Combination Definition and 525 Threads

Hello, I'm trying to get my head around linear transformations, and there are a few things I'm not grasping too well. I'm trying to understand combinations of linear transformations, but I can't find a lot of clear information on them. As far as I can tell, any two linear transformations of the...

Homework Statement Is N/m^2 a si unit I know Newton is and meters but togeather are there or is m^2 Homework Equations The Attempt at a Solution N/m^2 m^2

Homework Statement "Let ##X,Y## be independent r.v.'s (EDITED) normally distributed with ##\mu=0,\sigma^2=1##. Find the distribution of ##W=2X-Y##. Homework Equations "If ##X,Y## are independent, then if ##Z=X+Y##, ##f_{Z}=\int_{\mathbb{R}} f_X(x)f_Y(z-x)\, dx##. The Attempt at a Solution...

Could somebody help me out with this combination circuit? The answer that I get is 62K but that is not one of the answers. At first, I thought the 10kohm and 20kohm wherein series and the other side as well. Then I thought they are all in parallel because of the different current flow they all...

Homework Statement A flat cushion of mass m is released from rest at the corner of the roof of a building, at height h. A wind blowing along the side of the building exerts a constant horizontal force of magnitude F on the cushion as it drops as shown in the figure below. The air exerts no...

Homework Statement Between the plates of parallel plate condenser having charge Q,a plate of thickness t1 and dielectric constant k1 is placed.In the rest of the space,there is another plate of thickness t2 and dielectric constant K2.The potential difference across the condenser will be...

Hello, We defined a k-form on a smooth manifold M as a transfromation Where the right space is the one of the alternating k-linear forms over the tangent space in p. If we suppose we know, that we get a basis of this space by using the wedge-product and a basis of the dual space, then we might...

I'm making a ventilation system with a fan that will blow air through a 1700mm long pipe that has a 45 degree bent in the middle. I should decide on a pipe diameter of 125mm or 160mm. Also I need to choose between 3 different fans that has the following specs from the manufacturer: 120mm fan...

I'm trying to simplify the combination defined as : \binom{n}{\frac{n}{2}}. I did some calculations, starting from the factorial formula \frac{n!}{(\frac{n}{2})!(\frac{n}{2})!} and i found this form : 2^{n}(1-\frac{1}{n})(1-\frac{1}{n-2})(1-\frac{1}{n-4})... but i don't know how to continue...

Homework Statement One 18 watt lamp and two 60-watt light bulb are plugged into a 120V circuit. For either DC or AC, the two bulbs are connected each other in parallel and in series with the lamp in the same circuit. Calculate; i. the current flow through each light ii. the total...

I have before me that ##\cos 2x + \sin 2x = \sqrt{2} \cos (2x - \pi / 4)##. Where does this expression on the right come from? I tried to look on the internet but I couldn't really articulate it well enough to find anything on it.

Homework Statement Let ##X_1 \sim N(3,2^2)## and ##X_2 \sim N(-8,5^2)## be independent. Let ##U=aX_1+bX_2##. What is the distribution of ##U## Homework EquationsThe Attempt at a Solution As they are independent, we can write the distribution of ##U## as the convolution of the 2. So I get...

How do I accomplish this? The goal is to redraw the diagram of the ciruit shown below, until it becomes series in the end. Given: Here’s what I did: Diagram 1 2 3 4* 5 *I apologize for flipped images. iPhone camera is tricky. Is this correct? If not, why?

Homework Statement In how many different ways can you seat 11 men and 8 women in a row if no two women are to sit together? Homework Equations I have the combination and permutation equations The Attempt at a Solution I assume that given the context of this question if I have two, three...

Homework Statement Question: A cheese shop carries a large stock of 34 kinds of cheese. By the end of the day 48 cheese sales have been made and the items sold must be restocked. How many different restocking orders are possible? Homework Equations Combination and permutation equations The...

If I need 50,000 Nm of torque to rotate a wheel, and I am rotating it about its rim (like the London eye), would 5 10,000 Nm motors each connected to a set of tyres to rotate it (the motors are not connected to each other), or would these motors first need to be connected to each other and then...

Homework Statement Given random vector ##X'=[X_1,X_2,X_3,X_4]## with mean vector ##\mu '_X=[4,3,2,1]## and covariance matrix $$\Sigma_X=\begin{bmatrix} 3&0&2&2\\ 0&1&1&0\\ 2&1&9&-2\\ 2&0&-2&4 \end{bmatrix}.$$ Partition ##X## as $$X=\begin{bmatrix} X_1\\X_2\\\hline X_3\\X_4\end{bmatrix}...

Hello, I have been trying to solve this problem but I can't seem to find a way. Given are ##n## cards and each card can show one of two values: M or K. How many possible permutations are there in which there are as many cards with M as there are with K? Given that ##n## is an even amount of...

Homework Statement Say I have four categories which make up a "whole" that I'll call a unique "deal". Each deal can have "I" properties, "J" investors, "K" mortgages, and "L" credit lines, where "I" and "J" must be integers greater than zero and "K" and "L" are non-negative integers (i.e. 0 or...

Homework Statement I don't see why this is a combination problem, because to me dealing with bit strings means that order matters. How many bit strings contain exactly eight 0s and 10 1s if every 0 must be immediately followed by a 1? Homework EquationsThe Attempt at a Solution Since every 1...

The total number of different combinations of one or more letters which can be made from the letters of the word MISSISSIPPI is? First i don't understand what the question means and second my answer is completely different from that in my book My working- since there are 11 letter 4 I 4 S 2 P...

Is there any phenomenon (in physics: no wisecracks about human interactions ) in which A is attracted from further out to B until it gets close to B, whereupon A is repelled from B? (Sort of the opposite to the switch between the electromagnetic repulsion being overpowered by the strong force in...

Hello, I'm currently studying physics at the CSEC level in the caribbean, or what would be equivalent to the GCSE level in England I believe, and I've arrived at Logic Gates. I've gone through the various gates they ask for at this level such as: AND, OR, NAND, NOT and NOR gates. I believe I...

Hi, I read that linear combinations of a state, Psi, can be as: \begin{equation} \Psi = \alpha \psi + \beta \psi \end{equation} where ##\alpha## and ##\beta## are arbitrary constants. Can however this be a valid linear combination?\begin{equation} \Psi = \alpha \psi \times \beta \psi...

Suppose there are numbers 1, 2, 3, 4, 5, 6, 7, 8. Question is: How many ways can we pick 4 non adjacent numbers (order does not matter)? Now, as per formula it is C(n-r+1,r) = C(8-4+1,4) = C(5,4)=5. Crosschecking, I could find only four: 1,3,5,7 : 1,3,5,8 : 1,4,6,8 : 2,4,6,8 Not...

Hi, All! Prepping for the GRE here and definitely notice a weakness in calculating potential combination questions. Any advice on how to solve the following type of problem quickly? "An automotive manufacturer installed part A into 82 cars, part B into 73 cars, and part C into 25 cars. At...

Let us say there are two springs each of mass m and each having a spring constant k. If the two springs are connected in parallel to a mass M and are made to oscillate, what will be the time period of oscillations??

Homework Statement There are 22 students in a class. The professor will divide the class into 4 groups. Group 1 and 2 have 5 members each whilst Group 3 and 4 have 6. Given that the teacher forms the group at random, find the probabilities of : A = event where Paula, Trina, Gia all belong in...

Homework Statement Homework Equations ▪1/f=[(n2/n1)-1][1/R1 -1/R2] ▪1/f(eq)=1/f1 +1/f2 For combination of 2 lens ▪1/f(eq)=1/f(mirror) -2/f(lens) for combination of lens and mirror ▪1/v+1/u=1/f Mirror formula The Attempt at a Solution I just applied the above equations 1.Finding the individual...

In Bloch: The Real Numbers and Real Analysis we find, in the discussion on the construction of the rational numbers, a symbol for an equivalence relation that looks like a combination of a \smile and a \frown ... the symbol appears in Definition 1.5.1 and Lemma 1.5.2 below ... Can anyone tell me...

Hi I need some help with my electric system of my camping trailer. I have a 220V camping fridge freezer. On start-up it draws about 7A. I have a 1000W inverter connected to 2 x 105Ah 12V batteries connected in parallel. Connected to the batteries I have a 20A PWM solar charger / controller with...

Homework Statement Homework EquationsThe Attempt at a Solution the answer for no adjoining _W_W_W_W_W_ for 3 red balls, there are 6 positions so ## 6C_3 = 20## i'm curious, on other way to find arrangement? for adjoining = all arrangement - adjoining all arrangement = 3 red can get to any...

Homework Statement Hi everybody! In my quantum mechanics introductory course we were given an exercise about the 3D quantum harmonic oscillator. We are supposed to write the state ##l=2##, ##m=2## with energy ##E=\frac{7}{2}\hbar \omega## as a linear combination of Cartesian states...

Homework Statement Find the total resistance of the circuit Homework Equations Parallel resistance: 1/Rtotal = 1/R1 + 1/R2 + 1/R3 + ..., Series resistance: R1 + R2 + R3... The Attempt at a Solution The 1470 ohm resistor is parallel to the 50 ohm resistor and the 1000 ohm resistor, but there is...

discuss whether combination and permutation in math are useless in physics the undergraduate math courses related to physics always contain algebra,complex number and calculus. however we don't need to study discrete math /combination and permutation in those courses that means those stuffs...

Hints on here at a starting strategy?

Helo, I am in an electronic course and we just started studying diodes. I am stuck on the following problem: Place a 100 ohm resistance in series with a diode, and plot current versus voltage across the series combination. I am also given the following values for the diode: n = 1, Is =...

I'm getting these concepts confused. If I have an object called $x$, and I have five places or slots to put the object, how many ways could 2 $x$s be places in the 5 spaces? Example: x x _ _ _ x _ x _ _ x _ _ x _ x _ _ _ x _ x x _ _ _ x _ x _ _ x _ _ x _ _ x x _ _ _ x _ x _ _ _ x x So in...

Why is the Potential Difference equal in parallel combination of resistances ?

So here is the question: On a phone keypad, many of the numbers have letters associated with them. For instance, the letters A, B, and C are associated with the number 2. Write a program that accepts a number as input and prints all of the possible letter combinations associated with that...

From my understanding of semiconductors, we are able to create semiconductors by combining different group of elements that fulfill the octet rule to produce covalent bonds and where their electronegativities provide a energy band gap that is between that of a conductor and insulator. Why is the...

First of all I will use L to denote lambda the parameter of the distribution. X~Poission(nL), n$\in\Bbb{N}$, Y~Poisson(mL),m$\in\Bbb{N}$ with m$\ne$n S= aX+bY a,b real constants. Given observations x and y find the maximum likelihood estimator of L. The problem is I don't know what the pmf...

Hi everyone, this is something i know because i saw it many times, but i have never fully understand it. Suppose i have a quark field (singlet under SU(2) let's say) ##q## and i would like to build an invariant term to write in the Lagrangian. The obvious choice is to write a mass-term...

Homework Statement [/B] If the 2 charged capacitors are reconnected in parallel with plates of opposite polarity together then ? is common potential. In this condition how charge is conserved and same potential is maintainedHomework Equations [/B] Net charge Q=C1V1-C2V2 Where C1V1=q1 and...

Hey! :o We have the vectors $\overrightarrow{a_1}=\begin{pmatrix}1 \\ 2 \\ 3\end{pmatrix}, \overrightarrow{a_2}=\begin{pmatrix}-1 \\0 \\ 2\end{pmatrix}, \overrightarrow{a_3}=\begin{pmatrix}7 \\ 8 \\ 6\end{pmatrix}$. I have shown that these vectors are linearly dependent: $\begin{bmatrix}...

Homework Statement Construct a truth table for the combination of logic gates shown above. 2. The attempt at a solution First of all the combination of logic gates with added letters to the combination: The truth table: I think it should be correct. But just want to be sure.

A group consists of 5 boys and 8 girls. In how many ways can a team of four boys be chosen, if the team contains. no more than one boy So my attempt was this. I thought to myself well if I fix one girl and calculate the number on combination 5 boys can be chosen for 3 spaces which is 10, I...

Hey all, Is it correct to say that magnetic moment of particles with spin is because of the spin itself, and has nothing to do with any moving charge? The exception here would be the photon of course, but I'm not sure whether "photon spin" is the same kind of angular momentum as the spin of...

Homework Statement Find $$\sum_{k=1}^{64} {64 \choose k} 64k$$ Homework Equations Not sure The Attempt at a Solution Please give me hint how to start doing this question

Homework Statement Referencing the attached picture: a) Show that the RMS current in the 1 kΩ resistor is 6.5mA. b) If the AC voltage source was replaced by a battery, what would the current in the resistor be? Homework Equations V = IR Z = √(R^2 + X^2) The Attempt at a Solution To begin, I...