Composition Definition and 374 Threads

1. Homework Statement 9 V battery is connected to wire made up of three segments of different materials connected in a series: 10 cm copper, then 12 cm iron, then 18 cm tungsten. All wires are 0.26 mm diameter. Find potential difference across each wire. Constants: p Copper= 1.7 x...

Homework Statement For two endomorphisms ψ and φ on a vector space V over a field K, show that ψφ and φψ have the same eigenvalues. "Hint: consider the cases λ=0 and λ≠0 separately." The Attempt at a Solution I know that similar endomorphisms (φ and ψφ(ψ^-1)) have the same...

Hi, Two questions: 1) Compute the matrix product corresponding to the composition of the transformations. Let U = P4(R) [polynomial degree 4], V = P3(R) , and W = P2, and let S = d/dx (derivative) and T = d/dx (derivative). Then the composition TS = d^2/dx^2 (second deriv) Attempt...

Hi Does the color of a hot body depend on its material composition ? For eg. will bodies made of steel, Stainless steel, Ti, Cu etc. all look red in color if the temperature is ~ 550 deg C ? TIA

Homework Statement We have f(f(x))=4x-15 , what is f(2)? Homework Equations Don't know. The Attempt at a Solution Don't know how to start actually!

Homework Statement Derive an expression for the composition of 2 functions. Homework Equations The Attempt at a Solution I started with supposing that y(x) = f(g(x)). I know that dy/dx = df/dg * dg/dx (via the chain rule). Doing the derivative again, I started with the product...

Is it possible? With general knowledge about how the Earth must have started what can we know about the composition of different areas around the earth? How accurate is this information? Is there... like a density map I can look at?

Homework Statement hi guys, i have problem regarding this matters. Products : hydrocarbon if i have this : CO2 - 80% CO - 0.9% O[SIZE="2"]2 - 8.8% N[SIZE="2"]2 - 82.3% 1) how to determine the composition of the fuel? 2) the air fuel ratio? known , the air fuel ratio is...

What exactly is gauss composition? I've heard of Manjul Bhargava's work, which apparently generalized gauss composition, but what is gauss composition? I would like to add that I've been thinking about quadratics polynomials with rational coefficients, and I discovered this composition law that...

People have found ways to extend the definition of some operations that are ostensibly discrete (such as differentiation - e.g. 1st, 2nd, 3rd derivatives) to operations that are defined for fractions ( e.g. fractional derivatives). Is there an interesting way to extend the operation of...

aite, here goes f(f(x)=f(x), find all functions that satisfy this on [0,1], i know f(x)=x and f(x)=c satisfy this equation, but I am looking for something more outlandish, feel free to make it discontinuous, define it separately over the rationals and irrationals, or any sort of crazy function...

Hi guys, I'm facing a problem. I've read a paper where they tried to synthesise a crystal and they give the following reaction mixture molar composition: 3.0 SiO2 1.0 Al2O3 0.1 NaCl 276 H2O What does it means? It can't be the molar fraction since the sum of all the fraction must give 1 as...

Homework Statement Hi, I am having problems in showing that in practise the composition of two rotations represented by quaternions is still a rotation. The example I have constructed is: Rotate (1,1,0) by 45 degrees about the z axis. The quaternion to use is thus q = cos(22.5)+ksin(22.5)...

Hello. I would like to turn an equation (function) like 4x2+2 into an operator, L, acting on x. Lx. I want to get into operator algebra so that I can manipulate equations like √(4x2+2) using operators (e.g. the last equation could be RLx). I'm finding difficulties:- 1. Many common...

Homework Statement Find two linear operators T and U on R^2 such that TU = 0 but UT ≠ 0. The Attempt at a Solution Let T(x1,x2)=(0,x2) Let U(x1,x2)=(x2,0) TU(x1,x2)=T(x2,0)=(0,0) Am I right? 'Cause I can't remember if TU(x1,x2)=T[U(x1,x2)] Or TU(x1,x2)=U[T(x1,x2)]

hi, i have been reading this book about antimatter, "Antimatter" by Frank Close, and have a question. CAN ATOMS BE COMPRISED OF DIFFERENT FERMIONS OTHER THAN PROTONS, NEUTRONS, AND ELECTRONS? could they be comprised of those fermions if they have the same charges as protons, neutrons, and...

Hi all, I have some integrals involving Heaviside theta functions of non-trivial arguments, in particular \theta(1-x^2) and \theta(x^2-1). As x is a radial coordinate it's easy enough for me to break these up by hand, but it's cumbersome for me to implement in Mathematica and I can't work out...

Homework Statement "A mixture of calcium carbonate and magnesium carbonate with a mass of 10.000g was heated to constant mass, with the final mass being 5.096g. Calculate the percentage composition of the mixture, by mass." Homework Equations Decomposition equations. The Attempt at a Solution...

Hi. I am trying to express the following in finite differences: [ tex ] \frac{d}{x}\left[ A(x)\frac{d\, u(x)}{x} \right] [ /tex ] If I take centered differences I get: [ tex ] \left{ \frac{d}{x}\left[ A(x)\frac{d\, u(x)}{x} \right] \right}_i = \frac{[A(x)\frac{d\, u(x)}{x}]_{i+1/2} -...

Homework Statement Suppose that T : R2 → R2 is linear and has matrix -2 1 5 2 with respect to the standard basis S of R2. B = 1 1 5 6 (B is another poorly constructed matrix) What is the matrix of T with...

what is eutectoid composition for an iron-carbon alloy? what would happen to the iron-carbon alloy while cooled from the alpha phase to room temperature at this composition?

Most of what I've learned about Special Relativity is self taught using Google and Wikipedia because I'm still in high school, so forgive me if I'm saying something wrong. Does anyone have the exact equation for the composition of two boosts, without the rotation that's induced by combining two...

Hello, I have one short question. Can I somehow get the information of the composition of the material (percantage of certain metals inside) if I have these data about it: carbon steel API 5L Grade B Schedule 40? I would appreciate your help veeery much! Regards Amy

I'm studying the S_n groups and I've been calculating a bunch of compositions of m-cycles. I haven't, however, been able to find a general pattern in how to do this for arbitrarily complicated cycles. Are there any general composition rules or is there no other way to find the compositions...

Homework Statement Let G be a finite cyclic group and \ell(G) be the composition length of G (that is, the length of a maximal composition series for G). Compute \ell(G) in terms of |G|. Extend this to all finite solvable groups. The Attempt at a Solution Decompose |G| into its prime...

I have hard time understanding composition of functions in several variables. Suppose f(x,y)=(xcosy,\frac {x-y}{y-x}), how should I write f(f(x,y))?

Hello everyone. I'm not a physicist however have been doing some research on the concepts behind dark energy and string theory and it has presented me with a question: Is it possible that dark matter could be the components of quarks that haven't pulled together to form the quarks. We can't...

in general I'm trying to figure out a way to work with taylor series more efficiently. this means i want to be able to write down the taylor series of a complicated function just by knowing the taylor series(es?) of the component functions. I've figured out how to do products and quotients...

Homework Statement Let T: U-->V be a linear map between vector spaces U and V and let E be basis for U and F be a basis for V. Explain what is meant by the matrix m(T)^{F}_{E} of T taken with respect to E on the left and F on the right. Homework Equations The Attempt at a Solution...

Homework Statement a) Let g: A => B, and f: B => C. Prove that f is one-to-one if f o g is one-to-one. b) Let g: A => B, and f: B => C. Prove that f is onto if f o g is onto. Homework Equations a) Since f o g is onto, then (f o g)(a) = (f o g)(b) => a = b. b) Since f o g is onto, every element...

Homework Statement In general, let f: A -> T and g: B -> C. Find a condition on the domain of g (other than B = T) that results in a meaningful definition of the composite function g((f(x)): A -> C. Homework Equations None. The Attempt at a Solution I could not find a...

Homework Statement If f is some function defined at points "s" and "t," is there any way to simplify the following expression? f((f(t)-f(s)) Homework Equations None that I know of. The Attempt at a Solution I've been tinkering with this for a while and so far, I've determined...

How can one determine the color of another planet's sky from its atmosphere composition and parent star color? Earth's atmosphere is blue for most of the day, then turns red at sunset. Mars is sort of the opposite: it has a red sky which turns to a bluish hue at sunset. Until someone tells me...

Why is the eta particle written as 1/sqrt(6) *(uu(bar) + dd(bar) -2ss(bar))? Thanks

Hello everyone, A 20 year old insulin dependent diabetic female was admitted to casuality in a semiconscious state. Her plasma values are as follows. a) on admission, b)eight hour after therapy with insulin,saline etc. Na+ a) 127, b)134, normal- 132-144 mmol/l...

Homework Statement Fe3(Co)x, Fe is 33.26% by mass. Find the value of x. The Attempt at a Solution 167.5425 g / 0.3326 = x ( 58.9326 g) / 0.6628 x = 5.6... but the right answer given was x=12. question...

elllllo :D Homework Statement <q> <Q>A particle is subjected to 2 simple harmonic motions in the same direction having equal amplitudes and equal frequency. If the resultant amplitude is equal to the individual motions,find the phase difference between the individual motions. Homework...

I have two functions: f(x,y,z)=\sqrt{x^{2}+y^{2}+z^{2}} \vec{c}(t)=<cos(t),sin(t),1> I need to find: (f \circ c)'(t) and (f \circ c)'(0) I don't have any answers to work with, but I'm guessing I just stick f into c to get this...

Homework Statement I have a question. If meson K^{0} consists of d\bar{s} then its antiparticle \bar{K}^{0} consists of \bar{d}s ? Homework Equations The Attempt at a Solution

Is composition of functions defined in such a way as to automatically restrict the domain of the outer function, if need be, to the range (image) of the inner one, so that it's always possible to write f^{-1} \circ f\left ( x \right ) = x, providing f is an injective function? Or is composition...

In our Solar System, how does the ratio of gas planets to terrestrial planets compare with that of gas moons to terrestrial moons?

Homework Statement What is the percentage of carbon in dimethylsulfoxide, C2 H6 SO4? Homework Equations mass of C / total mass x 100 = percentage of carbon The Attempt at a Solution The total mass = 126 total mass of C = 24 Wouldn't it be 24 / 126 x 100 = 19 % But...

So when it says that 10% of the body mass consists of Hydrogen, does it mean only 1H(single proton) or it also includes other natural isotopes of hydrogen (deuterium and tritium ) ? I know that 1H is the most common hydrogen isotope with an abundance of more than 99.98%, but I just wanted to...

Homework Statement One kg of steam at 100 degrees Celsius is added to 1 kg of ice at 0 degrees Celsius. What is the composition and temperature of the resulting mixture. The heat of fusion for water is 79.7 kcal/kg, the heat of vaporization is 539 kcal/kg, and specific heats of ice and water...

cabbage chemical composition? Does anyone know what the chemical composition of cabbage is? I've looked all over the internet and can't find ANY information on this.

Let u (not equal to 0) be a vector in R^2 and let T: v --> proju(v) 1. Show that T is a linear transformation. 2. Describe the composition T  T. 3. If ~u = [1,−1], find the standard matrix for T. I'm good with 1 and 3, but I'm not sure what 2 is asking. Excuse the poor notation...

Homework Statement [PLAIN]http://img230.imageshack.us/img230/4203/vectoro.jpg Homework Equations The Attempt at a Solution I know I need to find (f\circ p)'(0) which is 2-dimensional vector and then show it equals \alpha (a,1) where the number \alpha depends on v_1 and v_2 but...

We have three functions: f:A->A, g:A->A and h:A->A with both f and g bijective and h bijective. We know that f ° h = h ° g for every x in A. Is it true that f=g for every x in A? I have tried to solve it and I am pretty sure it is true but I cannot find neither a counterexample nor a...

We have three functions: f:A->A, g:A->A and h:A->A with both f and g bijective and h bijective. We know that f ° h = h ° g for every x in A. Is it true that f=g for every x in A? I have tried to solve it and I am pretty sure it is true but I can find neither a counterexample nor a...

I understand that the sun is made of 91% hydrogen, 8.7% Helium, and 0.3% other stuff. I looked up the atomic spectrum for helium and hydrogen [within the visible portion] and they leave most of the spectrum blank, albeit few lines of colour here and there, yet the white light that reaches us has...