. Is it a formula "by definition" ? See...

Homework Statement I want to integrate: \int (\frac{x-a}{b-x})^{c/d}dx Homework Equations given: c<d The Attempt at a Solution I have no idea which integration method to use. i tried to make the integrand look easier by rewriting it as: (1+\frac{b-a}{x-b})^{c/d} but...

Homework Statement arctan(sin((3 / 4) * pi) * 2) = 0.955316618 I want to express that in terms of a fraction with reference to pi. The Attempt at a Solution I thought of first dividing that by pi itself, and then convert the resulting number into a fraction and tack pi on at the...

Partial fraction decomposition for... [b]1. 3x-1 / x(x^2 +4) Homework Equations [b]3. A/x + Bx + C/ x^2 +4 after multiplying through by the denominator and my attempt at finding A,B,C i get this: 3x-1/x(x^2+4) = - one fourth / x + one fourth + 3/ x^2 +4. I don't feel...

I noticed that in this case this is the answer: http://img804.imageshack.us/img804/3513/1con.jpg But this is what I turned up with: http://img163.imageshack.us/img163/4083/reupp.jpg And you can add a +c to that. What did I do wrong?

does pi over infinity equal .00000...314159...? if not please post opinions. :(

Homework Statement 2 = x+2 over x-6 Homework Equations The Attempt at a Solution So, multiply both sides by 2 right? For some reason I am not getting what my book says is right. The end answer is x = 14 I must be doing a step wrong. Can someone show me the steps...

Assume you have a (closed) system with only one component (for instance water) which is in a pressure-temperature-point (p,T) *on the saturation curve* (i.e. liquid and vapor/gas can coexist). Are the mass fractions in the vapor and liquid phases unique? Or is it possible to change the mass...

I came across this problem + solution: http://imageshack.us/m/715/2962/inteyk.png but I don't understand the calculus there. How can you integrate the stuff inside the brackets but not integrate that fraction?

Homework Statement [PLAIN]http://webwork2.math.utah.edu/webwork2_files/tmp/equations/60/0cff8a5107e21ae393dee5038fb6b31.png Homework Equations The Attempt at a Solution I've been attempting to use the general method of solving found at this website...

Homework Statement Simplify: \frac{3a(a^2-4ab+4b^2)}{6a^2(a^2+3ab-10b^2)} Homework Equations The Attempt at a Solution Tried factoring stuff out, etc. This "teach yourself albebra" book is getting more and more annoying. Even mathway.com can't solve them (which is what I used to see steps).

Homework Statement x^2 + x + \frac{1}{4} Homework Equations This should be written in the form: (x+y)^2 Just to add a bit more info, the exercise is to "Write each of the following as the square of a binomial expression". So basically the book teachs to take the rook of x^2 and 1/2...

Homework Statement Hi there, I am trying to complete a thermodynamics assignment. I am doing fine until I get to the following question. "Hx = Specific enthalpy at dryness fraction = hf + x . hfg" - I am not quite sure where Hf came from, I guess they want a value for Saturated liquid from...

Homework Statement http://img64.imageshack.us/img64/7782/circleb.jpg I'm supposed to find the slope equation of the tangent line to the circle at point A. A = (2, 7) The circle's formula is (x+1)2+(y+3)2 = 25 The center point of the circle is therefor (-1, 3) So the slope from the...

Attempt solution attached Manual says the answers is -1 + i

Homework Statement Find the coefficient on the x^2 term in ∫[(x+9)/3] * [log(x+1)] * dx Answer: -1/12 Homework Equations Integration by parts ∫dv * u = u * v - ∫du * v The Attempt at a Solution 1. I integrated by parts to get ------------------------- ∫[(x+9)/3] * [log(x+1)] * dx] =...

Hello, I was wondering what fraction of the energy delivered by the sun is due to UV-radiation. For example, when I have a solar panel which "catches" 1kJ of solar energy. What will happen if there would be no UV frequencies in the solar spectrum? How many percent less energy will I capture...

Homework Statement A 2.0 mm diameter iron ball is charged to +48 nC. What fraction of its electrons have been removed? The density of iron is 7,870 kg/m3. Homework Equations Q = Ne; N = number of atoms in 1 mole, e is atomic charge, Q = point charge N = Avagadro's Constant =...

Homework Statement You want to do an experiment using 47Ca (half-life=4.53 days). You will need 3.25 μg of the nuclide. What mass of CaCO3 (100% enriched in 47Ca) must you order if it will take 50 hours to be delivered to you from the nuclear facility where it is prepared? Homework...

Separate the fraction!:) Hi! Could somebody can me, please? I want to separate this expression ([G + 1/T]*Omega^2) / ([4*Delta^2] + [G + 1/T]^2) into two parts so that one would be (G * Omega^2) / (4*[Delta^2 + G^2/4]) or separate this expression Omega^2/(4*[Delta^2 + G^2/4]) into two...

As a mathematical novice I have been following with great interest the recent debates (in more than one forum!) as to whether 0.999... = 1. The question is whether two ostensibly different natural numbers are equivalent, equal and synonymous. (I quote the three terms because mathematicians...

Homework Statement The question asks for the fraction of all 2M(sun) stars ever made in the Galaxy that are still burning on the main sequence. It assumes star formation at constant rate. The age of the Galaxy is 10GYRS To do this I imagine you use the salpeter IMF and find the constant...

5x^2 + 8/x3 + x2 I got a 5x^2 + 8 = A/x^2 + B/x + 1 A(x+1) + B(x^2) (Ax+A) + (Bx^2) (Ax + Bx^2) + A 5x^2 + 8 = (A + B) x + (A)x^2 5x^2+x+8=(A+B) + (A) This is about as far as I can get but I think I made a mistake somewhere but I don't know where? Can someone help me?

Determine A and B in terms of a and b. ax + b divided by x^2− 9=A/x-3 + B=x+3 When i calculate it i get a+b/2 and a-b/2 but that's wrong. I need help with this one.

Homework Statement Find the first derivate of \frac{2}{x+1}. Formula: \frac{f(x+h)-f(x)}{h} Homework Equations Formula: \frac{f(x+h)-f(x)}{h} The Attempt at a Solution \frac{\frac{2}{x+h+1}-\frac{2}{x+1}}{h} h(\frac{2}{x+h+1}-\frac{2}{x+1}) h(\frac{2(x+1)-2(x+h+1)}{(x+1)(x+h+1)}...

Homework Statement I am to derive an expression for the fractional recoil energy over all scattering angles from the equation given below. Homework Equations The following is the expression for the kinetic energy of Compton recoil electrons as a fraction of the incident photon energy...

I need to integrate the function 1/(X^7 + x) which simplifies to 1/x(x3 + 1)(x3 - 1) or any other problem where the degree of the denominator is at least 2 larger than the numerator. how do I do this?

Homework Statement A 10% (by wt) solution of KNO3 would have what molality and what mole fraction Homework Equations mole fraction = moles of KNO3/total moles wt % = # g of solute/total g molality = # moles KNO3/kg H2O The Attempt at a Solution 1 g KNO3/10 g total 1 g KNO3/101.1...

The equation i currently have is (-7s+52)/(s^2-8s+16) I need to convert it into a partial fraction decomposition to do a inverse Laplace Transform, but i seem to be stuck with the algebra of the what I am supposed to do. The equation I am supposed to use to set them is A/(s+a) +...

Homework Statement Use substitution to find the integral of (12x2 + X -12)/(3x - 2) Homework Equations The Attempt at a Solution I know I need to use long division to work it down to a proper fraction. That is where my real problem lies. Using long division I get that...

Hello everyone, I don't understand the importance of this. Now I don't exactly understand what is the importance of filtration fraction. If normal GFR is 125 ml, in aortic stenosis filtration fraction increases, what does this mean? Does it mean that kidney has to now work harder to...