Composite Definition and 401 Threads

Let N be composite number containing only two primes a and b That is, N=a*b, where a and b are primes Factorizing N[even on a computer] is an impossible task if N is very large,for example if it has 400 digits. But we can eliminate a huge number of divisors by the following rules: 1.If n...

hi.. This is abdul I am carrying a impact of sphere on a composite laminated plate. i wanted to calculate the contact force when sphere impacts the plate.. or can anyone help me how to get the stiffness of plate.. or deflections in plate.. with respect to time Thanking you Your help will...

hi! I'm hoping to have something cleared up if i have a beam made out of two materials, and it gets bent, and i need to analysis the transformed section for whatever reason, i have learned that you need to sort of 'pretend' that you're looking at a beam of a single material. in order to do...

Homework Statement Remember to show your working explicitly throughout your answer to this question. (a) (i) Use the Composite Rule to differentiate the function f(x) = (x^2− 6x + 23)^(3/2) (ii) Use the Quotient Rule and your answer to part (a)(i) to show that the function: g(x) = (x −...

Function p and q are defined by: p (x) = 3x2+1, x∈R, Domain 0≤x≤2 q (x) = x2 - 2, x∈R (q∘p) - State the range: I got -1 ≤ y ≤ 167 The book says 0 ≤ y ≤ 167 Any idea where I went wrong? The composite function I got so then I could sub was: 9x4 + 6x2 - 1 Thanks, Peter G.

I have to calculate the elongation of a pencil under a load. I know I have to use deflection = PL/AE but since the pencil has 2 materials in it I have to modify that equation. I know that both materials extend by the same amount. Could anyone explain to me how to get that equation?

Hello guys :smile: Given that: f(x) = e2x and g(x) = (2x-1) Find: (g ° f)-1(x) So, what I did first was to put f into g: 2 x e2x - 1 = y 2 x e2x = y + 1 e2x = y + 1 / 2 (ex)2 = y + 1 / 2 ln (y+1/2) = x Is that ok? Thanks, Peter G.

Lets say I have a beam with a cross section made of half aluminium and half steel glued together. I would like to know how to calculate the deflection of this beam due to bending moment but I am unsure of how to use the virtual work equation to accomplish this. Should I use a different...

Homework Statement I have the specific gravities of two materials(1.5 and 1.9) and i want to calculate the matrix volume(Vm). The only information who i had is the specific gravities and that the matrix form is continuous and oriented. Homework Equations Vm+Vf=1 (not sure) The...

Hi, I am trying to understand some more on composite materials and i have a question. Let's say i have two materials and i want to produce a composite from those materials. How can i check if a composite is possible from these materials? I have found an equation on the web but i am newbie on...

Homework Statement Two strings are joint together, then their other ends are fixed. What is the lowest frequency that must be applied by an external source in order to produce a standing wave on the composite string, with a node on the junction of the two strings? The lengths of the two...

Homework Statement The moment of inertia (in4) about the y-axis is most nearly (a) 39,500 (b) 37,600 (c) 38,700 (d) 36,400 Homework Equations Iy(circle)= .25(pi)(r^4) Iy(triangle)= (1/12)h(b^3) parralel axis theorem= Iy=Iy'+A[d(x)]^2 The Attempt at a Solution Iy(circle)=...

Homework Statement Suppose that the function f is defined on an interval by the formula f(x) = \sqrt{tan^{2}x - 1}. If f is continuous, which of the following intervals could be its domain? (A) (\frac{3\pi}{4},\pi) (B) ( \frac{\pi}{4},\frac{\pi}{2} ) (C) ( \frac{\pi}{4},\frac{3\pi}{4}...

Is it possible to produce massive composite particles from a non abelian gauge theory of massless fermions? I know that if the quarks were massless, the pions will be massless too (goldstone bosons). But what about baryons? Will they be also massless? If so, can we make a general statement that...

Homework Statement Consider a two particle system of which one particle has spin s1 and the other s2. 1. If one particle is taken from each of two sources characterized by the state vectors |s1,m1> and |s2,m2> respectively, what is the probability that the resultant two particle system will...

Homework Statement Use differentiation to verify that the following integrals are correct (where a is not = 0 is a constant and c is an arbitrary constant (a) integrate xsinax dx= ( −x/a ) (cosax) +(1/a2) sinax+c (b) integrate tanax dx=(−1/a) ln(cosax)+c Homework Equations Composite rule...

Homework Statement Please see attached problem Homework Equations The Attempt at a Solution Ok so I am just stuck on the bit that asks us to write down the appropriate form of the interaction hamiltonian H int for two oscillating particles connected by a weak spring. Is it 1/2...

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 everyone I posted this in the classical physics forum but maybe it is more suitable for this forum. I'm currently trying to select 2 hydraulic motors to rotate a relatively sizeable structure, I'm hoping to rotate it through .5pi radians over a period of 30 mins (0.052 RPM), I'm hoping...

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...

Cosider a sinusoidal wave traveling along a composite string. The string is under constant tension, F, and consists of a light portion (x<0) with mass per unit length mu1 joined in a continuous manner to a heavier portion (x>0) with mass per unit length mu2. Let y_1i(x,t)=A_1i*sin(wt-k_1x) be...

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