Combination Definition and 525 Threads

Homework Statement Show that any vector in a vector space V can be written as a linear combination of a basis set for that same space V. Homework Equations http://linear.ups.edu/html/section-VS.html We are suppose to use the 10 rules in the above link, plus the fact that if you have a lineraly...

Sorry if this is more of a HW question (if so then moderator please move my question. Thanks!) Hi, I'm trying to get an expression for a best fit curve of the combination formula (##_nC_r##). As far as I can tell, the curve is a simple parabolic curve, and its shape doesn't change. It's just...

Homework Statement Consider the four vectors (1, 1, 1), (2, −1, 3), (1, 7, −1) and (1, 4, 0). Calculate how many ways you can write (1, 1, 1) as a linear combination of the other three, explaining your reasoning. The Attempt at a Solution wouldn't any of these combinations give the correct...

Find n if P(n, 3) = 6 C(n, 5). My attempt $\frac{n!}{(n-3)!}=6\frac{n!}{(n-5)5!}$ I don't know how to proceed

Hi i am fatih from turkey.i am high school student.question is "how many squares are in an rectangle subdivided into unit squares?"(a<=b) My theorem about this question.Please write your comments.Thanks For your time, thanks all mathematicians !:)

Homework Statement A convex lens which focus point is 10 cm is placed face-to-face with plane/flat mirror in a 20 cm distance. If a candle is placed 5 cm in front of the plane mirror which will get reflected by the mirror and refracted by the lens, so the distance between two first image in...

[Note: Thread has been moved to the homework forums by a mentor] This is the Given problem This is my solution part 1 - What I did here is I series the R3 and R4 (R3 + R4), and I parallel the R34 to R5 (most of the calculation are from the calculator) This is my solution part 2 The...

Homework Statement You have 4 red, 7 blue, and 12 white bricks and grab a random handful of 6 bricks. a) How many handfuls will contain exactly 3 red bricks? b) How many handfuls will contain exactly 2 of each color? c) How many handfuls will be all the same color? d) How many handfuls will...

Homework Statement In how many ways can 12 balls be arranged into 4 different rows with each row having at least one ball (a) if the balls are identical? (b) if there are 6 identical red balls and 6 identical blue balls? Homework EquationsThe Attempt at a Solution a) Put 4 balls in each row...

Given the non-zero vectors u, v and w in ℝ3 Show that there is a non-zero linear combination of u and v that is orthogonal to w. u and v must be linearly independant. I am not really sure at all. But I have done this: This is a screenshot of what I have done. Basicly, I assumed in the end...

.The number of points, having both co-ordinates as integers, that lie in the interior of the triangle with vertices (0, 0), (0, 41) and (41, 0), is (1) 901 (2) 861 (3) 820 (4) 780 my attempt: for this to be true i know that sum of x and y coordinate should be 41 but i don't know how to proceed.

I am in a group we cannot agree on how to answer the following word problem... "Let me tell you a little dirty secret about the mutual dislike between mathematicians and physicists. It can escalate into a full blown war if diplomacy is not attempted properly. It happens that a graduate...

Homework Statement Counting problems are a very tough subject to me, so if someone could give me tips, examples explaining what's really happening, that would be great. Homework Equations I know what permutations, variations, combinations, ... are. The problems involving only one of those...

hello, in numerical fluid dynamics there are field methods like finite-volume, finite-element, etc. and particle methods like Smoothed-Particle-Hydrodynamics – SPH and others. Both approaches have advantages and disadvantages depending on the application. Both, in principal completely different...

suppose you have 2 bins each with cross section \sigma_1, \sigma_2... if you combine those bins, is it a logical assumption to say that the cross section will also be added? I suppose from the equality of the luminosity one can get: \frac{1}{2}[ N_1 / \sigma_1 + N_2 /\sigma_2] = N_{1+2}/...

Homework Statement hello, i want to calculate the inertia tensor of the combination of a point mass and a sphere in the object's frame, the center of mass is at the origin. The point mass remains at the surface of the phere The sphere is uniform, radius r and mass M, and the point mass has mass...

How many ways can you arrange 52 things into 4 groups BUT the groups do not have to be the same size?!?

Find the number of subsets of S = {1,2,3,...,10} that contain (a) the number 5. (b) neither 5 nor 6. (c) both 5 and 6. (d) no odd numbers. e) exactly three elements. (f) exactly three elements, all of them even. (g) exactly five elements, including 3 or 4 but not both. (h) exactly five...

According to A Borobantu, regarding superposition, where Ψ is a state vector or a wave amplitude, given Ψ1, Ψ3, Ψ3... Ψncan by physically realized, then the following statement holds for all linear combinations Ψ = ∑ciΨi where ci can satisfy 1 = ∑|ck|2 to be called a complete and closed...

Homework Statement Given the vectors a = (5,2,-1), b = (3,2,1), c = (1,2,3), b' = (1,1,0), c' = (3,-3,-2) We assume that the vector a is a linear combination of the vectors b and c and b' and c' respectively, so that: a = xb + yc = x'b' + y'c' a) Determine the factors x and y through...

Homework Statement Assume that (|v_1>, |v_2>, |v_3>) is an orthonormal basis for V. Show that any vector in V which is orthogonal to |v_3> can be expressed as a linear combination of |v_1> and |v_2>.Homework Equations Orthonormality conditions: |v_i>*|v_j> = 0 if i≠j OR 1 if i=j. The Attempt...

Moderator's note: this is a spin off from a previous thread here. I confess to a very limited understanding of QM. I understand (somewhat) that a state of a particle can be a combination of possible states. I do not understand how a particle can be a combination of two particles. In...

Homework Statement There are 30 students in a class. In how many ways can we arrange them if : a)we must have three group, group one must have 5 students , group two 10 students and group three 15 students. answer=\frac{30!}{5!*10!*15!} b)we must have three group and all must have 10 students...

Ok so my teacher gave us this as an assignment: and was tasked with drawing the output voltage. The input voltage is a sine wave with 10v and -10v as its peaks. So I know that the positive cycle will have both diodes be forward biased and the negative cycle will have 3 parts. First is when...

Homework Statement From the numbers 4,5,6,8,9 we make 5 digits numbers (each number can be used only once). h)How many of these numbers are divisible by 8? The correct answer is 20 Homework Equations a number is divisible by 8 if the last 3 digits are divisible by 8 If the hundreds digit is...

S={v1, v2, v3} v1=[1, -1], v2=[-2, 2], v3=[3, a] a) For what value(s) a is the set S linearly dependent? b)For what value(s) a can v3 be expressed as a linear combination of v1 and v2? a) p=3 and m=2 3-2=1 free variable Therefore the set has non-trivial solutions and is linearly dependent b)...

Homework Statement A= \begin{bmatrix} 1 & 1 & 1 & 2 & 5 \\ 2 & 3 & 1 & -1 & -5 \\ 1 & 0 & 2 & 0 & -1 \\ 1 & 2 & 0 & 1 & 2 \end{bmatrix} Homework Equations I get this RREF \begin{bmatrix} 1 & 0 & 2 & 0 & 0 \\ 0 & 1 & -1 & 0 & 0 \\ 0 & 0 & 0 & 1 & 3 \\ 0 & 0 & 0 & 0 & 0...

For theoretical sake, would a collapsed wave function combined with a non-collapsed wave function result in a wave function between that of a collapsed and non- collapsed wave function? Thank you and please excuse the stupidity of the question

Homework Statement Okay I am given a matrix A = [2 1 ; 3 4] The first step is to find numbers of a and b such that A2 + aA + bI = [0 0; 0 0] I is an identity matrix (2x2). Part B - After that is says to use the result of the above to express A5 as a linear combination of A and I Homework...

How can we derive the formula for finding equivalent power in a series and parallel combination of 'n' resistors (with fixed resistance)?

Homework Statement There are 7 different postbox, and 10 identical letters. How many ways can the letters put into the boxes so that there is at least one letter in a postbox? Homework Equations nCr=n!/(n-r)!r! If M,N,O... things can be done in m,n,o... ways then ways of doing them together...

Hi there, My group is working on a final semester project that involves the design of a small fufural (C5H4O2) plant. Pretty much most commercial processes uses distillation after the reaction process and then it is further distilled to purify the fufural which results in a costly process...

Homework Statement so for a side task I'm supposed to assign people to groups for an icebreaker in python, can anyone give me links to theories that I could read up on or give me suggestion X number of people at my company signed up for a dinner roulette as a way to meet new people. Everyone...

Ψ (x,0)= ΣcnΨn Ψ is a linear combination of all Ψn and Ψn are the bases. What does this statement actually mean..?? I mean, does it says that Ψ(x,0) contains c1 part of Ψ1 and c2 part of Ψ2 and so on...like we represent a vector : R= 3x+4y+7z...??

Homework Statement From 5 consonants and 4 vowels, how many words can be formed consisting of 3 consonants and 2 vowels The book solved it using combination C(5,3) * C(4,2) * 5! = 7200 i.e I understand the 1st two term give the unique 5 words that can be formed with 5 consonants and 4 vowels...

Homework Statement A bag contains 4 black and 5 white balls from which 6 balls are drawn. Determine the number of ways in which at least 3 black balls can be drawn. The book has solved it as combination. Homework EquationsThe Attempt at a Solution When we are drawing say black ball, isn't it...

good evening to all if two ideal cells with emf 6 volt and 3 volt are connected in parellel to supply current how the net emf can be decided

Homework Statement The combination of n different object, taken r at a time(repeatation allowed) is given by Cnr = (n-1+r)! / [(n-1)! r!]Homework EquationsThe Attempt at a Solution The above formula is deducted, as it is same as no. of ways of placing n-1 bar in n-1+r places, which is same as...

!subprogram for combination !Author:: mannaf function fact(n) implicit none integer ::fact,n,i fact=1 do i=1,n fact=fact*i end do return end program comb implicit none integer ::fact,n,r,combination print*,'enter the value of nCr' read*,n,r...

Homework Statement a convex lens forms a real image of a point object at a distance of 50 cm from convex lens. a concave lens is placed 10 cm behind convex lens on image side. on placing a plane mirror on the image side and facing the concave lens it is observed that final image now coincides...

Homework Statement \dbinom{7}{r} = 21 Homework Equations \dbinom{n}{r} = \frac{n!}{(n-r)!r!} The Attempt at a Solution \dbinom{7}{r} = 21 \frac{7!}{(7-r)!r!} = 21 7! = 21(7-r)!r! 240 = (7-r)!r! So I get here and the convention is to guess in check (to my knowledge). I...

Homework Statement Homework Equations The Attempt at a Solution a) I am not sure exactly what they are looking for, but I said that the operators associate, distribute, and do not necessarily commute. b) I know by definition ##\langle a' \mid a \rangle = \int a'^{*}a dx = \delta_{a'a}##...

Hi, I've seen on on several sites that you can prove that nCr, where r<=n, is a natural number. I'm not sure how to do this by induction. So I need help on this proof. How do I write this as a mathematical statement at the start of the induction proof? Thank you

Hello, Respected teachers. Why wheel+axle combination is used? Why can we not only use the wheel? I'm confused about this, please explain it to me the reason. And one more question; please give me an example of daily life in which we apply force on axle to turn the wheel. Many many thanks.

When the learning combination formula the formula nCr is usually derived using a deck of cards. There are n=52 different card. If you choose r number of cards, each is different so you basically start with n!/(n-r)! , then because the order is unimportant multiply by 1/r!. This explanation is...

I was reading my book and it states that the lack of anti-symmetry in the total wave function of the Δ++ particle led to the introduction of the missing degree of freedom, or color. It states that free particles are colorless so they must be in color singlet states. From there, it just lists the...

Homework Statement All the batteries shown are 1 V. What voltage is supplied by the batteries in this circuit? What is the current through the branch of the circuit containing the 20 Ω resistor? What is the current through the branch of the circuit containing the 30 Ω resistor? What is the...

Homework Statement I will denote operators by capital letters. The question is calculate <p | XXPP | x> / <p | x > Homework Equations X |x> = x |x> P |p> = p |p> P |x> = -i(hbar)d/dx X |p> = i(hbar)d/dp The Attempt at a Solution If I start on the RHS and take PP out I get...

I've been trying to solve this question all day. If somebody could point me in the right direction I would really appreciate it! (ii) A particle’s motion is described by the following position vector r(t) = 4txˆ + (10t − t)ˆy Determine the polar coordinate unit vectors ˆr and ˆθ for r. [4]...

Homework Statement 1007n+1703m=1 when n and m are integers Homework EquationsThe Attempt at a Solution i hv tried for so many times, but i can't find it the GCD of 1007 and 1703 is 1, so it is possible to find n and m