Combination Definition and 538 Threads

Homework Statement Find the ##gcd(x^3+x^2-x, x^5+x^4+2x^2-x-1) ##and write it as a linear combination. Homework Equations The Attempt at a Solution I know the ##gcd(x^3+x^2-x, x^5+x^4+2x^2-x-1)=1## What I have so far is ##1. x^5+x^4+2x^2-x-1=(x^3+x^2-x)(x^2+1)+(x^2-1)## ##2...

Homework Statement Prove: \sum^{n}_{r=0}2r(^{n}_{r}) = 3n Homework Equations The Attempt at a Solution I proceeded by induction: Testing the base case for n=0 is correct. Moving right along to try to show: \sum^{n+1}_{r=0}2r(^{n}_{r}) = 3n+1 This is where...

There are 12 questions on an exam, and each student must answer 8 questions including at least 4 of the first 5 questions. How many different combinations of questions could a student choose to answer? So I got the number of ways a student can choose to answer the first 5 questions which is 6...

A bridge hand consists of 13 cards. How many bridge hands include 5 cards of one suit, 6 cards of a second suit and 2 cards of a third suit?

What do textbooks mean when the gas laws are "combined" to make the ideal gas law? I think that if the equations were combined, the result would look something like this: P = k(T)T P = k(V)/V P = k(n)n P^3 = (k(T)T * k(V)*k(n)n)/V or P/T = k(T) PV = k(V) P/n =...

Hi there, As my Maths skills suck, I'm not entirely sure if I've worked out the following correctly: Using the combinations calculator - http://www.mathsisfun.com/combinatorics/combinations-permutations-calculator.html - the total amount of possible numbers drawn in a game (80), and how...

A particle of mass m is trapped in a one-dimensional infinite square well running from x= -L/2 to L/2. The particle is in a linear combination of its ground state and first excited state such that its expectation value of momentum takes on its largest possible value at t=0.I know the process of...

Green and orange light pass through a diffraction grating that contains 6000 lines/cm. Compare the appearance of the fringe at m = 0 with all the others. So far I've only dealt with light with one wavelength, so I just want to make sure I have the right thought process here for two...

Homework Statement An accounting professional association is considering six hotels as possible sites for their next two meetings in 2001 and 2002. In how many ways can the association select the hotels... a) if the two meetings may be held at the same hotel? b)if the two meetings may not be...

1. Homework Statement Draw an LCAO representation of all of the bonding orbitals for C2H2O. Be sure to clearly state the hybridization of the two carbons and the oxygen in addition to drawing the orbital representation. Also show clearly what orbital any unshared pairs occupy. 2...

Homework Statement 1. A particular solution \Psin(x,t) of the TDSE, -iℏ∂\Psi/∂t=\hat{H}\Psi, can be constructed by taking \Psin(x,t)=ψn(x)exp(-iEnt/ℏ) where the ψn are solutions of the TISE. a) Show that a linear combination of 2 such solutions c1\Psi1(x,t) + c2\Psi2(x,t) is also a...

Homework Statement There are 2n points on a circle, we want to connect each two of them to make a pattern of connection in the way that there is no cross between the lines of connection, and all the lines have to be inside the circle and on the plane of the circle. Question: How many different...

Homework Statement By using integration, find the value of 100C0+\frac{1}{2}100C1+\frac{1}{3}100C2+\frac{1}{4}100C3+...+\frac{1}{101}100C100 Homework Equations Integration Combination The Attempt at a Solution I don't even have any ideas to start. Can this really be solved by...

hi, i read in quantum mechanics wave function is a combination of eigenfunctions and according to Orthodox interpretation measurement causes the wave function to collapse into one of the eigenfunction of the quantity being measured. Is this explanation still valid?

Homework Statement A circuit contains a single 250 pF capacitor hooked across a battery. It is desired to store three times as much energy in a combination of two capacitors by adding a single capacitor to this one. How would you hook it up, and what would its value be? Homework Equations...

Homework Statement Compute the equivalent capacitance for the network between points A and B.Homework Equations 1/(Ceq) = 1/C1 + 1/C2 + 1/C3... (series) Ceq = C1 + C2 + C3... (parallel) C1 = 6.9 nF C2 = 4.6 nF The Attempt at a Solution I have been getting stuck on a lot of these questions. A...

I quote a question from Yahoo! Answers I have given a link to the topic there so the OP can see my response.

Homework Statement In the attached circuit diagram, I have to find the Total resistance of the cicuit, the current at I1, the voltage over R6 and the current through I5. Homework Equations V = IR The Attempt at a Solution Rt = 12Ohms I1 = 1A R6 = 6v I5 = 1A Homework Statement

Homework Statement a standard combination lock consists of a password which is 3 distinct numbers between 00 and 59. a) compute the number of valid passwords b) compute the probability that the password is a palindrome. eg. 03 - 22 - 30 is a palindrome (same backward as it is forward) c) the...

I understand the concepts of whether a resistor is in parallel or in series with each other. But I thought of a weird case that i can't seem to find examples for. http://imgur.com/b2YMOnAIn this case, would R3 be in parallel or in series to R2? Or could this just be an impossible case? Thanks...

Homework Statement Suppose there is 7 chairs arranged in a straight line, each of the 3 boys will sit randomly on one of the chair . In how many ways the boys can be seated if the 3 boys cannot sit next to each other? Assume that the boys are indistinguishable. I listed out all the...

HELLO, I hav a UG degree in electronics and i am completely passionate about electronic circuits & stuff but on the other hand i am also interested in space & rockets. any chance where in i can switch over to space industry with my electronics ?? do i have any specific masters course which will...

Homework Statement What is the compensative system of this combination of resistors? http://img545.imageshack.us/img545/6610/circuitoi.jpg

Homework Statement An object is placed 400 mm in front of a convex lens of focal length 80 mm. Find the position of the image formed. State the nature of this image. A second concave lens of focal length 25 mm is placed 80 mm behind the first convex lens. Find the position of the final...

Hello Everyone, I am trying to compute the standard error of a stress related calculation. Let's consider the following: A ± ΔA B ± ΔB where A and B are the mean values while ΔA and ΔB are the respective standard errors. The common combination of errors formulas are as follows: y = A +...

Hello Everyone, I am trying to compute the standard error of a stress related calculation. Let's consider the following: A \pm \DeltaA B \pm \DeltaB where A and B are the mean values while \DeltaA and \DeltaB are the respective standard errors. The common combination of errors...

Two thin lenses having focal lengths of +15 cm and -15 cm are positioned 60 cm apart. A bird stands 25 cm in front of of the converging lens. a. describe the image of the bird. Is it real or virtual? Upright or inverted? Magnified or reduced? b. If the bird is 10 cm in height, what is the...

Homework Statement Find the resistance in resistor MN. Diagram is attached Homework Equations in series circuit R = R1+R2+R2+...Rn in parallel circuit \frac{1}{R} = \frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}+... \frac{1}{R_n} The Attempt at a Solution I have no idea on how to get...

Homework Statement The total number of ways in which 5 balls of different colours can be distributed among 3 persons so that each person gets at least one ball is ... Homework Equations The Attempt at a Solution I began by finding the number of ways of distributing 5 balls among...

Hello, I'm hoping I might be able to get some help in creating a forecasting model (in sports) looking at 2 variables that are not independent of each other. I'll take US Football (same applies to rugby) as an example. The specific forecast I'm interested in here is the expected supremacy...

I've been working on a breadboard project in which 8 dip switches must be in the right combination in order to light an LED. But it simply refuses to work. I don't exactly know what is happening, so I can't explain the results. I have triple checked my logic in both my head and on simulation...

Hi guys. I've solved an exercise but the solution sheet says what doesn't make sense to me. Could you please help with this problem? Determine if vector b is a linear combination of vectors a1, a2, a3. a1=[1, -2, 0], a2=[0, 1, 2], a3=[5, -6, 8], b=[2, -1, 6]. b is a linear combination...

Homework Statement express the vector (6,-4,7) as a linear combination of (4,-2,1) and (-3,1,2) Homework Equations The Attempt at a Solution I am not quite sure how to go at it but this is what I am assuming to do: (C1*4,C2*-2,C3*1)=(6,-4,7) C1=3/2 C2=2 C3=7 and the...

Homework Statement Show that the following wave function eigenfunction decomposition is viable and find it's expected energy. ψ(x, t) = [1/(1+i)]ψ1(x)e^(-iw1t) - (1/√2)ψ2(x)e^(-iw2t) Homework Equations ∫ψ(x)*ψ(x)dx = 1 probability ∫ψm(x)*ψn(x)dx = 0 orthogonality ∫ψm(x)*ψn(x)dx...

When the book says "Members of [[S]] are linear combinations of linear combinations of members of S". [S] basically means the span of the members in subspace S. Since [S] = {c1s1 +...
+ cnsn|c1...cnεR and s1...snεS} what does [[S]] mean? does it mean a linear combination of atleast one linear...

Form a team by choosing 4 persons among 4 women and 7 men. You need at least 2 women in the team. How many ways to do it? My solution: 1. Choose 2 women among the 4 availaible women. There is 2C4 ways of doing it. and 2. Choose 2 persons among the 9 remaining people, there is 2C9 of doing it...

Homework Statement If three different number are taken from the set {0, 1, 3, 5, 7} to be used as the coefficient of a standard quadratic equation, how many such quadratic equations can be formed? How many of these have real roots?Homework Equations The Attempt at a Solution Part a: "How many...

Thirty items are arranged in a 6-by-5 array. Calculate the number of ways to form a set of three distinct items such that no two of the selected items are in the same row or same column. I am told the answer is 1200. I do not believe that I am able to use the standard combination formula...

This is NOT homework. This is a personal project I am working on. First and foremost, THANK YOU in advance for helping me with my statistics project that I have been unable to solve on my own or through the help of my statistics book and google. I am working on an excel spreadsheet for use...

Hi all, I need to calculate the probability density function f\left( Y \right) of a function Y of two variables A and B with known individual probability density functions f\left( A \right) and f\left( B \right). What is the correct way to combine the PDF's? Specifically, I have a...

Volume of a convex combination of convex sets,,,,sort of Hi all, I hope someone can tell me whether this is true or not: Let A_{i},i=\{1,...,m\} be m \times n matrices, and let H_{i}=\{x\in \mathbb{R}^{n}:A_{i}x\geq 0\},i=\{1,...,m\}. Also let a probability measure \mu be given. Define...

I am creating a random combination(code) for a client. I need to see what the total number of combinations there can be. Please let me know if I am using the wrong word Combination vs Permutations. Formula: 2 letters + 2 numbers + 2 letters example: TR12FR The random letters are...

Hi, If you have 3 variables A, B and C. Variable A can range from 5 to 960 in blocks of 5 (192 blocks). Variable B can range from 0 to 100 in blocks of 5 ( 20 blocks) Variable C can range from 2 to 70 in blocks of 2 ( 35 blocks). How many combinations of the numbers can you...

Right I am having an issue with the proof to permutation, I really can see the n-r-1 I think the confusion stems because it is in the general term, which throws me a bit, if possible could someone maybe write it in numbers and the underneath write in the general term if not too much trouble. The...

A theorem from number theory states that, if a and b are nonzero integers, then there exists a smallest positive linear combination of a and b. This is my proof: Let S be a set such that S = {w\inNatural numbers : w=am+bn} , where a and b are positive integers, m and n are any integers...

I wonder how to find linear combination of 2 numbers, that is: ax+by=t, with t=m*GCD(a,b), and m,a,b \in Z. Find x,y.

Homework Statement At the height of H, from a plane with the speed of V, there is an object "thrown off". H = 10km = 10 000m V = 300m/s To be determined: - total distance from the plane to the falling point - S - the time the fall takes - T do not have to take aerial friction into...

Homework Statement An electron in a hydrogen atom is in a state described by the wave function: ψ(r,θ,φ)=R(r)[cos(θ)+eiφ(1+cos(θ))] What is the probability that measurement of L2 will give 6ℏ2 and measurement of Lz will give ℏ? Homework Equations The spherical harmonics The...

Homework Statement A crew of an 8 oar boat has to be selected from 11 people, out of which 5 can oar only on one side, 4 can oar only on the other side and 2 can oar on either sides, find in how many ways can the selection be done? The Attempt at a Solution What I did here is assumed...

Homework Statement how many 4 digit numbers are there which do not contain more than 2 different numbers? Homework Equations The Attempt at a Solution all can contain the same digit any 3 out of the 4 places can be occupied by the same digit and any 2 out of the 4 places can...