Fraction Definition and 640 Threads

Homework Statement Question is attached in this post. Homework Equations Question is attached in this post. The Attempt at a Solution Disk Method with the radius equal to 1/(x^2+5x+6) ∫A/(x+2) + B/(x+2)^2 + C/(x+3) + D/(x+3)^2 from 0 to 3 I've used algebra to solve for...

Ok I'm stuck I have $$\int \frac{x^2 - 5x + 16}{(2x + 1)(x - 2)^2} \, dx$$ and I got to this part: $$x^2 - 5x + 16 = A(x - 2)^2 + B(x - 2)(x + \frac{1}{2}) + c(x + \frac{1}{2})$$So do i need to distribute all of these and factor out or is there a simpler way? I found a solution where they are...

Homework Statement Here is the problem in the book: Here is the solution: What I don't get is why the solution defines the fraction to be ni/(5*1022). Shouldn't it be 2*ni/(5*1022) since we have both donors and acceptors, so there are actually twice the number of atoms. Also...

Quick question... I know that if the numerator is greater than the denominator I need to divide out by long division BUT If the numerator is equal to the denominator (the exponent is what I'm talking about to be specific) then, do I need to do anything? Because I'm stuck on this problem $$\int...

Homework Statement (t4+9)/(t4+9t2) Homework Equations The Attempt at a Solution I'm not completely sure if I'm using the correct method to solve this. Since the degrees of the numerator and denominator are the same, wouldn't you divide the denominator into the numerator? Here is...

Homework Statement Radioactive decay of elements in the Earth's interior results in a mean heat flux through the Earth's surface of 5x10^-2 W/m^2. What is this flux expressed as a fraction of the energy flux due to thermal re-radiation of absorbed solar energy? If radioactive decay were the...

Here is the question: I have posted a link there to this thread so the OP can view my work.

Please could somebody explain how the coefficient of static friction can be quoted as a constant in tables etc? \mu_s = F_s/ R In most cases the reaction force is constant but as I push the box harder the friction force increases. Is \mu_s actually the coefficient of limiting friction? Or...

how would i convert 7.8 x 10^-3 = 39/5000 / 7.8 x 10^-3 into a fraction on my calculator? I know the result is 0.0078 but I don't know how to get it, thanks!

Q3.) Express as partial fractions. a) $$\frac{3x+4}{x^2+3x+2}$$ b) $$\frac{5x^2+5x+8}{(x+2)\left(x^2+2 \right)}$$ c) $$\frac{x^2+15x+21}{(x+2)^2(x-3)}$$

If a worker can wash all the glass windows of a building in 9 days, what part of the job can said workers finish in 6 days?1. ¼ 2. 1/3 3. 2/3 4. 3/5 5. ¾

Here is the question: I have posted a link there so the OP can view my work.

http://en.wikipedia.org/wiki/Partial_fraction_decomposition In general, if you have a proper rational function, then: if ## R(x) = \frac {P(x)}{Q(x)} ## and ## Q(x) = (mx + b)^n ... (ax^2 + bx + c)^p ## where ##Q(x)## is composed of distinct linear powers and/or distinct irreducible...

Why does the molar fraction of a solution not depend on temperature? In other words, why will heating a solution preserve its composition? It seems to me that if I have two substances that evaporate at different rates, the substance with the faster evaporation rate will pass more moles into...

Homework Statement I'm taking the Laplace transform of F(s), and the first thing is to expand it by partial fraction or something so that I can match F(s) with a table of laplace transforms. Homework Equations The Attempt at a Solution Does partial fraction even work? I've got two...

Homework Statement An engine is operated with a special fuel mixture solely composed of carbon, hydrogen and oxygen. A fuel breakdown showed the following values: mass fraction carbon mass fraction hydrogen ,fuel density c = 0.81 h = 0.15 ρ=0.75 kg/dm³ fuel mass flow rate m_b=2 g/s relative...

If the flux entering such an atmosphere from the core of the star at a radius is r0 is F0, the flux that reaches radius r is given by F(r)=F0*e^k(r^-2-r0^-2) where k is a constant a) Write down a formula for the fraction of the incident flux that escapes from the star entirely...

Homework Statement A spherical object with moment of inertia 0.57mr2 rolls without slipping down an incline. At the bottom of the incline. Homework Equations For a sphere (or cylinder) rolling without slipping ω = v/r. Rotational KE = ½Iω² The translational kinetic energy = ½mv²...

EDIT: I left out something of major importance, I want to maximize with respect to a! Good day, I've run into an issue in solving a certain problem with matlab, and I was hoping if anyone could help me out. I am relatively new to matlab, so I don't even know if this is possible, but I...

EDIT: I left out something of major importance, I want to maximize with respect to a! Homework Statement My problem is rather complex, but in the end it boils down to maximizing the fraction Homework Equations With the calculus I know, I can't evaluate these integrals, so I have no applicable...

First of all, THIS IS NOT HOMEWORK. It's related to my research. And forgive me if this is rather elementary (sadly, I was something of an underachiever at school, which has left some gaps in my maths education that I've been working on since I returned to education) but I have a question...

Let $x_1, x_2, x_3, x_4, x_5$ be real numbers satisfying the following equation: $\dfrac{x_1}{m^2+1}+\dfrac{x_2}{m^2+2}+\dfrac{x_3}{m^2+3}+\dfrac{x_4}{m^2+4}+\dfrac{x_5}{m^2+5}= \dfrac{1}{m^2}$ for $m=1, 2, 3, 4, 5$. Find the value of $\dfrac{x_1}{37}+\dfrac{x_2}{38}+\dfrac{x_3}{39}+...

Suppose A and B form an ideal solution under a piston. The vapor pressure of pure A is 300 mmHg and that of pure B is 800 mmHg (at the same temperature). If the piston maintains 700 mmHg, what fraction of vapor is present in a 40 mole% A and 60 mole% B mixture. The answer is "there is no...

if b is the mean proportion between a and c ; prove that (a^2 - b^2 + c^2) / (a^-2 - b^-2 + c^-2) = b^4

Homework Statement Show that: Ʃ(-1)n/(n^2+a^2) (from n=0 to ∞) = pi/[asinh(pi*a)], a\neq in, n\in Z. Homework Equations f(z) = f(0) + Ʃbn(1/(z-an)+1/an) (from n=1 to ∞) , where bn is the residue of f(z) at an. The Attempt at a Solution The main problem is I don't how to pick the...

Homework Statement Solids consist of a crystalline lattice of atoms-a unit cell that has a certain configuration of atoms that is repeated over and over. The picture that I can't post here, shows a pyramidal structure of metal spheres. The base is 8 spheres by 8 spheres with a height of 8...

Homework Statement I'm having a brain fart, how do you factor/simplify a fraction such as \frac{ab}{ab+cd} I keep thinking multiply by ab-bc but I'm not sure.

so I was reading my textbook and was showing steps on applying the quotient rule to the function: y=ex/(1+x2) it went from (1+x2)(ex)-(ex)(2x)/(1+x2)2 to ex(1-x)2/(1+x2)2 I understand the first step, but don't get how they got to ex(1-x)2 in the numerator. can someone please explain the...

Homework Statement Consider the following aqueous solution at 25°C Cr2(SO4)3, 1.26 mol/L, 1.37 mol/kg Calculate the mole fraction, density and % w/w Homework Equations χ = n Cr2(SO4)3 / n Cr2(SO4)3 + n H2O Unit conversions ρ= g solvent / mL solution % w/w = mass solvent / 100 g...

My professor asks us to solve the integral of: [x/(x^4 + 1)]dx This expression is not factorable; what should I do? She is asking us to solve specifically using PFD, not u-substitution.

Homework Statement Radiation of intensity I is normally incident on an object that absorbs a fraction frac of it and reflects the rest back along the original path. What is the radiation pressure on the object? Homework Equations Radiation pressure Pr (force/unit area) Pra = I/c...

2h/h2 + 2h + 2 does the 2h cancel out?

ok so i have this code: import java.util.Scanner; class doubleEncodingClass { public static void main(String args[]) { byte largestPositiveByte = 127; short largestPositiveShort = 32767; int largestPositiveInt = 2147483647; long largestPositiveLong =...

Homework Statement A cross country team race is about to begin and team Beta decides to use their one-dimensional kinematics knowledge that they learned from their first year physics course. Each team consists of two people and one horse. The clock is started when the team crosses the...

Homework Statement ∫(2e^x)/(e^(2x)-1)dx Homework Equations The Attempt at a Solution I was told to solve using partial fractions. When I set up the partial fraction I got: A/e^x+1 + B/e^x-1 = 2e^x When I broke it up, I solved for A and B and got that A and B should both...

I'm having problem with task (a) in this problem The question My attempt The solution Why don't I get the same after I take the partial fraction using my calculator? And where does this R(s)=1/s^2 come from

Homework Statement A 48.7 g ball of copper has a net charge of 2.2 µC. What fraction of the copper's electrons have been removed? (Each copper atom has 29 protons, and copper has an atomic mass of 63.5.). Homework Equations The Attempt at a Solution Number of electrons normally present ...

$\displaystyle\frac{-9b^2(a+3b)^{m+2}(2b-4c)^{2+m}}{4(3a+9b)^{2m+2}(b^2-2b^2)^{2-m}}$ my answer to this is $\displaystyle-\left[\frac{2(b-2c)^2b}{9(a+3b)}\right]^m$ i used some factorization of some quantity to arrive to this answer. but I'm not sure how did that technique works. for...

I feel stupid asking this, but I just can't see it. I need to simply this and I already know the answer, but I don't know why this is the answer. simplify 3p-3q 5p-5q My first reaction was to remove a factor of p-q but that would leave p-q(3-3) p-q(5-5) Which would be 0/0. I...

This is more of a pre calc question but it dose however come from diff eqs, just in case I have made fundamental mistakes, i have posted it here. I have been studying this topic for few days by myself, never had any problems with algebra until here. really appreciate all of your help...

Homework Statement Find Partial Fraction Decomposition of ##(x^4 - 1) / (x^3 + x^2 + x)## Homework Equations The Attempt at a Solution ##(x^4 - 1) / (x^3 + x^2 + x) = (x^4 - 1) / (x)(x^2 + x + 1) = A/x + B/(x^2 + x + 1)## ##(x^4 - 1) = A(x^2 + x + 1) + B(x)## ##(x^4 - 1) = Ax^2 + Ax...

Which of the fractions is greater? $$A=\frac{\overbrace{333\cdots331}^{ \large{\text{2012 pieces}}}}{\underbrace{333\cdots334}_{ \large{\text{2012 pieces}}}}$$ or $$B=\frac{\overbrace{222\cdots221}^{ \large{\text{2012 pieces}}}}{\underbrace{222\cdots223}_{ \large{\text{2012 pieces}}}}$$?

Here is the question: I have posted a link there to this topic so the OP can see my work.

if there is something like (x^2+3x+6) in the denominator for one of the terms in a partial fraction problem, why do we put Ax+B instead of just A? and if the denominator is (x^2+3x+6)^2, why do we do {(Ax+B)/(x^2+3x+6)}+{(Cx+D)/(x^2+3x+6)^2}? i was always just told to memorize it, but why do we...

Homework Statement Homework Equations The Attempt at a Solution I have to solve this question and I know that partial fractions is the intended method. I can do the long division easy, which gives: Setting up for A and B, I get: which produces: 4x-15= A(x-2)2 + B(x-2) From here, I...

Hello I am stuck on an ODE involving substitution. I have done the correct substitutions, but have become stuck on decomposing the fraction. i have the following ∫(1/x)dx + ∫(u+1)/(u^2+1)du = 0 Im stuck on breaking the u down into a partial decomposition. Could anyone offer some advice on...

Find $$\sum_{x=0}^{101}\frac{\frac{2x}{101}-1}{\frac{3x^2}{10201}-\frac{3x}{101}+1}$$.

Is there any way to nicely LaTeX a "slashed" fraction? In other words, if I want to write $a_1/a_2$ instead of $\frac{a_1}{a_2}$ or even $\dfrac{a_1}{a_2}$, is there a way to make it look nice?

I have the following two equations C, L, and R are all constants. I need to somehow get the above two equations and get it to look like this: But I can't get mine to look that nice. I have V1(s) = V2(s)(1+sCR) and I substituded it into equation 1 and it ends up looking messy...

Homework Statement A sample of oxygen gas with molar mass 32 g/mol contains 5.0 moles and is at a temperature of 500 K. How many moles of the gas have speeds between 375 m/s and 380 m/s? Homework Equations Maxwell Boltzmann Distribution: f(v) = 4\pi[\frac{M}{2pi RT}]^(3/2) * v^2 *...