Composite Definition and 378 Threads

I'm confused, by composite particle we probably mean when we use something to smash it, something new will come up, right? Then what's so different about fundamental particles? For example if we "smash" a electron with a positron, we also get something new--photon. I guess I am making some...

Homework Statement Hey, I've been working through a book and one problem just gets me that I know should be a piece of cake. I don't know if I'm just being an idiot or not seeing something but the problem is to take int e^(ax)cos(bx)dx and int e^(ax)sin(bx)dx simultaneously by multiplying the...

Homework Statement If lim f(x) as x->0 is = 0 then lim \frac{sin(f(x))}{f(x)} as x->0 = 1? dont know how to start proving this . thanks for the replies

Hey Guys, Does anyone have a general idea of the circuit needed to generate a composite video signal?

1. Prove that (h\circ g)\circ f = h\circ (g\circ f) Homework Equations f:A\longmapsto B, g:B\longmapsto C, h:C\longmapsto D The Attempt at a Solution (h\circ g)\circ f =\{(b,d):d=h(c)\}\circ f =\{(b,d):d=h(g(b))\}\circ f I reach there and get stuck to continue...

Im looking for g(f(5)) where f(x) = X^2 - 3x and g(x) = 8 + 2x - x^2 xER and x is greater than or equal to 1 I have first found f(5) (5)^2-3(5) which equals 10 However when i do g(10) 8+2(10)-(10)^2 that gives me a negative number of -72! Which can't be...

Homework Statement give an example of functions f and g, both continuous at x=0, for which the composite f(g(x)) is discontinuous at x=0. Does this contradict the sandwich theorem? Give reasons for your answer. Homework Equations The Attempt at a Solution I understand the...

Homework Statement I need to find functions f and g both continuouis at x = 0 for which the composite f at g is discontinuous at x = 0 Homework Equations The Attempt at a Solution I thnk it is a matter of looking for a composite function that results in 0 being in the...

Hi. I am having a bit of trouble working through all the formulas for calculating the total composite mass of moving particles. If I could just fill in this 'black and white' and very intuitive example then I will be able to use it as a guide to test everything I'm doing. If we have 2...

Homework Statement Every triple of consecutive odd natural numbers, with the first being at least 5, contains at least on composite. Homework Equations N/A The Attempt at a Solution I know from number theory that of every set of consecutive odd integers, one of them is divisible...

Hi, I'm stuck on this problem here about composite function, help is appreciated: Let g : [a,b] -> [c,d] be Riemann integrable on [c,d] and f : [c,d] -> R is Riemann integrable on [c,d]. Prove that f o g is Riemann integrable on [a,b] if either f or g is a step function I was able to solve...

Homework Statement Hopefully simple. Do composite functions have to have the same Codomain? What if they do not, does the smaller Codomain get canceled out? f(x) : R ->R g(x) :Z->Z f(x) g(x) : R->R Is this correct? Or do I need to hit the books a bit more? Homework...

Hi, I need to find the stress taken up by the fibres in the longitudinal direction, when a load of 25kN is applied to a continuous aligned composite with the diameter of 2cm. 60% matirx with E=2.8Gpa and 40% glass fibre E=73Gpa. Attempt at solution Known values V_m = 0.6, E_m =...

Why is the traverse loading strength of continuous fibre reinforced composites weaker compared to the longitudinal strength? I sort of arrived at the conclusion, that since the composite is in an isostress state and due to the fibre having a very low tensile strength in the transverse...

If p >= 5 is prime, prove that p^2 + 2 is composite. So i noticed if we divide any p >= 5 by 6 we only get remainders of 1 or 5. 6 | 5 , r = 5 6 | 7 , r = 1 6 | 11, r = 5 6 | 13, r = 1 6 | 17, r = 5 and so on so for my proof i am saying for p >= 5, p = 6k + 1 or 6k = 5 so for the first ...

is (2^{58}+1)/5 a prime number or a composite number trust me this one has got an interesting solution

Is it true that the domain of a composite function say gf(x) is the intersection of domain of f(x) and the domain of gf(x) ? If so, why? Also, is the composite function gf(x) the intersection of function f(x) and function g(x)? Thanks in advance.

Homework Statement That's what I'm supposed to prove. Homework Equations A function f is an injection if f(x1)=f(x2) ---> x1=x2 The Attempt at a Solution I'm just having trouble constructing a formal proof. I mean, it's obvious that f(g(x1))=f(g(x2)) then either g(x1)=g(x2)...

Good day, I just need someone to tell me if this is correct. If L and K are subfields of M, their composite LK is the smallest subfield of M that contains both L and K. is this correct \alpha \in LK if and only if there are positive integers n and m, polynomials f(x_1,x_2,...,x_n) \in...

Homework Statement posted in title Homework Equations none The Attempt at a Solution f+g would be (2x^2+1) + (x-1) = 2x^2 + x so the domain for f+g is all real numbers but i don't know how to find the one for the composite. i am still confused as to what a composite function is...

Sorry if I'm writing on wrong board. Homework Statement 1) Write an existentially quantified statement to express conditions for composite number ( composite number m is greater than 1 and there is a natural number greater than besides 1 and m, that divides m) 2) Writing definition using...

Homework Statement Determine the moments of the inertia of the Z-section about its centroidal x0 and y0 axes. I didn't draw them in, but the x0 axis is 80[mm] up from the bottom and the y0 axis is 90[mm] from the left most point. So it is in the middle of the piece. The Attempt at a...

Homework Statement Hi, I have trouble proving this claim and would really appreciate your help =). Thank you in advance! So here's the question: Suppose that f is a continuous function for all x>= 0 and differentiable for all x> 0. Also, f(0) = 0 and f' (1st derivative of f) is increasing on...

Homework Statement a) (f ° g)′(−2) = ? b) (g ° f)′(2) = ? Homework Equations f(−2) = −3, g(−2) = −4, f(2) = 3, g(2) = −3, f ′(−2) = −1, f ′(−4) = −2, f ′(2) = 5, g ′(−2) = 1, g ′(2) = 2, g ′(3) = −4. The Attempt at a Solution I have no idea how to do it every thing I've tried...

I'll be very thankful is someone will tell me where I'm wrong. We know: 1) f is uniform continuous. 2) g is uniform continuous. We want to prove: fg(x) is uniform continuous. proof: from 1 we know -> for every |a-b|<d_0 exists |f(a)-f(b)|<e from 2 we know -> for every |x-y|<d...

Homework Statement I need to prove that a composite integer n>1 has a prime divisor p with p<=sqrt(n). Homework Equations The Attempt at a Solution Im not sure how to do this, any help getting started would be great thanks.

Homework Statement The sets A and B are defined respectively by A={x\in R : 0\leq x\leq 1} B={x\in R : 1\leq x\leq 2} and the functions f and g are defined respectively by f(x)=x^2-2x+2 g(x)=\frac{x+2}{x-1} where f(A)=B , g(B)=C with C as the range of the function g ...

Hi guys, I'm using a composite trapezoidal rule to approximate the integral of functions. Up till now I have been using a uniform composite mesh, ie, there are J intervals, each interval being 1/J wide (since the integral is between 0 and 1). How do I find the most efficient non-uniform mesh...

I've been working on this one for quite some time... Consider a sinusoidal wave traveling along a string composed of two sections, one with a lighter mass/length density than the other. A pulse is traveling in the light region and about to hit the junction. If the incident wave is given by...

1. An 80-cm-long wire is made by welding a 5.50 mm-diameter, 20-cm-long copper wire to a 5.50 mm-diameter, 60-cm-long iron wire. What is the resistance of the composite wire? 2. p = resistivity, R = pL/A 3. r = 0.001375 m goes into A = pi*r2. I used the above equation for R separately for the...

i really need to see the proof of this theorem: if f and g are bijective then the inverse of (g o f) = inverse of f o inverse of g

Original question: A system contains two particles: the spin of particle 1 is 3/2 and the spin of particle 2 is 1. Motion of particles can be ignored. Part A asked to find the total spin state |5/2 3/2> using Clebsch-Gordon coefficients. I did so, and came up with, \mid 5/2\ \ \ 3/2\...

Hi,all. My lecture said, two fermion can form a composite boson. two spin half plus together get 1. Yes I agree, but i think that's depend on whose frame of reference. say A and B is two fermions, C and D is another two fermions (observers). AB form a boson. if: AB...

Homework Statement The forward-back function is f (t) = 2t for 0\leq{t}\leq{3} , f(t)= 12-2t for 3\leq{t}\leq{6}. Graph f(f(t)) and find its four-part formula. First try t = 1.5 and 3. The Attempt at a Solution There are four possible composite functions from the two given...

Homework Statement let A,B,C be sets, and let f : A--> B and g : B--> C be functions. The composite function denoted by g o f is a function from A to C defined as follows: Homework Equations g o f(x)=g(f(x)) for every x in A. Prove that if g o f is one-to one, then f is one-to...

Homework Statement Given g(x)=|x| and f(x)=secx 1)Determine an equation for (f(g(x)) 2)State the domain 3)x and y intercepts 4)any asymptotes Homework Equations N/A The Attempt at a Solution f(g(x))=sec|x| or 1/cos|x|

[b]1.) If (-4,8) is the image under the composite transformation Th,3 x T-2,k(-3,0), what are the coordinates of the image of (2,-1) under the same composite transformation? The Attempt at a Solution I'm lost on this one.

Homework Statement Given the equation y= f(x) , at a certain point the slope of the curve is 1/2 and the x-coordinate decreases at 3 units/s. At that point, how fast is the y-coordinate of the object changing? The Attempt at a Solution Dy/dx = f ' (x) dx/dt Would that be...

can u help me with this question If n ≥ 6 is a composite integer, then n |(n − 1)! If n is a prime number, then n does not divide (n−1)!

This is not so much a problem as it is a conceptual question. You're calculating the moment of inertia of a composite shape, let's say a square and a triangle. The square however has a hole inside of it. How does this change the computation of the moment of inertia? This is in a 2-D plane. My...

1. Find the domain of f(g(x)) where f(x)= radical 25-x^2 and g(x)= ln(x+3) 2. For the domain of f I got x < or equal to +/- 5 and for the domain of ln(x+3) I got x+3 > 0 3. (0, 145) Thanks for your time. :P

Homework Statement Determine the deformation of a composite bar is subjected to a centric force P. This is a general question. The composite bar is made of 2 materials. The top and bottom layer is material 1, and the middle layer is material 2. I can't think of a better way to describe...

f o g (x) = Abs(x) f(x)=? g(x)= root(x) im thinking f(x) is = to root(x) correct me if I am wrong?

Homework Statement The attempt at a solution g(f(x)) = h(x) 4f(x) + y = 4x - 1 4x + 16 + y = 4x - 1 y = -1 - 16 y = -17 so, g(x)= 4x + y = 4x - 17 Is this the correct way of going about this question? I used a guessing approach to this question. Is enough work shown to get...

Homework Statement Given: a\partial\psi/\partial t = \widehat{H}\psi Consider a is an unspecified constant. Show this equation has the following property. Let \widehat{H} be the Hamiltonian of the system composed of two independant parts: \widehat{H}(x_{1},x_{2}) =...

Homework Statement If f(x) = x3+3x2+4x+5 and g(x)=5, then g(f(x)) = ? Homework Equations The Attempt at a Solution I don't know if I am correct. g(f(x)) = g(x3+3x2+4x+5)= 225? I plugged 5 into the equation. Am I right?

Homework Statement http://img171.imageshack.us/img171/543/pro3.png The Attempt at a Solution = f(g(h(x))) = f(g(\sqrt{x+3})) = f(cos\sqrt{x+3}) = \frac{2}{cos\sqrt{x+3}+1} Is this right, and am I showing enough work to get full marks? Do I need restrictions for example?

Homework Statement If p>=5 is prime, prove that p^2 +2 is composite. Homework Equations If we took p and divided it by 6 we would get remainder possibilities of 0, 1, 2,3,4,5 The Attempt at a Solution p=6q p^2=36q^2 P^2=6(r) P^2+2=6r+2=2(3r+1) composite p=6q+1...

First of all, I hope this problem is supposed to be here - I'm Swedish and in Sweden "calculus" & "precalculus" are rather odd terms. Anyway..Homework Statement Prove that n3 - n is divisible by 6 if n is a natural number, and divisible by 24 if n is an odd natural number.Homework Equations The...

Does it correspond with the centroid of the transformed section? For example, if a wood beam had a steel plate fixed along the bottom, would the neutral axis be lower than that of a pure wood beam of similar cross section? Any links showing example probs would be nice too. Sorry that this is...