Fraction Definition and 653 Threads

Homework Statement Differentiate the following functions with respect to x Homework Equations (√2x-1)/ (lnx)? The Attempt at a Solution ln x (2x-10)^-1/2 -√(2x-1)(1/x)/(ln x)^2 ..........{This is a denominator} thank you [/B]

Homework Statement if $$y = \frac{2x^5-3x^3+x^2}{x^3}$$ then $$\frac{dy}{dx} =$$ Homework Equations if $$f(x) = x^n$$ then $$f'(x) = nx^{n-1}$$ The Attempt at a Solution $$\frac{2x^5-3x^3+x^2}{x^3} = \frac{2x^5}{x^3} - \frac{3x^3}{x^3} + \frac{x^2}{x^3}$$ $$ f'(\frac{2x^5-3x^3+x^2}{x^3}) =...

when I am adding, subtracting, multiplying and dividing fractions and I get an answer is there a way I can check to make sure my answer is in lowest terms ?

1. Evaluate the limit http://www4a.wolframalpha.com/Calculate/MSP/MSP64511d2754i3f4iaefab00001fa62g875680a1ia?MSPStoreType=image/gif&s=44&w=125.&h=45. 2. No formulas 3.The answer is -1/9. I have tried multiplying the top by the conjugate but that seems wrong as there are no square roots...

What fraction of adult human cells are not replaced over a normal lifetime ?. see ... http://en.wikipedia.org/wiki/Ship_of_Theseus / [ aka "Trigger's broom" ]. I'm guessing it's a minority : brain and heart only account for about 3% of body weight.[ skeleton is replaced every decade , but...

Hi all, I found that the branching fraction ## b \to s \gamma ## decay is given by ## B \to K \gamma ## ~ 10^-4 , but now I want to know if I calculate the decay width of ## b \to s \gamma ##, what it should equals ? In other words I don't understand what does a branching fraction mean ...

so what i understand is that packing fraction is mass defect per nucleon. mass defect is the difference between total mass of the nucleons and the actual mass of the nucleus of an atom. if A=mass number [M][/p]=mass of proton [M][/n]=mass of neutron M=mass of nucleus then packing...

Part (1) of this question posted in post 3. Is it a type-o or correct. Not looking for solution.

I'm trying to take the derivative of [x/x^2+1]^3. Where do I start?

What's the best approach to solving the partial-fraction decomposition of the following expression? $$\frac{1}{(a-y)(b-y)}$$ The expression is not of the following forms: But I know the solution is $$= \frac{1}{(a-b)(y-a)}-\frac{1}{(a-b)(y-b)}$$

Homework Statement The chemical analysis of a fuel is determined to be: 84.60 wt% C, 11.12 wt% H, 1.95 wt % S and the balance, inerts. The fuel is consumed in a steam generating furnace with 33% excess theoretical air. The air is preheated to 190degreesC and enters the furnace at a gauge...

Hi. I have a problem with some calculations. I have to find atom or weight fraction in MOX fuel. MOX fuel is a mixture of UO2 and PuO2. It can be mixed with a various enrichment of PuO2. The fraction of isotopes of uranium and plutonium are as here: U234 234,041...

Hi guys I am trying to calculate athe dryness fraction of wet steam at a pressure of 0.5Bar has a specific volume of 1.75m3/kg. can someone walk me through it? much appreciated!

I am new to this forum, i don't know if it's here i should post this simple question. I have to find the peak of the function: ##\frac{x}{\sqrt{x^2+R^2}(x^2+R^2)}=\frac{x}{(x^2+R^2)^{3/2}}## I differentiate: ##\left( \frac{x}{(x^2+R^2)^{3/2}} \right)'=\frac{(x^2+R^2)^{3/2}+x\left(...

For the fermi dirac distribution function for temperatures higher than 0 K, how do we approximate the number of electrons available for conduction?

Homework Statement A proton beam of energy E=7mpc2 is incident on a cylindrical volume (V=20 cm3) of liquid hydrogen (density ρ=0.071 g cm-3) at rest. The spot area of the beam is A=4 cm2 and the total cross section is σ=30 mb. What fraction of the protons entering the target will interact...

Homework Statement The CsCl structure is stable when the ratio of the smaller ion radius to larger ion radius is ##r > 0.73##. Why is this so? Show that the packing fraction, ##p##, is given by $$p = \frac{\sqrt{3} \pi}{2} \frac{1+r^3}{(1+r)^3}$$ Homework Equations volume of sphere, volume of...

Homework Statement "Calculate the following limit if it exists. If it does not exist, motivate why. \displaystyle\lim_{x\rightarrow 0} {\frac{x + x^2 +\sin(3x)}{tan(2x) + 3x}} Do not use l'Hôpital's rule." Homework Equations (1) \sin(a\pm b) = \cos(a)\sin(b)\pm\cos(b)\sin(a) (2)...

Homework Statement During fusion of hydrogen to helium, 4 billion kg of matter are converted to energy each second. What fraction of the Sun’s total mass is lost each year to this process? Homework Equations None. The Attempt at a Solution First: Convert how many seconds are there in a year 1...

I have: sq rt 2 +sq rt 2 over 2 , sq rt 5 + sq rt 5 over 2 I got (sq rt 4 over 2, and 0) = 1, 0 but the answer is actually (sq rt 2, 0) so is my answer still wrong?

please help decompose$\frac{4x^2y}{(x^2-2xy+2y^2)(x^2+2xy+2y^2)}$ I've used the cases I know for this problem but to no avail. please help me.

Homework Statement Show that the ratio of atomic sphere to unit cell volume in HCP (hexagonal close packing) is 0.74. Homework Equations volumes of spheres, geometry The Attempt at a Solution I did the same problem for FCC and BCC and it was fine. My unit cell structure is that...

1/6(3/4x-2)=-1/5 The answer is 16/15 So to get that you multiply by reciprocal, right? So you take the -1/5 and make it a 1 by fliping it over to -5/1. Then you do to the other side the -5/1 and so that's -5/6(3/4x-2)=1 and then there's a -2 so you +2 it and do it to the other side so...

Homework Statement To find the decomposition of a polynomial with a repeated factor in the denominator, you should separate them into (x+a)^1 + ... + (x+a)^n. But, my question is why? For example, why should you decompose it in the following way: \frac{x+2}{(x+1)(x+3)^2} = \frac{A}{x+1}...

Homework Statement Imagine any recurring decimal in base 10, call it X. examples: .1111111111... .2222222222... .23232323... my question is - can you convert it to binary without rewriting X in fractional form. I know how to do it in fractional form. I know how to convert it to fractional form...

Homework Statement Doing a homework question and I ran it through wolfram and I get a different answer to what I'm working it out as...and I can't see where I'm going wrong. Anyone able to give a pointer? my equation is \frac{1}{s(0.641s + 1)} Wolfram gives the answer as...

I always see people when doing partial fraction decomposition just plug in arbitrary values of x to cancel out some constant terms like A,B,C in order to solve it. I just want to know how this works. I've heard that since A,B, and C are constants it has to hold true for any values of x(like a...

Hello, Wondering how to simplify this fraction... 3/90 * (36x+54)

If $x,\,y$ are positive integers such that $\dfrac{x^2+y^2}{1+xy}$ is an integer, then $\dfrac{x^2+y^2}{1+xy}$ is a perfect square.

Alright, I am here again with another question... When I have a rational function, let's say (x+4)/(x-2)(x-3) I rewrite it like A/(x-2) + B(x-3) and then solve it for A & B. But when we have for e.g (x^2 + 3x + 2)/(x(x^2 +1 )) the book tells me to rewrite it like: A/x + (Bx + C)/(x^2 + 1)...

\int \frac{7dx}{x(x^2+8)^2} so I am thinking its going to be set up like: \frac{A}{x} + \frac{Bx + C}{x^2 + 8} + \frac{Dx + E}{(x^2 + 8)^2} Practice problem I'm stuck on. so I cleared fractions and got A = 7/64 , b = -7/64 and C = 105/64 and now I'm lost... can anyone work this problem for me...

Without being too concerned how we got there. The answer to a partial fraction question a friend and I are doing is 24/5 ln(2) - 8/5ln(3) The system does not accept this answer however, it wants the simplified form 8/5 ln (8/3) We're not sure how to get that form. More specifically 8/5...

f(z) = sq. rt of z-1 / z+1 --- both numerator and denominator are inside the radical. I can write it as (z-1)^1/2 over (z+1)^1/2, right? If I simplify it using derivative of a quotient. Should I simplify (z-1)^1/2 and (z+1)^1/2 as whole numbers and multiply them to other terms, including...

Find the partial fraction decomposition for the rational function. \frac{-4x^2 - 8x - 19}{(x^2 + 2)(x-9)} I'm not sure what to do.

Evaluate, without the aid of a calculator, of the following fraction: $\dfrac{(30^4+324)(42^4+324)(54^4+324)(66^4+324)(78^4+324)}{(24^4+324)(36^4+324)(48^4+324)(60^4+324)(72^4+324)}$. I hope you will find this problem interesting, if it's not too difficult or intriguing to solve for.:o

Homework Statement I need to know whether a ping pong ball bounces the same fraction of the previous height or does the fraction change? For ex. if I drop the ball from 1m and it bounces back to 0.7m, it decreased by 30%, will it always decrease by 30%, or will the percentage change...

So, I was thinking about how we would simplify say 2/4 -> 1/2. But without any memorization and guessing and checking how do we know if a fraction can be simplified? I was looking all over the internet and I can't seem to find anything. I am especially curious when it comes to a large...

I am going to assume everyone was taught the method where if you want to divide to fractions then you simply flip the second and then multiply them. I've been trying to see if I could find a reason as to why it works but I can't seem to. Does anyone know why or want to give me some hints...

Homework Statement Solve the formula f=1/1/a+1/b for a in terms of b and f. The Attempt at a Solution My attempt at this problem was to first multiply all terms by ab, thus getting rid of the fractions in the denominator on the right. I was then left with the equation fab=ab/(b+a)...

Homework Statement \int \frac{-2x + 4}{(x-1)^{(2)}(x^{(2)}+1)}Homework Equations The Attempt at a Solution I've done the problem a couple times but the answers keep coming out differently so I'm assuming I am messing up the setup. This is what I have for the first part of the setup: -2x +...

Homework Statement Evaluate ∫((secx)^2)/[((tanx)^2)+(3tanx)+2] Homework Equations Partial fraction decomposition The Attempt at a Solution So here's what I did: But this is incorrect. It says the correct answer is -2lnabs(\frac{1}{2tanx+3}+\sqrt{4(tanx+3/2)^{2}-1}), which was...

Let $x,\,y,\,z$ be not necessarily distinct integers between 1 and 2011, inclusive. Find the smallest possible value of $\dfrac{xy+z}{x+y+z}$.

Okay so the partial fraction decomposition theorem is that if f(z) is a rational function, f(z)=sum of the principal parts of a laurent expansion of f(z) about each root. I'm working through an example in my book, I am fine to follow it. (method 1 below) But instinctively , I would have...

Homework Statement use partial fraction decomposition to re-write 1/(s2(s2+4) The Attempt at a Solution I thought it would break down into (A/s) + (B/s2) + ((cx+d)/(s2+4) but it doesn't.

When I'm evaluating a problem like \int \frac{2x^2 + 8x + 9}{(x^2 + 2x + 5)(x + 2)} = \frac{Ax + B}{x^2 + 2x + 5} + \frac{C}{x+2} I understand how to get the C part, that's simple. But what is a Good trick to know that I need to have Ax + B over the x^2 + 2x + 5 denominator? Is there a way I...

Hello i want to solve a complex integral that in one of the first step its better to dissociation fraction.i want to know how can dissociation main fraction to two separate fraction and find "? " ? Thanks

Hi, I am having awful trouble working this out and have been going round in circles. Can you help me please? Its: x/x+1 - 4/x - 2 = 2

Homework Statement ∫(5x2+20x+6)/(x3+2x2+x Homework Equations The Attempt at a Solution (5x2+20x+6)/(x3+(x(x2+2x+1) (5x2+20x+6)=(A/x)+(B/(x+1))+(C/(x+1)) (5x2+20x+6)=x2(A+B+C)+x(2A+B+C)+A 5=A+B+C 20=2A+B+C 6=A It's not coming out quite right. Did I maybe factor the...

Homework Statement ∫(2x3-4x-8)/(x2-x)(x2+4) dx Homework Equations The Attempt at a Solution ∫(2x3-4x-8)/x(x-1)(x2+4) dx Next I left off the integral sign so I could do the partial fractions: 2x3-4x-8=(A/x)+(B/(x-1))+((Cx+D)/(x2+4))...

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...