Fraction Definition and 653 Threads

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 Given the equation for Roaults law and Antoine equation for 2 species I need to recast these into a pair of coupled non linear equations to compute the mole fraction of species one and the temperature for given values of vapor fraction and the total pressure, Antoines...

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!

Homework Statement I basically need to find the integral of (-5x^3-1x^2+4)/(x^4+2x^3) Homework Equations Just the basic rules associated with partial fractions when re-writing a polynomial with constants. The Attempt at a Solution Since the degree of the denominator is 4 and...

Hi there! 1)It's a very common problem for me . I don't get when do I have to multiply or divide a fraction in unitary method e.g. 10 men do 1 work in 40 days 10 men does 3/4 work in 40*3/4 days or should i do 10 men does 3/4 work in 40*4/3 days I do't undestand!Plz give me a reason...

Homework Statement If i have 1/2 + 1 = 1,5 (on the calculator), how do i make this into a fraction? I know this answer would be 1/2 + 1 = 3/2 But how excactly is this done? Homework Equations The Attempt at a Solution

Homework Statement Solve for t: [-2(t2+1) / 9(t2-1)] < 0 The Attempt at a Solution I know that the answer is -inf<t<-1 and 1<t<inf, but how do I show the calculation to get that answer? When I tried, I narrowed it down to t<root-1, but that's not possible (without complex...

Ok, so why do some answers contain an A/something + (Bx + C)/something and others contain just an A/something + B/something. I hope someone knows what I'm talking about!

Homework Statement integral using partial fraction Hi everyone ,, got the following question : The attempt at a solution I reached the following ,, integral ( 4/(X^2+x+1) + (-4x-1)/(X^2+x+1)^2) ) and now I don't know how to integrate .. -_- help please

1. Homework Statement The normal boiling points of benzene and toluene aer 80.1C and 110.6C, respectively. Both liquids obey Trouton's rule well. For a benzene-toluene liquid solution at 120C, with the molar fraction of benzene in the solution equalling 0.68, estimate the vapor pressure...

Homework Statement Very pure liquid water can be subcooled at atmospheric pressure to temperatures well below 0ºC. Assume that 1kg has been cooled as a liquid to -6ºC. A small ice crystal (negligible mass) is added to "seed" the subcooled liquid. If the subsequent change occurs adiabatically...

contrary to AGW theory. I have not yet read the actual study. http://bristol.ac.uk/news/2009/6649.html"

prove that limit of --- (x^{n}-a^{n}) ---------- ---------------- (x-a) when " x " tends to " a " equals to ---- n.a^{n-1} ----- ****where " n " is a fraction.. we have been given this and I've...

Homework Statement Find the convergents to the fraction 57/44. Homework Equations Could anyone provide any good internet resuorces about "finding the convergents to the fraction"? The Attempt at a Solution

Homework Statement Obviously, we can make rockets to go very fast, but what is a reasonable top speed? Assume that a rocket is fired from rest at a space station in deep space, where gravity is negligible. If the rocket ejects gas at a relative speed of 1100 and you want the rocket's...

My algebra is really rusty, anyway I'm trying to simplify a Transfer Function so I have H(jw)=ZL/R+ZL so ZL is the impedance of an inductor and R is the impedance of the Resistor, my question is how would I go about simplifying that transfer function into it's simplest form? Thanks...

So I've been thinking about this problem for quite some time now any help will be appreciated. A sample of C_{2}H_{2}(g) has a pressure of 7.4 kPa. After some time a portion of it reacts to form {C}_6{H}_6 (g). The total pressure of the mixture of gases is then 3.6 kPa. Assume the volume and...

I'm looking at this particular splitting of a fraction in a book and I'm not completely sure what rule is being invoked. Here it is: http://www.apthtml.com/images/split.png Can anyone identify what this is?

Homework Statement \frac{(cos60 - isin60)^5 * (cos45 - isin45)^3}{(cos15-isin15)^7} Homework Equations The Attempt at a Solution I have had several tries so far, but simply do not know what to do. Would somebody be so kind and simplify this expression step by step. I...

Homework Statement What is f'(x) of f(x) 1/sqrt(2x)? 2. The attempt at a solution In applying the problem to the derivative formula: (1 / sqrt(2(x + h)) - 1 / sqrt(2x)) / h I multiplied the problem by a special form of one but that only put the rationals on the bottom of the...

Homework Statement I need to solve the following integral: { x * ((1-x)/3)^(1/7) dx where { represents the integral symbol b/c I don't know how to type that. The Attempt at a Solution I've tried integration by parts and don't get anywhere. None of the integration techiques I...

I am having trouble to find a straight forward method for finding coefficients using partial fraction expansion with repeated or complex roots. My study notes arent too clear so I am finding the differentiation method hard to follow for repeated roots. As for complex roots I can find the roots...

Hello, Is there any recommended reference for the subject "General Partial Fraction Exapnsion"? Thanks in advance

Homework Statement 1/[s*(s^2 + 4)] Homework Equations The Attempt at a Solution 1/[s*(s^2 + 4)] = A/(s) + (Bs + C)/(s^2 + 4) => 1 = A(s^2 + 4) + (Bs + C)s s = 0 1 = A(0 + 4) + (B*0 + C)*0 A = 1/4 s = i 1 = A(i^2 + 4) + (Bi + C)i 1 = A(i^2 + 4) + Bi^2 + Ci 1 =...

Homework Statement I just can't understand it I've read plenty of guides online, I just can't figure it out. How do you do partial fraction decomposition the farthest i can get is below 1/[(s^2 + 1)(s+1)] Homework Equations The Attempt at a Solution 1/[(s^2 + 1)(s+1)] = A/(s+1)...

Homework Statement If \lim_{z\rightarrow z_0}f(z)=A and \lim_{z\rightarrow z_0}g(z)=B then prove that \lim_{z\rightarrow z_0}\frac{f(z)}{g(z)}=\frac{A}{B} for B\neq0 The Attempt at a Solution I write f(z)=A+\epsilon_1(z) and g(z)=B+\epsilon_2(z), where the epsilon-functions tend to zero as z...

Homework Statement Show that the fraction of electrons within kT of the fermi level is equal to 3kT/2Ef, if D(E) = E^1/2. Homework Equations f(E) = 1 / ( exp(E-Ef)/kT + 1 ) fermi distribution N = integral from 0 to inf of D(E)f(E)dE = total no. of electrons The Attempt at a...

My TI 83 plus has a function called "Frac" which makes decimal numbers into fractions. If I have 0.33333... on the screen and press Frac the calculator returns 1/3. My question is how does this function work.

Derive the following equation for the fraction of a solute in layer 1 of the 2 layers formed by two immiscible liquids; Fraction of solute in layer 1 = (KD*V1)/((KD*V1)+V2) where KD=Distribution coefficient for the solute between chemical in V1 and chemical in V2 V1=Volume of liquid...

Homework Statement A small piece of aluminum(atomic number 13) contains 1015 . (The atomic number is the number of protons; it determines the (positive) electric charge of the nucleus and, thus, the number of electrons in a neutral atom.) If the piece of aluminum has a net positive charge of...

Find the area of the region under the graph of the function f on the interval [5, 10]. F(x) = 9/x

Homework Statement hey guys just wondering if anyone could help me simplify this. thansk [1-(y2/x2)]/[1+(y2/x2)] Homework Equations The Attempt at a Solution

I am just coming back to math after a, oh 30 year or so, vacation. In the class I'm taking, we are studying Partial Fraction Decomposition ( Px/Qx:Qx). It doesn't entirely make sense to me, tho like a monkey typing the great American novel, I can solve them given enough time. I am just having...

I am trying to find the integral of the following: \int\left({\frac{3 + 5x - 6x^2 - 7x^3}{2x^2}}\right)dx What I did was to split up the fraction like so: \int\left({\frac{3}{2x^2}}\right)dx + \int\left({\frac{5x}{2x^2}}\right)dx + \int\left({\frac{6x^2}{2x^2}}\right)dx +...

Hello, Is there a general form for the nth derivative for a fraction? Thanks in advance.

This might be a silly question: Is there a meaningful way to use L'Hospital's rule to determine \lim_{\vec{\mathbf{x}} \rightarrow \vec{\mathbf{0}}}\frac{x^3}{x^2+y^2}? where \vec{\mathbf{x}}=\left(\begin{array}{c}x\\y\end{array}\right)

3.741 (41 is recurring) answer is 1852/495 but ii don't know how to work it out thanks :)

Homework Statement It is a really long word problem, but I only need help with integrating one part of the proble. Homework Equations I need to know how to integrate 2+5sin((4*pi*x)/(25)) The Attempt at a Solution I tried using the chain rule by first integrating the sin into...

Homework Statement Find the partial fraction decomposition of : \frac{x^2}{(1-x^4)^2} The Attempt at a Solution \frac{x^2}{(1-x^4)^2}=\frac{A}{(1-x^4)}+\frac {B}{(1-x^4)^2} =A(1-x^4)+B when x=1 1=A(1-1^4)+B Hence B=1 and A=0 \frac{x^2}{(1-x^4)^2}=\frac{0}{(1-x^4)}+ \frac{1}{(1-x^4)^2}...

Homework Statement A "pulse oximeter" operates by using light and a photocell to measure oxygen saturation in arterial blood. The transmission of light energy as it passes through a solution of light-absorbing molecules is described by the Beer-Lambert law, given below, which gives the...

Homework Statement The coefficient of the restitution of an object is defined as the ratio of its outgoing to incoming speed when the object collides with a rigid surface. For an object with a coefficient of 0.59, what fraction of the object's kinetic energy is lost during a single...

Homework Statement 2 solutions of C12H22O11 are mixed. Solution A is .150M with density of 1.05 g/mL. Solution B is 10% C12H22O11 by mass with density of 1.03g/mL. 100 mL of solution A is mixed with 100g of B. What is the mole fraction of C12H22O11 in the mixed solution? Homework...

Homework Statement do we look at the nominator or the denominator? are we trying to separate them? factoring them? thanks

I wasn't exactly sure where to put this, so I decided to try this section. It may be more appropriate to put this in the Calculus / Analysis section... I don't know. Can anybody tell me whether or not it's possible to find the value of the continued fraction 0 + 1 / (2 + 3 / (4 + 5 / (6 +...

Homework Statement I am just looking for a hint on which rule to follow first; what would you tell me if I already know how to deal with an ordinary complex fraction? I tried using x (and multiplied everything) as the LCD and got the wrong answer. 3 - \frac...