Composition Definition and 374 Threads

Hello, Given (in spherical coordinates) the resulting 4-vector K of the composition of 2 Lorentz pure rotations R1 and R2, where only R1 is known, I would like to find the angle of the "overall" rotation resulting from this composition. In other words, I want to find the symbolic expression...

Theorem 2.15: Let A be an m x n matrix with entries from F. Then the left-multiplication transformation L_A: F^n --> F^m. Furthermore, if B is any other m x n matrix ( with entries from F ) and B and D are the standard ordered bases for F^n and F^m, respectively, then we have the following...

Homework Statement I've been looking at how integrable functions behave under composition, and I know that if f and g are integrable, f(g(x)) is not necessarily integrable, but it -is- necessarily integrable if f is continuous, regardless of whether g is. So I was wondering, what about if g is...

Theorem 2.12: Let A be an mxn matrix, B and C be nxp matrices, and D and E b qxm matrices. Then (d.) If V is an n-dimensional vector space with an ordered basis B, then [IV]B = In. My question: What does [IV]B mean? Is this the identity matrix with respect to the vector space V which is...

I am reading (theorem 2.14) from a textbook, and don't understand how g = Tf and (#1) line of reasoning. The theorem and proof is as follows: Theorem 2.14: Let V and W be finite-dimensional vector spaces having ordered bases B and C, respectively, and let T: V-->W be linear. Then, for...

Hi, Homework Statement Given: f(x)=x^2+2 and g (x)=\sqrt{x} Find: f \circ g and g \circ f 2. The attempt at a solution f \circ g =f(g(x))=x+2 , where x\in (-\infty ; +\infty) g \circ f =g(f(x))=\sqrt{x^2+2} where x\in (-\infty ;+ \infty) I haven't done this for a...

Homework Statement Let a=fx+g and b=hx+i. For which real numbers f,g,h,i a∘ b = b∘ a Homework Equations The Attempt at a Solution a∘ b(x)=(a(b(x))= h(fx+g)+i= fhx+gh+i b∘ a(x)=(b(a(x))= f(hx+i)+g= fhx+fi+g I'm kind of stuck here as I don't think I know what the question is...

A metal alloy consists of magnesium and aluminum.When a 1.00g sample of the alloy is reacted with excess HCl, 0.0989g of hydrogen gas forms. Calculate the percent composition of the alloy. Ok I got the following balanced equations : Mg + 2HCl -> MgCl2 + H2 2Al + 6Hcl -> 2AlCl3 + 3H2...

This might be a silly question: given a function g is it possible to find a function f such that f = f \circ g?

Hi, given two functions f and g, is there any known condition under which the following is valid: (f \circ g^{-1}) = (f^{-1} \circ g) Basically I have to find out the requirements for f and g for which composition is commutative in respect to inversion.

Homework Statement A rigid cylinder of 1000cm cubed contains 4.168grams of an ideal gas mixture. The gas mixture consists of methane and ethane at a temperature of 100C and a pressure of 500kPa a) Estimate the average molar mass of the mixure b) Calculate the composition of the mixture on a...

Homework Statement Here's the question form the text. (I have the answer, but don't know how to do part c. "A solution contains 50.0g of heptane (C7H16) and 50.0g of octane (C8H18) at 25 C. the vapor pressures of pure heptane and pure octane at 25 C are 45.8 torr and 10.9 torr...

Homework Statement Consider the map F: C0([a,b],Rn) --> R, F(\phi)=\int\phi(t)\phi(t)dt (This is the integral from a to b). Write F as a composition of three maps, each of which is linear or bilinear. Then use the chain rule and generalized product rule to compute DF(\phi). Homework...

Homework Statement Calculate and tabulate the fractions of the total mass of the Earth which would be accounted for by O, Na, Mg, Al, Si, S, Ca and Fe under the following hypothese. i) All the elements above are fully oxidized, except that no S is accreted and the Fe is entirely metallic...

Homework Statement A 5.00g sample of natural gas, containing methane, CH4, and ethylene, C2H4, was burned in excess oxygen, yielding 14.5g CO2 and some H2O as products. What percent of the sample was ethylene? Homework Equations Moles and percent composition The Attempt at a...

Homework Statement F o G(x) F(x)=1/x+1 g(x)=2x-x/x+3 Simplify Homework Equations F o G=f(g(x)) The Attempt at a Solution Here is the order of things I did. F(2x-1/x+3) to 1/(2x-1/x+3)+1 Ok, this sounds stupid but, I can solve these, but when I get stuff like this that has...

Homework Statement a.) F = {(1, a), (2, b), (3, a), (4, c)} G = {(b, 1), (a, 2), (c, 3)} i. Find F o G ii. Find G o F b.) A function F: N x N --> N is represented 2(m + n) + 1 for F(m, n) i. Is F one-to-one? ii. Is F onto? c.) Prove by Mathematical Induction...

Homework Statement Describe the composition and temperature of the equilibrium mixture after 1.0 kg of ice at -40*C is added to 1.0 kg of water at 5.0*C.Homework Equations \begin{gathered} Q = mc\Delta T \hfill \\ Q = mL \hfill \\ \end{gathered} Book answer:1.2kg ice, 0.80 kg water...

Homework Statement Find the function g(x), if there are h=g \circ f f(x)=x+1, x \in \mathbb{R} and h(x)=x^3+3x+1 Homework Equations (g \circ f)(x)=g(f(x))=h(x) f \circ g \neq g \circ f The Attempt at a Solution h=g \circ f h(x)=g(f(x)) x^3+3x+1=g(x+1) Is there any...

Whats the chemical composition of oak wood? I want to know because I am trying to cut wood by changing the chemical compound of the places that i want to cut it at by putting a chemical that would bond to the wood, and the new compund of my chemical and wood would be a gas. I don't know if...

what is the composition of black hole? is it a matter or antimatter or energy?

Homework Statement Initially a mixture contains 0.723 mol each of N2 and O2 in an 7.20 L vessel. Find the composition of the mixture when equilibrium is reached at 3900°C. For the reaction below, the Kc = 0.0123 at 3900°C. N2(g) + O2(g) 2 NO(g) Homework Equations I.C.E Tables (not...

how do i take the derivative of sqr(4 + sqr(3x))? My teacher wants me to do it as a chain rule composition function so i separated it into F(x)= (4+x)^1/2 and G(x)= (3x)^1/2 but i don't know where to go from here because i don't know how to take the derivative of f(x)

1. For a problem I require the atomic density of uranium atoms per cm^3 in a solution of water. The atomic fraction of natural uranium to water is 1 per 100 and the net density of the solution is 1 g/cm^3. (Natural uranium is assumed to be U-235 at 0.72% of uranium atoms and the rest is U-238)...

In Micheal C. Gemignani, "Elementary Topology" in section 1.1 there is the following exercise 2) i) If f:S \rightarrow T and G: T \rightarrow W , then (g \circ f)^{-1}(A) = f^{-1}(g^{-1}(A)) for any A \subset W . I think the above is only true if A is in the image of g yet the book says...

Homework Statement If you invest x dollars at 4% interest compounded annually, then the amount A(x) = 1.04x. Find A o A, A o A o A, and A o A o A o A. What do these compositions represent? Find a formula for the composition of n copies of A. Homework Equations f o g = f(g(x)) The...

Homework Statement Prove that if f: G \to H and g: H \to K are homomorphisms, then so is g \circ f: G \to K. 2. The attempt at a solution Since f is a homomorphism (G, * ) and (H, \circ) are groups and f(a*b)= f(a) \circ f(b), \forall a,b \in G. Likewise, (K, +) is a group and g(f(a)...

What is ...Dust? I know this is quite ackward and may not be the right place to ask such a question but I am a bit curious to know something good about it: Earth is composed of soil; Soil is a mixture of elements and compounds; But we don't use the soil around us to extract those compounds...

In regards to two types of engines.. What gases (by percentage) are to be found in conventional petrol driven internal combustion engines, such as found in cars ? What gases (by percentage) are to be found in conventioanl diesel driven internal combustion engines, such as found in trucks ...

[SOLVED] pH question... i'm writing a research paper on the organic medicinal massage oils. i need to know the chemical composition of citric acid and it's pH. can anyone help me?

when you have .283 moles of water and .503 moles of copper sulfate, how do you find the mole ratio between the water and coopper sulfate?

I need to determine the quark composition of the neutral antikaon. Below is a copy of my multiple choice question. http://img166.imageshack.us/img166/2025/quarksec1.jpg Here is my attempt at a solution: First, a neutral antikaon is a meson. This means it must be composed of a...

Homework Statement The superposition of two waves, [see attachment - it doesn't let me link the attachment because I'm new ;P] at the location x = 0 in space results in what kind of wave behavior? [As in, how often does it beat and what frequency is the sound?] Homework Equations Wave...

I understand that most scientists believe that the Earth's core is composed of iron, nickel and perhaps some other elements such as sulfur and oxygen. I also understand that they believe that the Earth's core formed during a time when the Earth was molten and that the core was formed by heavier...

Homework Statement Prove or give a counterexample: the product of any two self-adjoint operators on a finite-dimensional inner-product space is self-adjoint.Homework Equations The only two equations I've used so far are: \left\langle T v, w\right\rangle = \left\langle v, T^{*}w\right\rangle and...

Homework Statement The densities (at 25*C) of tin and lead are 7.3 g/cm3 and 11.3 g/cm3 respectively. Plumber's solder is an alloy of tin and lead and has a density of 9.7 g/cm3. Estimate the composition by mass, of the two metals in this solder. Homework Equations The Attempt...

I'm currently doing a little research in PCM for asbestos ID. My background is in chemistry and I've had to wade through a good deal of mineral classification terminology. My question is this; If cummingtonite and anthophyllite - two of the six recognized species of commercial asbestos fiber -...

% Composition and Finding Formula - Chemistry 50.0g of Sulphur is mixed with 100.0g of iron and heated strongly. When the reaction is complete 12.5g of iron remains. What is the formula of the sulphide formed? What i have done so far is i got the 2 mols of each element. Fe=1.79 S=1.56...

% Composition & Finding Formula - Chemistry 50.0g of Sulphur is mixed with 100.0g of iron and heated strongly. When the reaction is complete 12.5g of iron remains. What is the formula of sulphide formed? duno where to start

Two forces of 200N are acting at a common point. The first force acts due East and the second force is acting 40 degrees North of East. Find the magnitude of the resultant force by cosine law and the direction using sine law.

Homework Statement From the relativistic law of composition of velocities one deduces that if a particle has velocity ui in O, then in a system O' moving at -vi relative to O, its velocity will be u'i where: u'=(u+v)/(1+(uv/c^2)) Show, mathematically, that if 0<u<c and 0<v<c, then...

A 1.00-g solid sample containing a mixture of table salt (NaCl) and citric acid (H3C6H5O7, a triprotic acid) is dissolved in 15 mL of water. Titration of the acid solution requires 40.00 mL of 0.2003 M NaOH solution to reach the endpoint. Calculate the mass percent H3C6H5O7 in the solid...

Homework Statement Well its not really a problem, I'm just trying to see it there's a different method to solve the problem. My textbooks gives a CAS problem: Find f(f(f(f(f(f(x)))))) if f(x)= x^2+xHomework Equations None (or atleast that I know of)The Attempt at a Solution Since it's a...

When the Sun burns out entirely and reaches the ambient temperature of outer space, what will be its radius, mass, and composition? What would we call such a thing?

I was wondering what the chemical composition of the slime from the slippery elm tree (Ulmus rubra) is.

How is it possible to have a pion that is made up of a linear combination of quarks? I mean, what are the physical constituents of the neutral pion? is it uubar or ddbar? Or does the linear combination mean that there is a 50 50 chance of a neutral pion being a made of uubar and ddbar?

Homework Statement Aut(R) denotes the set of ring automorphisms of a ring R Show formally that Aut(R) is a group under composition. Homework Equations The Attempt at a Solution I Have a very similar question to which I have the solution viz Aut(G) denotes the set of group...

Good evening guys, i have two stupid questions that I'm stuck on and i would be grateful if anyone could help Question 1: f(x)= x+1 g(x)=x^2 the domain in each case is the interval [-1,1] and belongs to the set of real numbers then find the range of: (fog)(x) My Answer...

Suppose that f: D-->R and g: R-->Y are two continuous transfromations, where D, R, and Y are subsets of the plane. Show that the composition g o f is a continuous transformation.

[SIZE="6"] just started my precalculus class and i can not understand what's going on and its makes me mad too. In our book we are on 1-2 Composition and Inverses of Functions like for this one problem: Find [f of g] (x) and [g of f] (x). 1. f(x)= 1/2x-7 g(x)= x=6 and this problem...