Fraction Definition and 653 Threads

Homework Statement Via iteration. A continued fraction for pi is: Write an algorithm to compute this to n terms using Matlab. 1st term would be 3+1/9 The Attempt at a Solution p = '1'; for k = 1:n p=3+(-1+2^n)/(3+p); end p I'm very new to programming, and I can...

Basically I don't know how F(s) can be split up to below. F(s) = \frac{1}{s^{2}(s-2)} = \frac{1}{4} ( - \frac{1}{s} - 2 \frac{1}{s^{2}} + \frac{1}{s-2} ) I thought it would be 1/s^2 - 1 / s-2 How does this work? Please explain. thanks

I started calculus in September (as part of A-Level Maths/Further Maths), and we've been told time after time not to look at derivatives as fractions. We recently did the Chain Rule, and we were told that a way to remember it was that if dy/dx = dy/du * du/dx, then the 'du's 'cancel out' -...

Suppose the neutron decay time n was 89 sec. AND the difference in rest mass between neutron to proton, Qn, was 0.129 MeV. What would the maximum Helium fraction, Yp, be?

\frac{7}{3s^{2}(3s+1)} Can this be decomposed, and how?

does a high dryness fraction mean that the steam is dry or wet?

Homework Statement Go here: http://www.unl.edu/amc/a-activities/a7-problems/putnam/-pdf/1999s.pdf You do not need to read the problem. In solution two for 1999 A3, I can do the partial fraction decomposition but I get something different from that... I am wondering whether that comes from...

an increase of $0,15 on a price of 2,50 is an increse by a fraction of 0.15/2.50=0,06 expressed as a percentage,therefore a 6% increase I don,t understand this and why we put 0.15 is numerator

I'm having trouble understanding a simple identity and was wondering if anyone could explain it to me: Why is it that a_{o}+a_{1}+a_{1}a_{2}+a_{1}a_{2}a_{3}+a_{1}a_{2}a_{3}a_{4}... is equivalent to the continued fraction in the...

Homework Statement \int \frac{dx}{(x+1)(x^2+1)(x^3+1)} The Attempt at a Solution I tried to solve it in 3 ways. 1)\frac{A}{(x+1)}+\frac{B}{(x^2+1)}+\frac{C}{(x^3+1)} 2)\frac{A}{(x+1)}+\frac{B+Dx}{(x^2+1)}+\frac{C+Ex}{(x^3+1)}...

Homework Statement \displaystyle \int{\frac{dx}{a^2+\left(x-\frac{1}{x} \right)^2}} Homework Equations - The Attempt at a Solution This one looks a bit odd. Had the denominator been a^2 + x^2, it is in one of the standard forms, whose integral is \frac{1}{a} \atan{\frac{x}{a}} . But the...

Homework Statement Solve: (x+1)/(x+6) >or= 0 Homework Equations The Attempt at a Solution Don't know where to even start.

Hiya, Just found the forums and loving them so far, going to spend some time tomorrow trauling through some of the intersting discusssions I've seen. I am starting a course soon and have been going over some maths problems to prepare, however there is one that I never used to be able to...

Heres a question I am stuck with Crosslinked polymers consisting of 62 wt% ethylene and 38 wt% propylene may have elastic properties similar those for natural rubber. For a copolymer of this composition, determine the fraction of the ethylene mer. Express your answer with three decimal...

Homework Statement I know how to use the method of partial fractions in most circumstances, but I'm working on a problem that has gotten the best of me. How do I get from the left side of the following identity to the right side? \frac{-2-2\omega^2}{-\omega^2+\sqrt{2}i\omega+1} \ = \ \ 2 \...

Hi Im trying to find the derivative of y=9/x+5 I tried using the quotient rule and and the derivative of (x+5)^-1*9 but both methods don't work.

Homework Statement Calculate the maximum packing fraction of the unit cell volume that can be filled by hard spheres in the Hexagonal structure Relevant eq: Volume of spheres is number of lattice points multiplied with the maximum volume of one sphere. The Attempt at a Solution I...

Homework Statement Determine the fraction of the energy radiated by the sun in the visible region of the spectrum (350 nm to 700 nm). (Assume the sun's surface temperature is 5800 K.) Homework Equations R=\sigmaT^{4} for some reason i can't make the sigma come down, but it's a...

In an 8-gram solution of water and alcohol, the ratio by mass of water to alcohol is 3 to 1. If 12 grams of a solution consisting of 2 grams water for each gram of alcohol is added to the 8-gram solution, what fraction by mass of the new solution is alcohol? -- I know that the first thing you...

Does anyone know how to enter a mixed or compound fraction into the Ti-89 Titanium? (eg. 66½)

(2x+3)/(x+1)^2 so this is what i am thinking...but it does not make sense =(A/x+1)+(B/(x+1)^2) so then 2x+3=A(x+1)^2+B(x+1) 2x+3=Ax^2+A2x+A+Bx+1 so that would make... 0=A 2=2A+B 3=A+B this solution does not make any sense becuase if A=0 then according to the second...

Simplifying a fraction as a surd?? If I have a rather large fraction such as 115/36 there is no obvious way of cancelling this, but is there a way of expressing it as a surd?

Homework Statement integral((3X+4)/((x^2+4)(3-x)) Homework Equations The Attempt at a Solution I know I should be using partial fractions for this problem but the x^2 in the denom. screws me up. I think the partial fraction should be: (Ax+B)/(x^2+4) + C/(3-x) Then...

Homework Statement Express: \frac{1}{x-2}+\frac{2}{x+4} The Attempt at a Solution Well I got x² + 2x - 11 = 0 but I think that is wrong

Just wondering - is there anything you can do with 1/(a + b) to get something like A/a + B/b?

Homework Statement 1/[(x^2)(x-3)^2] I know that this can be separated by the long way of finding A,B,C,D constants and etc... But, I was curious if there is a shorter way to separate it by inspection like how you would do if you were using "heavyside" method for distinctive first order...

Homework Statement Simplify fully the following equation Homework Equations \frac{4x^{2}-6x}{4x^{2}-9} The Attempt at a Solution the 4x² cancel each other out and 3 goes into 6 and 9 so the answer is \frac{-2x}{-3} but that seems to easy for the penultinate question on a...

hey everyone, do you know the formula used to compute for the AGE of a substance if its half-life and fraction remaining are given? please help me.. thank you..:smile:

Its funny.. because I got this right on a test.. but.. I'm looking back at it.. and it doesn't make sense how I figured it out... I had to find the IC of d(\frac{x^2}{y}) this was my work... d(\frac{x^2}{y}) = 2xy - x^2y^2 - y^2 d(\frac{x^2}{y}) = \frac{2xy - x^2y}{y^2} I'm just confused...

Homework Statement I need to make this: \frac{100K}{x^2 + (25 + \alpha)x + (\alpha 25 + 100K)} look like this: \frac{K}{x^2 + \beta x + (K)} Homework Equations Beta and K can be any combination of variables, as long as the top K and bottom K are equal. A scaling factor is allowed to come...

Easy Fraction Problem (Forgot how to do it!) I came across a problem that I forgot how to do, please help me out here. thanks! Solve for x: \frac{1}{x-1}+\frac{3}{x+3}=1 My questions: I know the common denominator is (x-1)(x+3) but do you multiply this number on both sides of the equal...

I am plotting the in-hour equation. For the delayed neutron fraction, I was thinking of using a weighted dnf for the particular U fuel enrichment of interest, ie combination of U235 & U238 dnfs, as I cannot look one up for this particular enrichment. Any comment on the “validity” or otherwise...

Here is the fraction that I don't know how to combine and simplify, please help me out! Thanks! =] \frac{5}{a} + \frac{4}{2a-6} + \frac {-4a}{a^{2}-9} I found the common denominator I think: (x+3)(x-3) .. but how do you make {a} in that form?

Why is that when a positive fraction with a value less than 1 is squared, the result is always smaller than the original fraction?? I find this rather weird, not mathematically, but brain teasingly. :redface: I guess I relate squares to times (2x) too much. because 1^2 is 1.. Please, can...

Homework Statement Solve the separable equationHomework Equations dy/dx = 1-y^2The Attempt at a Solution dy/dx = 1-y^2 1/(1-y^2) dy = dx [Partial fraction] A/(1-y) + B/(1+y) = 1/(1-y^2) A + Ay + B - By = 1 y^1: A - B = 0 y^0: A + B = 1 => A=B=1/2 => (1/2)/(1-y) dy + (1/2)/(1+y) dy = dx...

Amazon has a list of 100 bestseller books in physics category. this includes popularizations, biographies, textbooks, Carl Sagan, Brian Greene, intelligent design, iffy-physics-of-the-supernatural, physics cartoons and comedy, ANYTHING if it has a connection with physics*. So the competition is...

Ok, so I have a TI-89 Titanium Edition calculator. I want to know how to setup fractions on it. Like I want to be able to do it like on a regular scientific calculator where you somethign like 2 Ab/c3 and then that would give you 2 over 3 (2/3). Is it possible to set up a fraction in the...

Homework Statement solve the following initial value problem using Laplace transforms y"+2y'+y=(8/3)cos(2t)-2sin(2t) y(0)=1 y'(0)=7/3 Homework Equations L[d^2y/dt^2]=s^2Y-sy(0)-y'(0) L[dy/dt]=sY-y(0) L[coswt]=s/(s^2+w^2) L[sinwt]=w/(s^2+w^2) The Attempt at a Solution so...

Hello, I was not sure if this belonged in the precalculus or calculus section so i hope no one minds that i posted it here. This is a problem that has completely lost me. http://img76.imageshack.us/img76/9191/continuousfractionrg3.gif T1 = 1 + 1 T1 = 1+ (1/1+1) T3 = 1+...

Hey, I'm terrible with fractions and would appreciate any help regarding this problem. This is a problem from my physics course. F2 = [ (v + v2)/(v + v1) ] F1 I need to solve for v1. I am given the values for F2, v, v2, and F1 and need to turn the formula around to solve for v1...

Determine from classical mechanics (using a head-on collision with recoil at 180 degrees) what fraction of an electron’s kinetic energy can be transferred to a mercury atom in an elastic collision. Derive an approximate value of the fraction. well ok let the mass of the electron be m_e...

Does X=n? X is the element fraction in a compound, and n is the mole number of an element.

This is actually part of a larger problem of solving a diff EQ by use of a laplce transform, but it's the partial fraction part that I'm stuck on. \frac{1}{s^2(s^2+w^2)} = \frac{A}{s}+\frac{B}{s^2}+\frac{C*s+D}{s^2+w^2} Good so far? If I then multiply through by the common denominator I...

Why is it that when you do A * b/c the answer is one (b/c)th of A? What is the operation of multiplication doing to the two numbers so that this happens? Also how does this logic work when A is also a fraction?

How can I find 0.13r(as in the 3 recurring) as a fraction Can anyone give me an idea of how I can find 0.13 as a fraction? :rolleyes:

This sounds like first grade mathematics but I need to know the reasoning. Why is it that to find a fraction of a number you multiply the number by that fraction? ie to find (a/b)th of X you do X*(a/b). What operation is the multiplication doing in reality? This is used in precentages...

I have search my gigantic physics book everywhere for this but I can't seem to find it...does anyone know what it means Seee the problem is What constant acceleration, in SI units, must a car have to go from zero to 71.0 mph in 13.0 s? I solved that it was 2.44 m/s^2 but then it askes What...

Hi, here is my question: \int \frac{dx}{(x-2)(x^2+4)}...for some reason I can't equate the coefficients?..is there something else.i used A/x-2 + B/(x^2+4)

Can anyone explain how to solve integration problems that involve partial fractions (problems like f(x) = P(x)/Q(x)) Thanks

I have an equation of the following form: \frac {dz}{z^2 - z} Of course, I factor this into: (z + \sqrt{z})(z - \sqrt{z}) then, \frac{A}{z + \sqrt{z}} + \frac{B}{z - \sqrt{z}} of course cross multiply the denominators to get: A(z - \sqrt{z}) + B(z + \sqrt{z}) = 1 But...