Fraction Definition and 640 Threads

Homework Statement Find the magnitude of \frac{6t(-3t^2\hat{i}+\hat{j})}{(1+9t^4)^2}Homework Equations The Attempt at a Solution I know how to take the magnitude for something simple like 3x \hat{i} + 8y \hat{j} + 2 z \hat{k} but not this. My lecture notes don't give me any examples of how to...

is there a general way of converting fractions involving square root like (1+x)/(1-x)1/2 to simpler fractions , like we have a method of converting rational fractions into sum of partial fractions ?

Hi Guys, I'm building a numerical Matlab simulation of a thermochemical heat storage device (using zeolites), and need to update the state of water vapor in the device at every time step. My question is, if I have an empty space with water in it, with temperature, pressure, density, etc. all...

Homework Statement This is a 2 part question and I already solved for part I. Part II is what I don't get. a) A 3.16 g object moving to the right at 24.3 cm/s makes an elastic head-on-collision with a 6.32 g object that is initially at rest. The acceleration of gravity is 9.8 m/s2 . 24.3 cm/s...

Homework Statement Find the speed (as a decimal fraction of c) and momentum of a proton that has a kinetic energy of 1000MeV. The proton mass is 1.673x10-27kg, or 938 MeV/c2. Homework Equations KE= (1/2)mv2 KE= \gammamc2 p=mv \gamma=1/(sqrt(1-(v2/c2))) The Attempt at a Solution...

I'm having some problems integrating fractions. If you could help me understand it, that would be great. Homework Statement \int\frac{2+3sin^{2}x}{5sin^{2}x}Homework Equations \int(x)dx=\frac{x^{n+1}}{n+1}The Attempt at a Solution...

Homework Statement \int\frac{x^{2}+2x+1}{x^{2}+1}Homework Equations INTEGRAL OF X=\frac{x^{n+1}}{n+1} I can't get the integral to work on the left side for some reason. The Attempt at a Solution I have completely forgotten how to integrate fractions. I know that "log(x^2+1)+C" would be...

Homework Statement Find dy/dx at x = 2. y = (1 + s)/(1 - s); s = t - 1/t; t = sqrt(x) Homework Equations I know if f = f(g(x)), then f1(x) = f1(g(x)) * g1(x) The Attempt at a Solution I think I may need to combine the chain rule and quotient rule, but all of the separate...

(3*e^(-2s))/(s(s+5)) I was hoping someone could tell me how to find the partial fraction for the above; the answer i ended up with was: (3/5)/s - (3*e^(10))/(s+5) and i went about it by: (3*e^(-2s))/(s(s+5))=A/s+B/(s+5) (3*e^(-2s))=A(s+5) + B(s) set s=-5 and found B=-3*e^(10)/5 set s=0...

How to calculate the fraction of stimulated photons that escape from a laser cavity with alpha=0.1 cm^-1 length of cavity=1mm refractive index of laser cavity=3.2 the photons are assumed to be escaping into air so approx refractive index is 1. Im assuming that alpha is some sort of...

For the following problem provide the "form" of the partial fraction decomposition for the given fractional expression. You do not have to solve the undetermined coefficients. 4. 2x^2 - 3x + 8 / x^3 + 9x I took an x out and it's no x(x^2+9) My answer is A/X + BX+C/x^2+9 5. x- 7 / x^4 - 16...

I'm a South African undergraduate physics student. In our textbook (Fundamentals of physics, John Wiley and sons, 2008) many formulas are derived by treating a differential fraction (like dq/dt) as an ordinary fraction -see example below. Can this differential fraction in all cases be treated...

as below, my math is getting rusty, hope some can help me out. thanks. \frac{1}{1+\frac{1}{x}}

Homework Statement I'm supposed to prove that an improper fraction with a finite binary expansion also can be written as a decimal. Homework Equations Obviously my fraction a/b, where a>b, will look like p1/21 + p2/22 + ... + pn/2n The Attempt at a Solution And I have no idea...

I'm trying to teach myself maths and I'm stuck at this problem: Homework Statement Which of the following fractions is nearest to \frac{1}{2}? You must show your working. \frac{3}{5} \frac{7}{10} \frac{11}{20} Homework Equations The Attempt at a Solution I know the answer...

Homework Statement dx/dt = 9-4x^2 , x(0) = 0 when I integrate, am I supposed to use the property below? int du / (a^2 - u^2) = 1/2a ln(u+a / u-a) + c or how do I integrate this by using partial fraction? tips anyone? Homework Equations The Attempt at a Solution

Find all integers n for which the fraction n ^ 3 + 2010 / (n ^ 2 + 2010) is equal to integer. please I need help :( Thank you

Hello! This is another conceptual understanding question. Any help is appreciated. I want to solve the following: The limit as x -> 1 of: \frac{x^{10}-1}{x^2-1} So I divide the numerator and denominator by x-1 and then find the derivative of them separately with respect to x. Then take...

Homework Statement Doing some Laplace transform stuffs and I've got Y(s) = \frac{1}{(s+1)(s^{2}+2s+2)} Using the normal method 1 = A((s+1)^{2}+1) + B(s+1) I'm not sure this method is valid though as we had a complicated term (s+1)² + 1 after A. I can find A to be 1, but I don't trust my...

No homework, just a problem I'm faced with at work. And being the granny I am, this is ages ago since I solved anything like this. x/36-x = 12/36-12 + 3.013/0.20(36-3.013) The solution to this is 17.6. The question is: how do I solve such equations for x? If I ignore the 36 on the left...

hi can anyone tell me what the branching fraction of B0 -> K* mu mu decay is and/or tell me a webpage i can find info on this decay which is accessible to ppl that doesn't have a huge knowledge in this field (i am an undergraduate) thanks

Hi, I found the following formula: \prod_{m=1}^{N_d} \frac{1}{(1-e^{\alpha_{(m)}}z^{-1})^{n_{(m)}}} = \sum_{m=1}^{N_d} \sum_{n=1}^{n_{(m)}} \frac{c_{m,n} }{(1-e^{\alpha_{(m)}}z^{-1})^{n_{(m)}}} What I want is finding the coefficients c_{m,n}. This looks like a simple partial...

Homework Statement Find the partial fraction decomposition 1. \frac{x^4}{(x-1)^3} 2. \frac{1}{a^2-x^2} Homework Equations The Attempt at a Solution 1. \frac{x^4}{(x-1)^3} \frac{x^4}{(x-1)^3}=\frac{a}{(x-1)}+\frac{b}{(x-1)^2}+\frac{c}{(x-1)^3} x^4=(x-1)^2+(x-1)b+c x^4=ax^2+(-2a+b)x+(a-b+c) I...

Homework Statement Write the Partial Fraction decomposition for: \frac{x}{16x^4-1} Homework Equations The Attempt at a Solution \frac{x}{16x^4-1} =\frac{x}{(2x-1)(2x+1)(4x^2+1)} =\frac{x}{(2x-1)(2x+1)(4x^2+1)}=\frac{a}{(2x-1)}+\frac{b}{(2x+1)}+\frac{cx+d}{4x^2+1}...

Homework Statement Find the Partial Fraction Decomposition. \frac{4x^2+2x-1}{x^2(x+1)} Homework Equations The Attempt at a Solution \frac{4x^2+2x-1}{x^2(x+1)}=\frac{a}{x}+\frac{b}{x^2}+\frac{c}{(x+1)} 4x^2+2x-1=x^2(x+1)a+x(x+1)b+x^2(x)c So i can solve for c by plugging in...

Homework Statement I must solve using partial fractions: \displaystyle\int_{}^{}\displaystyle\frac{dx}{8x^3+1} The Attempt at a Solution The only real root for the denominator: -\displaystyle\frac{1}{2} Then 8x^3+1=(x+\displaystyle\frac{1}{2})(8x^2-4x+2) Then I did...

Homework Statement \int 1/(x^{2}+4x+5)^{2} Homework Equations I am using partial fraction decomposition The Attempt at a Solution 1/(x^{2}+4x+5)^{2} = Ax+b/(X^2+4x+5) + Cx+D/(x^2+4x+5)^2 1 = (Ax+b)(X^2+4x+5) + Cx+D When i multiply through to find the values for A and b...

What is the value of the simple continued fraction [1;2,3,5,7,11,13,...,nth prime] as n goes to infinity?

n/(n-3) - n/(n+2) I have tried to solve this by giving n a value. I chose n = 6, which gives: 6/3 - 6/8 The LCM of 3 and 8 is 24 so... 6/3 - 6/8 = 48/24 - 18/24 which gives 30/24 Final answer = 5/4 Is that the correct answer and have I used the correct method of solving the...

Does anyone know how to derive a fraction? I want to be able to differentiate f(x)=\frac{x(20-x)}{36} Ill show you what I've done but think I've just simplified it. f(x)=\frac{x(20-x)}{36} f(x)=\frac{(20-x-x)}{36} f(x)=\frac{(10-x)}{18} Is this correct?...although not sure what...

How do I tackle this problem? Express the following as a single fraction in its simplest form: x/3x + 1 - 2/8x-1

Hello, I need write this equation and here's the code: \begin {displaymath} \[ \frac{\sum_{s_i \in S_{access}^{site}}{{e^{-\beta E(s_i)}}}}{Q} \] \end {displaymath} It is working well, the only problem being that the sum ''subscript'' is not directily underneath the sum symbol, but...

Homework Statement Hi, I have the following problem. These two equations are the same but I can not find the right route from one to the other. Is there someone who can help me? In other words, I start with the equation on the left and want to end with the equation on the right...

What is 0.541r as a fraction? I have a feeling the answer won't be as simple as 541/1000.

Can anyone explain to me what approach I need to take to solve this type of problem? Express x/3x+1 - 2/8x-1

What is the packing fraction for a body centred packed structure?

Homework Statement 1. Homework Statement The temperature of the surface of a certain star is 8000 K. Most hydrogen atoms at the surface of the star are in the electronic ground state. What is the approximate fraction of the hydrogen atoms that are in the first excited state (and therefore...

Homework Statement Convert 23.588 (the 88 is repeating) to an improper fraction. Homework Equations I don't have any. The Attempt at a Solution I'm not sure of the best way to go about this so I've taken a method that I've seen on some problems that were more simple as they...

Homework Statement \frac{2x + 2}{x^2 - 2x + 1}dxHomework Equations The Attempt at a Solution I factorized the denominator and got \frac{2x + 2}{(x - 1)^2} and I took a look at the solutions manual to see how they handled this but then I see this \frac{2x + 2}{(x - 1)^2} = \frac{A}{(x - 1)} +...

I thought they were unique, but given a fraction a/b, couldn't you always write it as the (decimal representation of a/b without the decimal place)/ 10^(n) ? thanks

What does the word mean when you are presented with a question like this? Evaluate 3 1/3 x 1 1/5 Is it simply asking us to work out the answer to the sum?

Hi, I understand that the maximum packing fraction for a particular atomic structure can be calculated assuming the nearset neighbours are touching but my question is how can the maximum packing fraction be calculated for a basis containing two different types of atoms? Thanks, James

Homework Statement How to break down: \frac{1}{(s^{2}+1)^{2}} into partial fractions? Homework Equations - The Attempt at a Solution I have tried: \frac{1}{(s^{2}+1)^{2}} = \frac{1}{(1+i)^{2}\times(1-i)^{2}} = \frac{A}{(s+i)} + \frac{B}{(s+i)^{2}} + \frac{C}{(s-i)}} +...

Homework Statement A system has damping ratio 0.5, natural freq. 100 rad/s, DC gain of 1. Find the response of the system to a unit step input. Homework Equations Im having trouble doing the partial fraction expansion. The Attempt at a Solution I have attached a word document...

Homework Statement This is from a Physics GRE practice test: An 8-cm-diameter by 8-cm-long NaI(Tl) detector detects gamma rays of a specific energy from a point source of radioactivity. When the source is placed just next to the detector at the center of the circular face, 50% of all emitted...

Homework Statement Write the partial fraction decomposition of the rational expression. Check your result algebraically. (x2 – 7x + 16)/[(x + 2)(x2 – 4x + 5)] The Attempt at a Solution [A/(x+2)] + [(Bx+C)/(x2-4x+5)] x2-7x+16= A(X2-4x+5)+(Bx+C)(x+2)...

I was reading this website, and I don't understand this last statement. http://hyperphysics.phy-astr.gsu.edu/hbase/solids/fermi.html It reads: "Since only a tiny fraction of the electrons in a metal are within the thermal energy kT of the Fermi energy, they are "frozen out" of the heat...

Homework Statement \int\frac{4y^2-7y-12}{y(y+2)(y-3)} with limits of integration [1, 2] Homework Equations The answer given in the book is \frac{27}{5}ln(2)-\frac{9}{5}ln(3) or \frac{9}{5}ln\frac{8}{3} The Attempt at a Solution \int\frac{4y^2-7y-12}{y(y+2)(y-3)}...

Homework Statement How do I simplify the following \frac{\sqrt[3]{m^2+m} . \sqrt{1+m^2}}{\sqrt{1+m^2}.\sqrt{1+m^2}} The Attempt at a Solution I know that the denominator will be 1+m^2 but I don't know how to simplify the numerator. Can anyone show me how?

Homework Statement Resolve the following into partial fractions. Homework Equations The Attempt at a Solution Is my first step correct? A/x + B/x^{2} + C/(x+1) + D/(x+1)^{2} Thanks in advance!