Composite Definition and 401 Threads

For positive integers $p,\,q,\,r,\,s$ such that $ps=q^2+qr+r^2$, prove that $p^2+q^2+r^2+s^2$ is a composite number.

Hey guys, Few more questions for the problem set I've been working on. I'm doubting some of my answers and I'd appreciate some help. Question: The first one starts off easy but I found that it gets progress more challenging later on. So the rate of spread should be p'(t) which is: p'(t) =...

Hey guys, I have a couple more questions about this problem set I've been working on. I'm doubting some of my answers and I'd appreciate some help. Question: For the first one, since f o g = √(√x+5)-2), the domain is [-1,infinity) Likewise, g o f = √(√x-2)+5) and the domain is [27,infinity)...

Consider a composite particle. Its spin is determined by the spins of its constituent particles. But the constituent particles are in a superposition of different spin states and so don't have a definite spin. So it seems it shouldn't be possible to ascribe a definite spin to the composite...

Good morning PF, I am having some difficulty finding info on calculating a composite moment of inertia. The section I am working with is 8 separate columns (WT5x15) arranged evenly spaced around the circumference of a circle. You can see what I'm taking about in the attached jpg. I found...

Can I use a 315MHz transmitter module to send a composite video signal to another reciever module?

Homework Statement I've been reading Leonard Susskind's Theoretical Minimum volume on QM, and enjoying it quite a bit - the book doesn't include exercise solutions at the end though, and if they exist online for this volume I haven't been able to find them. (Perhaps if such solutions...

Hey again! (Rock)(Wasntme) I want to show that there are infinitely many composite numbers $n$,for which stands: $$a^{n-1} \equiv 1 \pmod n$$ So,it must be: $n \mid a^{n-1}-1$ But how can I show that there are infinitely many such $n$ ?? (Thinking)

Hello! (Smile) I am looking at the following exercise: If $n>1$,show that $n^4+1$ is composite. According to my notes,it is like that: $$n^4+4=(n^2)^2+2^2+2 \cdot 2 \cdot n^2-2 \cdot 2 \cdot n^2=(n^2+2)^2-4n^2=(n^2+2-2n)(n^2+2+2n)$$ To check if it is composite,we have to check if...

Prove that the number $27x^6+27x^3y^3+8y^6$ is composite for any positive integers $x$ and $y$.

What is the difference between a functional and a composite function? Also, look those implicit equations: ##F(x, y(x))=0##, ##F(t, \vec{r}(t))=0##, ##F(x, y(x), y'(x), y''(x))=0##, ##F(t, \vec{r}(t), \vec{r}'(t))=0##... Can be understood that ##F## is the functional?

hey guys, So I'm working on a MATLAB function that uses simpsons 1/3 rule to find an integral. This is what I have done so far, but I'm not 100% confident.. I seem to get double when I use greater segments. If anyone would be able to have a look at give me some tips that would be very much...

Hi, I am trying to formulate a 2D model to calculate the temperature change over time in a composite material. The material consists of several layers, and is heated from all edges by a known temperature vs time profile. I was thinking of creating a finite element model. Can someone...

We are looking at designing a 10" diameter, 48" long payload shroud (Ogive nose cone) for a large hobby rocket. We have done an aeroheating analysis based on the trajectory, so we have the max temp. experienced during ascent at several body points. We want to make the shroud out of composites...

If I have a composite beam or an T beam where the top of the T is of significantly higher stiffness than the vertical part. is it true that the further a stiffness material is from the neutral axis the greater the effect on the overall stiffness is? is it possible to calculate a new flexural...

Homework Statement Given that I have a doubling function : f(x)=2x (for 0≤x<0.5) and 2x-1 (for 0.5≤ x<1) Homework Equations What is f(f(x))? The Attempt at a Solution f(f(x))=4x for the first one and 4x-3 for the second part but not sure what to do about the domain...

Let's say f(x) = sqrt(x-1) And g(x) =x^2 What is the domain of f(g(x)) Well the domain of g(x) is all real numbers and the equation for the new function is sqrt(x^2-1) Am I right to say that the domain for f(g(x)) is x greater than or equal to 1 and less than and equal to -1??

Dear All, I was reading the concept of stationary waves in composite string ABC made up of joining two strings AB AND BC with different mass per unit length and a joint at 'B'.the two ends of the composite string are clamped at 'A' and 'C' and a transverse wave is set up by an external source...

Hello, I'm working with a system of equations that has an infinite recursion function, and am wondering if its possible to simplify or remove the recursion in terms of the other functions in the system. Any insight into the framework or family of this system is appreciated. Given two...

Homework Statement Can someone describe the input and output method to find the domain and ranges of composite functions to me?? Homework Equations The Attempt at a Solution Example: f(g(x)) first you find the domain of g(x) Then you find the range of g(x) y= G(x) that will...

y=f(x),K=F(y), and dF(y)/dy=y^2/y', (1) then dF(x)=y^2*dx; so, F(x)=int(y^2*dx)=int((f(x)^2)*dx); then we obtain, F(x)=(f(x))^3/(3*f'(x))+C; substitution of y=f(x) into F(x), we get, F(y)=y^3/(3*y')+C; (2) using the result...

y =f(x), and y'=df(x)/dx, F(y)=y^3+(y')^2 how to deal with the (y')^2 when i calculate dF(y)/dy? thanks.

I was doing this example from my textbook and looked at the solution guide. I'm confused as to where the textbook got a certain number. In the numerator of their work, they got (1)(6)(2), which I'm assuming is the width of the skinny rectangle, the total length of the bottom section...

metals are generally considered more useful for high strength parts because ceramics break when exposed to sudden shock, but what about when a continuous force is applied to a ceramic and a metal of the same dimensions by a high strength ceramic i mean a higher hardness than the metal (such as...

Homework Statement Calculate the line integral: F = <xz, (xy2 + 2z), (xy + z)> along the curve given by: 1) x = 0, y2 + z2 = 1, z > 0, y: -1 → 1 2) z = 0, x + y = 1, y: 1→0 3) z = 0, x-y = 1, y: 0 → -1 Homework Equations The Attempt at a Solution I don't think the...

Hi, I recall some years ago seeing a composite picture of what our galaxy would look like from outside the galaxy, for example from Andromeda but was not able to find one or even how to search for it on the web. I was wondering if anyone here is familiar with it and perhaps even if we've...

I've been looking for work on this, and I was hoping someone could confirm or deny that anyone has done any before. I am referring to gravity being a composite of the electromagnetic (or maybe electro-magnetic-strong-weak) force between many different pieces of matter with a mostly nullified net...

Why is finding the gravitational force on the center of mass of a composite body the same as finding the gravitational force on each individual constituent of the composite body?

I have probably a silly question about correlation functions of composite operators. Why can't you just calculate a correlator with fields at different points x1, x2, x3, ... and then set a couple of the points equal at the end of the calculation to get the result? e.g., \langle 0...

g(x)=−4x2−5x f(x)=−3x2+7x−5(g(x)) f(g(−1))=? First, let's solve for the value of the inner function, g(−1). Then we'll know what to plug into the outer function. g(−1)=−4(−1)2+(−5)(−1)I don't understand why they transformed the minus symbol into an addition symbol. This has happened a few...

Homework Statement Under which class of materials would the following materials be categorized? What are/is the primary bond type(s) in each material/object? a. Tennis Ball Homework Equations The Attempt at a Solution We'll consider a very simple and standard tennis ball...

Hello MHB, I got stuck on integrate this function \int \frac{\sin^3(\sqrt{x})}{\sqrt{x}}dx my first thinking was rewrite it as \int \frac{\sin^2(\sqrt{x})\sin(\sqrt{x})}{\sqrt{x}}dx then use the identity \cos^2(x)+\sin^2(x)=1 \ \therefore \sin^2x=1- \cos^2(x) \int...

Problem Statement: Do the sieve of Eratosthenes from 2 to 100 and find all the primesSo I'm trying to do the sieve of Eratosthenes in fortran 90 (I'm using Plato IDE)My efforts to solve this/ method to use: Obviously, I want the program to do a LOOP starting with every whole number from 2...

Hello there, I am wondering if some specilalist would point in me in the direction of procedures to determine the load in a fiber in a composite material made of aligned fibers (let's say at alternating angles $$+/- \alpha$$). I understand you could simply compute the strain in a convenient...

Homework Statement In the image attached, I'm asked to find the mass moment of inertia about an axis at point O that's perpendicular to the page. The Attempt at a Solution The only question about this problem that I have is: Can I divide the composite body at point O and find the...

Given f:{0,1}n→{0,1}n, define f′:{0,1}2n→{0,1}2n as follows: for x,r∈{0,1}n define f′(x∘r):=f(x)∘r (where ∘ denotes concatenation). Prove that if f(⋅) is one way permutation then so is f′(⋅). i don't understand f′(x∘r):=f(x)∘r how to decompose it in order to prove it I tried proving it by...

Homework Statement Suppose f(x) and g(x) are non-zero polynomials with real coefficients, such that f(g(x))=f(x)⋅g(x). If g(2)=37, what is g(3)? Homework Equations The Attempt at a Solution I have no idea where to begin this with. At x=2, f(g(2))=f(2).g(2) f(37)=37f(2) What...

Homework Statement Prove that there are infinitely many n such that 6n+1 and 6n-1 are both composite. Homework Equations The Attempt at a Solution I have no idea where to start. I was thinking that this must be some form of Euclid's theorem but I don't know how to work that into...

Suppose you have an electron and a proton, which both can have either spin up or down. The possible combinations are: \uparrow\downarrow, \downarrow\uparrow, \uparrow\uparrow, \downarrow\downarrow But for some reason my book only allows a linear combination of the two first since they both...

Homework Statement Show that the partition function for a composite system, let's call it '3', composed of systems '1' and '2' is the product of the partition functions of '1' and '2' independently.Homework Equations Kittel defines partition functions using the fundamental temperature τ (which...

Homework Statement I just want to make sure that I am correct. if we have a composite function f(g(x)). Homework Equations f(g(x)) is onto if and only if both f(x) and g(x) are onto f(g(x)) is one to one if and only if or both f(x) and g(x) are one to one The Attempt at a Solution...

Is something wrong in my assertions below? Suppose we have two quantum systems N and X. Let N is described by discrete observable \hat{n} (bounded s.a. operator with discrete infinite spectrum) with eigenvectors |n\rangle. Let X is described by continuous observable \hat{x} (unbounded s.a...

Hi, For any odd composite 'N', let u = (N-1)/2, v = u+1, then u^2(mod p) = v^2(mod p) if and only if 'p' is a factor of 'N'.

Hi, For any odd composite 'N', let u = (N-1)/2, v = u+1, then u^2(mod p) = v^2(mod p) if and only if 'p' is a factor of 'N'. For more info please visit kadinumberprops.blogspot.in

Hey all, So the idea is that I'm trying to create a composite ranking system of items that are already in different categories. For example, suppose there are 4 houses that a buyer is choosing from. These 4 houses are ranked 1-4 in each of the categories such as affordability, location, and...

Homework Statement In the image below, calculate the center of mass (x-bar,y-bar) of the composite body. Homework Equations I've used all of the equations for area for the shapes needed (triangle, square, circle). The Attempt at a Solution I have attached my calculations and...

Hey, Let ##(f,g) \in B^A## where ##A## and ##B## are non-empty sets, ##B^A## denotes the set of bijective functions between ##A## and ##B##. We assume that there exists ##h_0: A \rightarrow A## and ##h_1: B \rightarrow B## such that ##f = h_1 \circ g \circ h_0 ##. This implies that ##g =...

Homework Statement While I was in school I thought to see what a function whose derivative is always perpendicular to another functions derivative would look like, so for example for X^2 we have -ln(x)/2. Homework Equations Well all those integration tables I guess The Attempt at a...

Homework Statement Find f°g for each pair of functions f and g.Homework Equations f(x) = {x+1, if x≤0 or 2x, if x>0 g(x) = {2x, if x≤-1 or -x, if x>-1 The Attempt at a Solution I am able to determine the following: (f°g)(x) = {2x+1, -2x, -x+1 However, these functions carry intervals, and...

Homework Statement A wall is required to be insulated by embedding wood within concrete. the total thickness of the concrete and wood are 10cm and 1 cm respectively and are fixed due to structural constraints. determine the minimum heat leak into the room if the location of the wood can be...