Composite Definition and 401 Threads

Homework Statement f(x)=x^3-\frac{3x^2}{2}+x+\frac{1}{4} find\int_{\frac{1}{4}}^{\frac{3}{4}} f(f(x))dx Homework Equations The Attempt at a Solution I am clueless here. I started by writing f(f(x)) as (f(x))^3-\frac{3(f(x))^2}{2}+f(x)+\frac{1}{4} I don't think expanding...

1. If F(x) = f(xf(xf(x))), where f(1) = 2, f(2) = 3, f '(1) = 4, f '(2) = 5, and f '(3) = 6, find F'(1). I feel I have a decent grasp on the chain rule, product rule, etc, but when faced with a problem like this I just blank out. I don't even really know where to begin. Unfortunately I...

Homework Statement A single-scoop ice cream cone is a composite body made from a single scoop of ice cream placed into a cone. Assume that the scoop of ice cream is a sphere with radius r = 3.65 cm that is placed into a 9.90 cm tall cone. The interior height of the cone is 9.00 cm. The cone...

Hi guys, I have this function f(g(t)) and I have to find the second time derivative of f, is it correct the following solution?: f''=∂f/∂g*g'=∇f*g' f ''=∇^2f*|g'|^2+∇f*g'' where ∇^2 is the laplacian function

Any help would be much appreciated - Is it possible to say the following? If z = g(s+at) + f(s-at), let u = s+at and v=s-at, where a is a constant. z = g(u) + f(v), \frac{∂z}{∂u} = g'(u), \frac{∂^{2}z}{∂v∂u} = 0? or can ∂u and ∂v not even exist because it depends on two variables (a and...

Homework Statement Ok, I just worked out a composite function, and it left me with: √2x^2+5) Now, how do I find the domain from that? I don't understand that my text says the domain of that is just all Real numbers ? What makes this different than other square functions that we are...

Homework Statement Here is the problem: Homework Equations The Attempt at a Solution I need help RIGHT from step one. Now, step one I would suppose I need to evaluate g(x) ? Which, would be x must be greater than or equal to -5. Correct? Then what?

Homework Statement The 2000 mm long composite bar shown in Fig. 1 consists of an aluminum bar having a modulus of elasticity EAl = 70 GPa and length LAl = 500 mm, which is securely fastened to a steel bar having modulus of elasticity ESt = 210 GPa and length LSt = 1500 mm. After the force P...

Thank you for the warm welcome. I am now wondering where i should ask my questions at, which forum. Its pre-algabra so i don't want to bother anyone with some really basic things that they don't care to see/For example, the question i have right now is a method for simply finding a composite...

Homework Statement A crossply composite is comprised of 3 plys of fiberglass reinforced epoxy with the fiber direction parallel to the test direction and 2 plys of carbon fiber reinforced epoxy with the fiber direction transverse to the fiberglass direction. Each ply is of equal thickness and...

Homework Statement Well I have these three different integrals: \int{\frac{1}{\sqrt{4x^2-1}}dx} \int{\frac{1}{4-x^2}dx} \int{\frac{1}{x^2+4x+8}dx}Homework Equations Yeah well not exactly sure how to approach this... Do you use integration by substitution, where you come up with some...

Homework Statement "A composit bar is made of two metals joined in series, with coefficients of linear thermal expansion 2.2E-5 and 0.9E-5 K^-1 respectively. The bar expands by 0.5% in length with a temperature rise of 500 K. Calculate the ratio of the initial lengths of the two metal...

Homework Statement Determine each of the following composite functions: a) gof(x) b)foh(x)Homework Equations Where f(x)=e^(3x+2) [e is the exponential function] g(x)= ln(4x+1) h(x)= 1/(2x-1)The Attempt at a Solution So I have found an answer, I am just unsure if I am correct though. This is...

hi gang, got a friend who lifes relatively close to a 1407kHz (multi kW) AM broadcast transmitter he has a ~ 50metre run of 75 Ohm coax between a security camera and the recording/viewing equip. The 1407 kHz is getting into the system and causing the usual herringbone pattern on the displayed...

Homework Statement Suppose that cotton is used to produce only two products, pillows and clothes. If the demand for pillows increases, what will happen to the price of clothes? Explain your answer. Assume that the laws of supply and demand hold. Homework Equations Laws of supply and...

Homework Statement The question I have is a more general one, but one I can't find an anser to since I don't have any access to a book on integration at the moment. How do we Integrate a composite function. ∫f(g(x)) dx Homework Equations The Attempt at a Solution

Hi all, This is my first post since I'm unable to find the answer myself & on the net too. My query is let's consider we have 3 types of system 1. Air tank at 10 bar pressure. It will have105*10*1= 1000 KJ energy. 2. Water tank of volume 1 cum and height of 1 m. It will have 5.04*h2 =...

Hi guys I'm thinking on this problem for long time :) Let be one function defined only on POSITIVE INTEGERS I) f(1) = 1 II) f(2n) = 2 . f(n) + 1, if n ≥ 1 III) f(f(n)) = 4n + 1, if n ≥ 2 Find f(1993) ______________ First I got this, I got to this milestone f(2n) = 2 . f(n) +...

Hi there, I need help about how to solve the flexural rigidity (D) of a composite. For instance, if I have two plies of a plate each with different material properties, i.e. ply 1 has different Young modulus from ply 2. Therefore, how can I determine the value of the overall D of the plate...

Hi there, I need help about how to solve the flexural rigidity (D) of a composite. For instance, if I have two plies of a plate each with different material properties, i.e. ply 1 has different Young modulus from ply 2. Therefore, how can I determine the value of the overall D of the plate...

Homework Statement A photon collides with a stationary particle of rest mass m0 and is absorbed. Find the mass and velocity of the composite particle Homework Equations Conservation of energy: E + m0 * c^2 = \gamma * mt *c^2 where mt is the total mass Conservation...

Please specify in a simple way.

Hi, I have a small question about this. Using the chain rule, I know that a composition of differentiable functions is differentiable. But is it also true that if a composition of functions is differentiable, then all the functions in the composition must be differentiable? For example, if...

Hey all! I have a question concerning the addition of 2 sine functions. Could anyone point me to the right direction as to what happens to the period and frequency when two sine functions are added together? Note: when adding, these two functions possesses two different frequencies. Thanks...

According to the Wikipedia article a composite number n is a strong pseudoprime to at most one quarter of all bases below n . Do Fermat pseudoprimes have some similar property ? Is it known what is the largest number of bases for which composite n , that is not Carmichael number is...

I asked about the first part of this problem in https://www.physicsforums.com/showthread.php?t=592408. I thought the best idea was to start another thread for the second part. Homework Statement Part a) Given f(x)=ax+b, and f(3)(x)=64x+21, find the values of the constants a and b. (note...

Given f(x)=ax+b, and f(3)(x)=64x+21, find the values of the constants a and b. (note: f(3)(x) means fff(x)) To me this seems like I have to use two equations to find the value of three variables, since when I have found a and b, I should be able to get the value of x. Even though it...

Hello everybody; does anyone know a good reference (possibly modern) where one can study quarks and leptons (as well as gauge bosons) as composite objects? By reference I mean papers, books, reviews and every other thing you might find useful :) Francesco

I have got t: P3 → P3 p(x) → p(x) + p(2) and s: P3 → P2 p(x) → p’(x) thus s o t gives P3→ P2gives p(x) → p’(x) next part says : use the composite rule to find a matrix representation of the linear transformation s o t when t: P3 → P3 p(x) : p(x) + p(2) and...

So I have been reading up on composite materials and have been geting a bit confused, from what I have read, composite materials consist of a matrix and reinforcement, the reinforcement can be fibers, I read that the way the fibres are placed will effect the machanical properties of the material...

I'm looking at Munkres: Topology Problems 1.2.4(c), 1.2.4(e), and 1.2.5(a). Problem 1.2.4(c) asks, "If g\circ f is injective, what can you say about the injectivity of f and g?" Problem 1.2.4(e) asks, "If g\circ f is surjective, what can you say about the surjectivity of f and g?" I concluded...

Hello all, I've posted an image below of a very basic maths question I can't seem to solve. Even after looking at the correct answer I cannot seem to figure out how they got it no matter what I try. The question is: http://img684.imageshack.us/img684/6179/mr2q19.jpg From what I can...

I cannot figure out how to do this problem completely: If U =x3y, find \frac{dU}{dt} if x5 + y = t and x2 + y3 = t2. I know that I am using the chain rule here and I have the partial derivates of U: \frac{∂U}{∂x} = 3x2y \frac{∂U}{∂y} = x3 So far I have the equation given below...

Homework Statement The function f has domain (-∞, ∞) and is defined by f(x) = 3e2x. The function g has domain (0, ∞) and is defined by g(x) = ln 4x. (a) Write down the domain and range of f∘g. (b) Solve the equation (f∘g)(x) = 12 2. The attempt at a solution (a) Is it correct...

Homework Statement If \lim_{x\rightarrow 0+}f(x)=A and \lim_{x\rightarrow 0-}f(x)=B find \lim_{x\rightarrow 0+}f(x^{3}-x) Homework Equations The Attempt at a Solution I don't have one. I am dumbfounded. Mostly i have been trying to understand the meaning of the composite...

Does de Broglie wave length apply to composite particles? For example a very low momentum neutron does it have a very large wave length? Or do we think in terms of the three quarks that make up the neutron? The three quarks do not have low momentum they are banging back and forth inside the...

In general how does one find the basis of a composite system of particles with different spin. Say for example spin 1, spin 1/2, and spin 5/2. My first thought was to consider the uncoupled basis wherein the particles with spin 1/2 and spin 5/2 have similar state kets. Would the basis for...

Homework Statement \begin{equation} f(x)= \begin{cases} 5x+2 &, x \leq 1 \\ 3x^2 &, 1<x<2\\ 4-x &, x\geq 2 \end{cases} \end{equation} \begin{equation} g(x)= \begin{cases} \frac{1}{5}(2+3 cos x) &, x <0 \\ 4-sin x &, x \geq 0 \end{cases} \end{equation} Find h = f...

Homework Statement A transmission wire is made of a cylindrical core of copper surrounded by a sheath of steel. The copper core is 1 cm in diameter, and the sheath has an outer diameter of 2 cm. What is the resistance of 1 km of wire? Homework Equations R=ρl/A The Attempt at a...

Homework Statement Stack a steel beam on top of an aluminum beam. If you are given the Young's Modulus values (in psi) of each beam, try to predict the deflection of the "composite" beams. Please view the "Hint" my teacher gave me in the pdf attachment in this post...

Homework Statement Let f:A->B and g:B->C be invertible mappings. Show (g o f)^-1 = f^-1 o g^-1. Homework Equations A mapping is invertible iff it is bijective The Attempt at a Solution I understand why these are equivalent statements; however, I can't figure out the wording of the...

Homework Statement Let f : A → B, g : B → C be functions where A,B,C are sets. ConsiderΓf ⊂A×B,the graph of f,Γg ⊂B×C,the graph of g. Now consider the sets Γ f ×C ⊂ A×B×C and A×Γg ⊂A×B×C. LetΓ=θ(Γf ×C∩A×Γg)⊂A×C where θ : A×B×C → A×C is the projection defined as θ((a,b,c))=(a,c). Show that Γ...

A spin-3/2 particle (labeled 1) and a spin-1/2 particle (labeled 2) are interacting via the Hamiltonian \lambda \vec S_1 \cdot \vec S_2 + g(S_{1z} + S_{2z})^2 where S1 is the spin operator of particle 1 (the spin-3/2) and S2 is the spin operator of particle 2 (the spin-1/2). λ and g...

Sometimes I like to find patterns in certain functions, for example, repeated Sigma (Summation) notation. But what if I wanted to do an arbitrary number of nested summations? Or something similar with other functions? Is there a compressed way of writing this? For example: \sum_{k_5=1}^{1}...

Homework Statement cos^-1(sin(5pi/4)) Homework Equations n/a The Attempt at a Solution I began by finding the reference angle of 5pi/4 by subtracting pi, and I got pi/4. pi/4 must be part of an isosceles right triangle, so I drew a diagram with sides 1,1, and √2. I found sin pi/4...

Homework Statement I started out with f(x)=sinx and g(x)=1-√x. I found f(g(x)) which is sin(1-√x) and now my problem is how to find the domain. I've really been struggling with the domain part and just need this one done step by step so i have an idea of how to actually do it. Homework...

Dear all, Iam trying to figure out how to reduce or simplified the flexural rigidity (D) of composite orthotropic laminates consists of many plies into a single layer isotropic model. I know that for an isotropic case, D = Et^3/12(1-v^2). However, for the case of, say, 3 plies...

Hi, I noticed that most modern tanks have barely any slope on their armour, unlike for example the old WW2 tanks like the T-34 using solid steel armour. Why exactly is this? Why is sloping of armour gone? I realize that modern armour isn't trying to deflect a shell, but still if armour is...

Hi everyone, I am working through Ballentine's Quantum Mechanics books, and I am stuck... I would be appreciative if someone could walk me through this section with some help. Here is my first confusion. In this case then |a_{m'}b_{n'}\rangle\langle a_{m'}b_{n'}| do not form a complete...

my question is regarding calculation of deflection of a composite beam, ie a beam with a cross section made up of 2 separate homogeneous materials. the methods i know for calculating deflections in homogenous beams are energy methods(catiglianos 2nd) and the elatic curve equations(second...