Combination Definition and 538 Threads

Homework Statement A small wooden block, of mass M, lies in the middle of a horizontal table of length L and height h above the floor. The coefficient of kinetic friction between this block and the surface of the table is μ. A bullet, of mass m, is shot with a horizontal velocity into...

Hi, I have to solve a numerical problem namely how air is flowing first through a porous medium followed by streaming of the air coming out of the porous medium in a very narrow channel flowing to the ambient (journal porous air bearing). This problem can be described with the use of two...

Question is attached I have spent a great deal of time on this problem and I am hoping someone can help me out. My attempt at problem. first for the heat engine QL/Qw1 = TL/Twaste so efficiency = 1- Tl/Twaste efficiency = 0.93808 and I know that efficiency = Wout/ Qw1 This is as...

Homework Statement (1) Is the following formula right? \sum_{l=0}^{m+n} \sum_{k=l-m}^{n} \binom nk \binom {m}{l-k} x^{l} = \sum_{k=0}^{n} \binom nk x^{k} \sum_{j=0}^{m} \binom mj x^{j} (2) If right, how do I prove it? If not, what is the right formula, and how do I prove it? (3) Could...

Homework Statement Hi In Griffiths (chapter 9) he states that any wave can be expressed as a linear combination of sinusoidal waves, f(z,t)=\int_{-\infty}^{\infty}{A(k)e^{i(kz-\omega t)}dk} = e^{-i\omega t}\int_{-\infty}^{\infty}{A(k)e^{ikz}dk} Is it correct to say that this in principle...

I have read at a lot of places that in 2D transformations rotation is a combination of scaling and simultaneous shear? What exactly does this mean & what's the proof for this?

Combination Formula with a "lockout" twist Hi! I am trying to figure out all possible combonations for 6 items among a group of 18 choices. So I turn to my old friend C(n,r) to calculate where n=18 and r=6. "But WAIT!" I tell you before you hastily begin scribbling, "There is a twist..." You...

Combination Formula with a "lockout" twist Hi! I am trying to figure out all possible combonations for 6 items among a group of 18 choices. So I turn to my old friend C(n,r) to calculate where n=18 and r=6. "But WAIT!" I tell you before you hastily begin scribbling, "There is a twist..." You...

I didn't get any bites in the Calculus section a few days ago so I'm hoping since this is likely a pretty basic part of spherical harmonics that someone here can aid me. Also hoping reposting in a new section after a few days is allowed. Thank you in advance for your assistance! Homework...

Homework Statement Hello forum, please see the attached image. This problem amounts to finding the equivalent resistance for the circuit and using Ohm's law to solve for the current. Homework Equations V=IR The Attempt at a Solution What I really need help with is learning how...

Okay, so I'm working on using spherical harmonics to fit a model to some data. The thing is, everything can apparently be described as a "linear combination of spherical harmonics" but nobody is explaining in plain English what that means, at least to me! :D I see lots of double sum...

Homework Statement A test consists of 5 pure math questions A, B, C, D, E and 6 statistics question F, G, H, I, J, K. The examiners want to arrange all eleven questions in a random order such that a pure math question must be separated from another with exactly one statistics question...

Homework Statement i_1=10+20sin(377t+(\pi /6)) i_2=-30 i_3=10+10sin(100t-(\pi/4)) i_4=10sin(377t) i_T=\sum _i i_i What I am wondering is how you go about calculating the average value for the linear combination of all three functions. Also, how would one calculate the rms for...

nC0+nC1+nC2+.....+nCn=2^n in the analytic proof for this my books say that it is the total number of combinations of n different things taken at least 1 at a time. they say that each object can be dealt in 2 ways, either it can be accepted or it can be rejected. hence n objects can be dealt...

Hi, I currently am having a problem where I wish to combine an AC signal and a DC signal. What I would like to know, is what parameters must be performed to combine the two together in a format where it would be akin to adding two waveforms. Aka, if I were to have a 1 Amplitude, Sine...

Homework Statement [PLAIN]http://www.smartphysics.com/images/content/mechanics/ch15/momentofinertia2new.png What is the moment of inertia of the object about an axis at the center of mass of the object? (Note: the center of mass can be calculated to be located at a point halfway between the...

http://imageshack.us/photo/my-images/266/unledzq.png/ Am I correct in thinking that C1 and C2 are in parallel, while C3 is in series with both C1 and C2, or their equivalent capacitor?

Hi there, I am writing a program to verify the total combination of dealing 10 cards to two players out of 52 cards. The math is simple. Firstly, the total way to draw 10 cards from 52 is C(52, 10) = 15820024220. From the drawn 10 cards, we pick any 5 for player A and the rest of player B...

Blanking quite a bit on this one Homework Statement Assuming that paraxial light from a distant object enters lens 1, find the image distance s′2 (due to the refraction at lens 2) as a function of the lens separation d. Your answer will also contain f, the unspecified focal length of the...

Homework Statement The integers 1 through 6 appear on the six faces of a cube, one on each face. If three such cubes are rolled, what is the probability that the sum of the numbers on the top faces is 17 or 18? Homework Equations Probability = # of desired outcomes / total # of outcomes The...

Homework Statement I am trying to come up with a logical explanation (using an example from real life modeled in Combination and/or Permutation) to show that 3^n = summation (from i=0 to n) of (n choose i)*(2^i). In other words, I am trying to pose a combinatorial/selection/combination...

Homework Statement I am trying to come up with a logical explanation (using an example from real life modeled in Combination and/or Permutation) to show that 3^n = summation (from i=0 to n) of (n choose i)*(2^i). In other words, I am trying to pose a combinatorial/selection/combination...

Hello all, I am trying to come up with a logical explanation (using an example from real life modeled in Combination and/or Permutation) to show that 3^n = summation (from i=0 to n) of (n choose i)*(2^i). My trial is that 3^n could be modeled as having 3 boxes and we are placing n items in...

How many sequences of zeros and ones of length 7 contain exactly 4 ones and 3 zeros? I'm having a hard time figuring out why it is 7 Chooses 4? thx

Let \mathcal B(\Omega) be the Borel algebra of \Omega (the σ-algebra of Borel sets in \Omega). I understand that if we define a "convex combination" of probability measures by \bigg(\sum_{k=1}^n w_k\mu_k\bigg)(E)=\sum_{k=1}^n w_k\mu_k(E), then every convex combination of probability measures is...

given a1=[1,-2.0] , a2=[0,1,2] , a3=[5,-6,8] , b=[2,-1,6] determine if b is a linear combination of a1, a2, a3. I put these vectors into an augmented matrix and row reduced. My result was columns 1 and 2 having pivots and the last row being all zeros. Please help me understand how this results...

Homework Statement You are given 8 balls, each of a different color. How many distinguishable ways can you: (1) Divide them (equally or unequally) between 2 urns. (2) Divide them (equally or unequally) between 2 children (and each child cares about the colors he or she receives)...

Homework Statement A history exam paper contains eight questions, four in part A and four in B. Candidates are required to attempt five questions. In how many ways can this be done if at least two questions from part and at least two questions from B must be attempted Homework Equations...

I would like to check my work with you all. :smile: Homework Statement Let \vec{u} = 2\vec{i}+\vec{j}, \vec{v} = \vec{i}+\vec{j}, and \vec{w} = \vec{i}-\vec{j}. Find scalars a and b such that \vec{u} = a\vec{v}+ b\vec{w}. Homework Equations Standard Unit Vectors: \vec{i}...

Im working on understanding Gröbner bases. I've understood how to show existence and uniqueness(of reduced Gröbner bases). To understand how to actually compute them, I need to understand Syzygies in free modules. The theorem reads thus: In a ring of multivariate polynomials over a field, if S...

Why the process of recombination is called "re"combination? The process in which the nucleus and electrons combined to form neutral atoms at early times is called recombination. But why it is added an "re" to "combination"? Is there any combination process before this process? Thx!

HOW MANY PACKETS DO I HAVE TO BUY? Hi all, I'm posing this question because I'm interested in the answer from a purely theoretical point of view - I'm not going to go out and test the answer afterwards, and it's not for my homework (I last did homework more than 10 years ago)...

1. An 85-kg man plans to tow a 109000-kg airplane along a runway by pulling horizontally on a cable attached to it. Suppose that he instead attempts the feat by pulling the cable at an angle of 9.00 above the horizontal. The coefficient of static friction between his shoes and the runway is...

Homework Statement As Shown in the Figure http://img713.imageshack.us/img713/3342/unledcdq.jpg Find the i1 and the power dissipated in 10 resistor ohms Homework Equations P=I^2 x R P= I x E Ohms law E= I x R The Attempt at a Solution @node A I=-i2 +Io @node B...

I'm getting so confused about this question, any help would be great. :) Homework Statement Two infinite waves Ψ1, Ψ2 have the same wavelength and polarisation and have amplitudes of E1 = 3 and E2 = 7 units. They are added together with a phase difference of 125 degrees. 1) What will be the...

Homework Statement Let F(x)=\begin{cases} .25e^{x} & -\infty<x<0\\ .5 & 0\leq x\leq1\\ 1-e^{-x} & 1<x<\infty\end{cases}$. Find a CDF of discrete type, F_d(x) and of continuous type, F_c(x) and a number 0<a<1 such that F(x)=aF_d(x)+(1-a)F_c(x) Homework Equations The Attempt at a...

I want to express the matrix product Ax as a linear combination of the column vectors in A. I know for that for (2,3;-1,4)(1;2) i just row reduce the 2 previous matrices and then the solutions give the multiples needed for each column. How would i go about solving a similar problem but...

What is the condition for the continuous time signal x(t) to be periodic if it is the linear combination of n periodic signals. where x(t) = a_{1}x_{1}(t)+a_{2}x_{2}(t)+a_{3}x_{3}(t)+......a_{n}x_{n}(t) where x_{i}(t) is periodic with fundamental period T_{i} \forall i, where i \in...

Ok so anti-matter and matter when combined give energy as the masses with opposite charges annihilate each other, giving off energy. Here's the thing, there is no such thing as pure energy, it comes in the forms kinetic, heat, sound and light. so in a vacuum, we take 1 anti-matter...

Hi, I want to buy two Quantum Mechanics books, but I am pondering what would be the best combination. My definition of BEST is resourceful, lucid, in-detail. As a physics student, I think two quantum mechanics books putting on my shelf is quite enough... My List: David Bohm, Quantum...

Homework Statement Find the equivalent resistance seen by the source and use the result to find i, i1, and v. Homework Equations V=IR for series circuits: RT=R1+R2+...+Rn VT=V1+V2+...+Vn for parallel circuits: IT=I1+I2+...+In 1/RT=(1/R1+1/R2+...+1/Rn) The Attempt at a Solution since 30Ω and...

I'm working on a personal project trying to figure out if lasers can be effectively used to generate plasma from a gas at specific rates. As part of this, I assumed that most of the ionization would take place because of the laser photons rather than the power generated by the laser. Working...

Homework Statement Given: a>=b>=c>=0, d>=e>=f>=0, a>=d a+b>=d+e a+b+c=d+e+f a,b,c,d,e,f belong to Real numbers Prove that d, e, f can be expressed as linear combinations of a, b and c in such way: d=(c1+c2)*a+(c3+c4)*b+(c5+c6)*c e = (c1+c6)*a+(c2+c4)*b+(c3+c5)*c...

So, in lectures we derived the equation for damped SHM by solving the differential equation relating position (x), mass (m), spring constant (s), and damping coefficient (r): m\ddot{x}=-\frac{s}{m}x-r\dot{x} Using a solution of the form Ae^{\alpha t}, we find that: x=Ae^{-pt}e^{\pm qt}...

Homework Statement Solve for _5C_n = 10 The Attempt at a Solution _5C_n = 10 \frac{5!}{n!(5-n)!}=10 \frac{120}{n!(5-n)!}=10 I can't go on from there. I remember that my teacher told me that for combinations and permutations, if the variable is the second number (or number to the right of...

All the texts and sites I can find discuss the rotational dynamics of pure rotation, pure translation, or a combination of an object rolling without slipping. I am trying to resolve some rotational dynamics regarding a spinning object that is moving linearly.. such as a planet in space or a tiny...

Homework Statement Give the features and the utilities of the series and parallel combination of resistors. The Attempt at a Solution Series combination:- (i)The current has a single path for its flow.Hence the same current passes through each resistor and so the potential difference...

Question involving the voltage when batteries are connected in different ways? What is the voltage across six 1.5 V batteries when they are connected a) in series b) in parallel, c) three in parallel with one another and this combination wired in series with the remaining three? I'm not sure...

Hello everyone, (First, I hope this is the right subsection of PhysicsForum for this type of question. I was unsure if this should go into the ME or EE section) To start, I am trying narrow down my Engineering Interests down to somewhat specific areas to solidify what majors to pursue in...

How can I prove that the any linear combination of multivariate normal distribution is also normal? I can prove it but I'm not sure that this is right or not. The point of my proof is as follows. --- The X and Y has the same dimensional random vector, and each random vector is...