Fraction Definition and 653 Threads

Homework Statement Find the solution of the givien initial value problem and draw its graph y''+2y'+2y = δ(t-π) y(0) = 1, y'(0) = 0 Homework Equations A Laplace transform chart would be very useful The Attempt at a Solution I chose to solve the equation with Laplace...

Q: Find a fraction between \frac {96}{35} and \frac {97}{36} that has the smallest possible denominator. My thoughts: Let's assume this fraction is of the form \frac pq where \gcd(p,q) = 1. Since \frac{96}{35} > \frac{97}{36}, we can write \frac{97}{36} < \frac {p}{q} < \frac{96}{35} \, . By...

Homework Statement Give the partial fraction decomposition of 1/z4+z2 Homework Equations The Attempt at a Solution My question is about the final answer. The book gives the answer to be 1/z2+ 1/2i(z+i)- 1/2i(z-i). For my answer I keep getting a negative for both of the 1/2i...

Find the value of the continued fraction $1$+$\frac{1}{1+\frac{1}{2+\frac{1}{1+\frac{1}{2+...}}}}$ and use it to find two positive solutions to pell's equation $x^2-3y^2=1$

Hello MHB, Simplify as far as possible without any calculator \frac{196707}{250971} Hint: Regards,

So i have a homework question which i can't figure out. Use the saha equation to determine the fraction of hydrogen atoms that are ionised at the centre of the sun (N_II/N_tot) T=15.7x10^6K number density n=6.1x10^31 m^-3 m = mass of electron the saha equation is N_(i+1)/Ni =...

Homework Statement (x^3+4)/((x^2-1)(x^2+3x+2))Homework Equations The Attempt at a Solution Try separating them into Ax+B and Cx+D, then expand until (A+C)x3+(3A+B+D)x2+(2A+3B-C)x+(2B-D) then, I was stuck. I can't find any value for A,B,C or D. Is my attempt correct or is there other way to...

Homework Statement Find the integral of This was the question. There is a way to do it by long division but I am confused with Long division. Instead I tried to do by the method below but I failed... Homework Equations NoneThe Attempt at a Solution I thought maybe I could reduce the...

Homework Statement Evaluate the integral. Homework Equations \displaystyle\int_0^∞ {\frac{dv}{(1+v^2)(1+arctanv)}} The Attempt at a Solution i am not sure how to do partial fractions with an inverse trig function in the denominator. i tried v=arctanv so i could do a substitution...

Homework Statement 25-2-EX9 The time rate of change of the displacement (velocity) of a robot arm is ds/dt = 8t/(t^2 + 4)^2. Find the expression for the displacement as a function of time if s = -1 m when t = 0 s. 26-5-9 Find the moment of inertia of a plate covering the first-quadrant region...

Homework Statement Hi! I am currently learning how to balance equations in chemistry but something that I don't understand is using fractions to balance an equation. I have a problem that I can't work out because I'm so confused! The problem says: Complete and balance the acid-base...

Here is the question: Here is a link to the question: Decompose the equation into two simpler fractions? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

Homework Statement The coefficient of static friction between a rope and the table on which it rests is μ. Find the fraction of the rope that can hang over the edge of the table before it begins to slip. Express your answer in terms of μ. Homework Equations The Attempt at a...

a^x means a*a*a*a... x times This makes sense for whole numbers to me, but I am sort of lost about transfering the definition one x becomes a fraction. I know that the denominator in a fraction in an exponent means "the denominator root"..., and I know what a root its. But it is a jump in...

Homework Statement Integrate (3x^2-10)/(x^2-4x+4) dx using partial fractions. Homework Equations None The Attempt at a Solution I tried using A/(x-2) + B/(x-2)^2 but I didnt get a coeffecient of an x^2. I've also tried using (Ax+B)/(x-2) + C/(x-2)^2 Though I...

Problem: Find the value of $\displaystyle \frac{1^4+2007^4+2008^4}{1^2+2007^2+2008^2}$. My Attempt: For the numerator, I expand them using the Binomial Theorem and get: $\displaystyle 1^4+2007^4+2008^4$ $\displaystyle=1+(2000+7)^4+(2000+8)^4$ $\displaystyle...

Do all steam have dryness fraction or only wet steam? Thanks.

I'm trying to figure out how to calculate the velocity of an orbit at apogee or perigee and I've figured out the derivation of the equation except for this one fraction... I replaced the radius quantities for x and y for ease of viewing. \frac{x-y}{x^2 - y^2} = \frac{1}{x + y} Can anybody...

Here is the question: Here is a link to the question: Help with Calculus BC: partial fractions!? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

Hello all, I would like to express the following as an equation, but don't know the nomenclature. 'The point at which a condition is true 95% of the time' ie. I have a function, f(x) which returns some value in the presence of random and uncharicterizable noise. I run this 1000 times. I...

Homework Statement A 50.0 g ball of copper has a net charge of 2.00µC. What fraction of the copper’s electrons has been removed? (Each copper atom has 29 protons, and copper has an atomic mass of 63.5.)Homework Equations 1.00 C× (1proton)/(1.60×10^−19C)=6.25×10^18 protons C = coloumb, the SI...

1. Find derivative: g(x) = (e^x)/(2 + 3x)2. The fraction confuses me... I wrote it instead as: (e^x)(3x^-1)(2^-1) 2^(-1) equals .5, so then I thought it was: (e^x)(1.5x^-1) And then I thought it's time to differentiate... So I got: (-1.5x^-2)(e^x) And then I thought, " Since these are...

Scientists can produce laser pulses of order one wavelength in "length" see, http://www.bbc.co.uk/news/science-environment-19489384 Do Maxwell's equations admit solutions of such short pulses? Can one approximate such a solution by multiplying a plane electromagnetic wave by the...

Homework Statement How to get partial fraction decomposition for \frac{1}{(x^2+a^2)(x^2+p^2)}Homework Equations The Attempt at a Solution I tried with \frac{1}{(x+ia)(x-ia)(x+ip)(x-ip)}=\frac{A}{x+ia}+\frac{B}{x-ia}+\frac{C}{x-ip}+\frac{D}{x+ip} and get the result at the end of the day. Is...

Homework Statement A quasi-3 level solid-state laser gain medium consists of a ground state manifold containing two energy levels within which a single electron can be promoted, with the second energy 10meV above that of the lowest level. A. Where the gain medium is not optically pumped...

For example, dividing by 2, means we cut something in two. But dividing by 0.5, can only be explained with multiplying something by 2. So, is there a "physical" explanation of dividing by 0.5? Is it "I divide by an entity that internally multiplies' or something as so bizarre?

Homework Statement We have a car with mass of 1200kg driving at 55km/h. It suddenly starts breaking. The breaks "work" on every of the 4 wheels with the constant torque of 12Nm. The radius of the wheels is 0,21m. Question 1: How long does the car travel before it stops if the wheels have...

Homework Statement I was looking at a solution for a practise question and in the last step they simplified -[(0.02)^4]/[4(0.98)^4] to 1/(4*49^4) How do you do this without a calculator?

I would just like someone to check my math on this, because I am not sure that I am doing it the right way. I will show step by step. Put over common denominator: \frac{1}{x} + \frac{x}{x+y} + \frac{y}{x-y} 1. common denominator: \frac{x^2-y^2}{x(x^2-y^2)} +...

I have trouble solving the following integral \frac{x-6}{x^2-4} If I let u= x^2 - 4, I'm left with 1/2du = x dx and I'm stuck trying to get rid of that 6 in the numerator? If someone can help me out, that would be good.

As asked above, what is mole fraction solubility? From what I've been taught, it is the following equation: mole fraction solubility = (number of moles of solute)/(number of moles of solute + number of moles of solvent) Is that even correct? In actual fact, there's a question that deals with...

Homework Statement \int\frac{8x^{2}+5x+8}{x^{3}-1} Homework Equations Because the denominator can be reduced to (x-1)(x^{2}+x+1), I set up the partial fractions to be \frac{A}{(x-1)} + \frac{Bx+C}{(x^{2}+x+1)} The Attempt at a Solution I've solved for A, B, and C, and now have...

So I'm trying to figure out how to decompose the following using octave: 85000/[(s^2+250^2)(0.2s^2+40s+10000)] I tried using the residue command but I think that only works if the polynomials have real roots, which these don't. When I do use residue I get the following: b =...

From a fraction with infinite sum in denominator to partial fractions?? I am currently studying a course on Perturbation Methods and in particular an example considering the following integral \int_{0}^{\frac{\pi}{4}} \frac{d\theta}{\epsilon^2 + \sin^2 \theta}. There's a section of the...

Homework Statement A ball moving translationally collides elastically with another, stationary, ball of the same mass. At the moment of impact the angle between the straight line passing through the centres of the balls and the direction of the initial motion of the striking ball is equal to α...

Taking the derivative of a polynomial fraction?? b]1. Homework Statement [/b] Ok, so the question wants me to differentiate f(x)= (x)/(x+1). We are supposed to use the definition of the derivative f'(x)= (limit as h->0) [f(x+h)-f(x)]/(h). We also have learned the power rule. I did the formula...

This is for my chemical engineering class...for some reason, I am struggling with this problem. I'm not quite sure how to connect the dots..I feel like I know how to do this, though. Homework Statement The mass fraction of benzene in a benzene-toluene mixture is 0.450. What is the mole...

Watsup! I'm taking this nano class which is awesome but I am getting stuck on the gen chem material! no bueno. just want to make sure i did this right. Thanks! Homework Statement [/B] "A blend contains 45wt% polystyrene and 55wt% polypropylene. What is the mole fraction of polystyrene in the...

Homework Statement Find ∫18/((x2+9)(x-3)) Homework Equations The Attempt at a Solution Im a little stuck on this. 18∫1/((x2+9)(x-3)) Im not sure how to turn this into a partial fraction.. help. Thanks

For PFE, can a denominator variables with coefficient of something other than 1, or does it have to be 1? For Example, can I have a term A/(3x+9)? It's been years since I've dealt with this and don't quite remember if this was a rule or not. Thanks! EDIT: This is in terms of taking the...

Homework Statement The answer to one of my maths questions is; $$\frac{60x^{4}-240x}{3x^{4}+x^{3}-14x^{2}+4x+8} $$ Homework Equations The Attempt at a Solution Can this be simplified to; $$\frac{20x^{4}-60x}{x^{3}-14x^{2}+8} $$

Homework Statement reduce the fraction \frac{943578}{1978935} to its lowest terms using Euclid's algorithm The Attempt at a Solution I start with finding the gcd of these two numbers using E.algorithm 1978935=943578*2+91779 942578=91779*10+25788 91779=25788*3+14415 25788=14415*1+11373...

I keep getting slightly confused with the algebraic method of finding a fraction between, two other fraction. Here is an example question, I have been doing Find the fraction between 13/15 and 14/15? I personally convert both to percentages and find the average between the two, the convert...

I have been having trouble of late with partial fraction decomposition. Not so much the maths, but the intuition behind it. What I mean by this, but a question in front of me, I now what procedure to follow to get the answer, but I don't get why you follow the said produced. I will give an...

Homework Statement I'm try to implicitly differentiate the function: xlny+√y=lnx The Attempt at a Solution And I got to the stage where I have: dy/dx = (1/x-lny)/(x/y+1/(2*√y)) which is where I have no idea on how to clean this up. Could someone please explain to me how to simplify a...

Homework Statement there are 2 blocks along a frictionless track. block 1 has a mass of m1 and block 2 has a mass of m2. Block 1 is initially moving at a speed of v0. it collides and sticks to the initial stationary block 2. (m2=9m1) what fraction of the inital kinetic energ of the system is...

Homework Statement Write the momentum four vector of a particle that has: Rest mass = 80 Gev/c^2 Energy = 100 Gev and moves along the z axis.What is its speed as a fraction of the speed of light. Homework Equations E^2 = p^2c^2 + m^2C^4 The Attempt at a Solution...

Say I have: \frac{x \cdot \frac{1}{z}}{y} How can I make it look like: \frac{x}{y \cdot \frac{1}{z}} I'm trying to figure out the algebraic rule(s) for this

Homework Statement Simplify the following expression: x3(1-x2) / x(x-1) Homework Equations The Attempt at a Solution I know that the top can be factored to x3(1-x)(1+x) to give x3(1-x)(1+x) / x(x-1) . However, after this step I seem to just go round in circles. I got an...

\frac{5}{15} \Sigma Is this what people mean by LaTeX. Just wondering. Thankyou.