Composite Definition and 401 Threads

  1. S

    Ratio of frequency between heavier and lighter part of composite cord

    Is the answer 1? Because the cord is connected to vibrating source and it vibrates with a frequency of 100 Hz so section A and B have the same frequency Thanks
  2. M

    B Origins of the no-cloning theorem

    I was watching this video by minutephysics on the No-cloning theorem. Henry very plainly shows why the no-cloning theorem holds, given the setup. However, I am no quantum physicist and lack the necessary background to truly understand what's going on there. What are the origins of the 3...
  3. emilmammadzada

    Atomic density of Oxygen in a composite

    Dear experts, how can I calculate the atomic density of Oxygen in a composite of 05 percent PuO2 and 95 percent UO2 (in atoms/barn-cm)? (5% U235 enriched)
  4. TitaniumVCarbon

    I irrationally dislike composites (Rant)

    A composite material is just two or more different materials put together, with the materials inside remaining the same. This is what I dislike about composites, they aren’t actually any stronger on a microscopic scale than normal materials. As an example, take pre stressed concrete beams. This...
  5. M

    Using continuity to evaluate a limit of a composite function

    For this problem, The solution is, However, I tried to solve this problem using my Graphics Calculator instead of completing the square. I got the zeros of ##x^2 - 2x - 4## to be ##x_1 = 3.236## and ##x_2 = -1.236## Therefore ##x_1 ≥ 3.236## and ##x_2 ≥ -1.236## Since ##x_1 > x_2## then...
  6. V

    Proving an integer is composite

    I am really struggling in how to begin this problem. So far I have considered using the Euclidean Algorithm and trying to find the gcd of each number like gcd(9,10) but each time they give me 1 so that doesn't work. My next idea is to do a proof by contradiction where I start with assuming that...
  7. M

    Finding the domain of a composite function

    For this problem, The solution is, However, I tried solving this problem by using the definition of composite function ##f(g(x)) = f(\frac{4}{3x -2}) = \frac{5}{\frac{4}{3x - 2} - 1} = \frac{5}{\frac{6 - 3x}{3x - 2}} = \frac {15x - 10}{6 - 3x}## which only gives a domain ##x ≠ 2##. Would some...
  8. S

    Calculate the density of composite materials

    Hello Please help me. I'm not a chemistry student and I don't have a chemistry-related course, so please explain in a very simple way. Thank you. I have a composite composition that I only have the weight percentage of atoms and I need to calculate the density so that I can check the properties...
  9. V

    Matlab Function for Composite Simpson

    function I=main_simpson(a,b,tol) f = @(x) sin(1./x); SO = 0; N = 10; S = 1; while (abs(S-SO)>tol) SO = S; h = (b-a)/(2*N); i = 0:N-1; xi = a+2*i*h; xi1 = a+2*(i+0.5)*h; xi2 = a+2*(i+1)*h; S = (h/3)*sum(f(xi)+4*f(xi1)+f(xi2)); N = 2*N; end end <Moderator's note...
  10. N

    Composite signal generation IC in DIFAR Sonobuoys

    Hi all I came to know about an old IC called probably "HE100" which was being used in DIFAR Sonobuoys for generation of composite signal. This IC takes 'Omni', 'Sin and Cosine Dipoles' signals as input and generates composite signals using internally generated 7.5 KHz and 15 KHz carriers. This...
  11. Rikudo

    Kinetic energy of a composite body

    This is my answer: $$KE_{total}=KE_{centermass}+KE_{uppermass}+KE_{bottommass}$$ $$KE_{total} = \frac 1 2 (mv^2 + 2m(\vec {v} + \vec {wL})^2) $$ But, the solution manual says that the answer is this: $$KE_{total} = \frac 1 2 (mv^2 + 2m(v^2+w^2L^2)) $$ I think he regard this composite body as...
  12. Rikudo

    What is the maximum coefficient of friction for a composite body on a slope?

    Here is the hint that the book gave me: "For the maximum value of μ, the rod must be to the extreme right i.e. horizontally rightwards of the axis of the pipe" I think what it meant is the same as this: Note: in the calculation below, ##r## is the distance from the center of pipe to the CoM...
  13. LCSphysicist

    I Current theory of composite quarks and leptons

    "M. Shupe [Phys. Lett. 86B, 87 (1979)] has proposed that all quarks and leptons are composed of two even more elementary constituents:" (Griffiths) I am redoing the book of elementary particles from Griffths, and this exercise has showed really interesting to me. How is the currently status of...
  14. M

    Show that any composite three-digit number must have a prime factor

    Proof: Suppose for the sake of contradiction that any composite three-digit number must have a prime factor not less than or equal to ## 31 ##. Let ## n ## be any composite three-digit number such that ## n=ab ## for some ## a,b\in\mathbb{Z} ## where ## a,b>1 ##. Note that the smallest prime...
  15. M

    Prove n^2+2^n Composite if n not 6k+3

    Proof: Suppose ## n>1 ## is an integer not of the form ## 6k+3 ##. Then we have ## n=6k ## for some ## k\in\mathbb{Z} ##. Thus ## n^{2}+2^{n}=(6k)^{2}+2^{6k} ## ## =36k^{2}+2^{6k} ## ## =2(18k^{2}+2^{6k-1}) ##...
  16. M

    If n>4 is composite, then n divides (n-1) ?

    Proof: Suppose ## n>4 ## is composite. Then ## n ## is either even or odd. Now we consider these two cases separately. Case #1: Let ## n=2k ## for some ## k\in\mathbb{Z} ##. Then we have ## n\mid (n-1)! = 2k\mid (2k-1)! ##. Thus, ## n ## divides ## (n-1)...
  17. M

    Each integer n>11 can be written as the sum of two composite numbers?

    Proof: Suppose n is an integer such that ## n>11 ##. Then n is either even or odd. Now we consider these two cases separately. Case #1: Let n be an even integer. Then we have ## n=2k ## for some ## k\in\mathbb{Z} ##. Consider the integer ## n-6 ##. Note...
  18. M

    Any integer of the form ## 8^n+1 ##, where n##\geq##1, is composite?

    Proof: Suppose ##a=8^n+1 ## for some ##a \in\mathbb{Z}## such that n##\geq##1. Then we have ##a=8^n+1 ## =## (2^3)^n+1 ## =## (2^n+1)(2^{2n} -2^n+1) ##. This means ## 2^n+1\mid 2^{3n} +1 ##. Since ##2^n+1>1## and ##2^{2n} -2^n+1>1## for all...
  19. M

    Every integer of the form n^4+4, with n>1, is composite?

    Proof: Suppose a=n^4+4 for some a##\in\mathbb{Z}## such that n>1. Then we have a=n^4+4=(n^2-2n+2)(n^2+2n+2). Note that n^2-2n+2>1 and n^2+2n+2>1 for n>1. Therefore, every integer of the form n^4+4, with n>1, is composite.
  20. M

    If p##\geq##5 is a prime number, show that p^{2}+2 is composite?

    Proof: Suppose p##\geq##5 is a prime number. Applying the Division Algorithm produces: p=6k, p=6k+1, p=6k+2, p=6k+3, p=6k+4 or p=6k+5 for some k##\in\mathbb{Z}##. Since p##\geq##5 is a prime number, it follows that p cannot...
  21. A

    I Plasma-like Description for Elementary and Composite Quantum Particles

    My article has been published in Entropy . Abstract: Schrödinger noticed in 1952 that a scalar complex wave function can be made real by a gauge transformation. The author showed recently that one real function is also enough to describe matter in the Dirac equation in an arbitrary...
  22. karush

    MHB Is the Calculation of $(3 \diamond 8) \square 2 = 1940$ Correct?

    define the binary operater $\diamond$ by $a\diamond b$=4a+4b and $s\square b$ by $a\square b=a^2+b^2$ find $(3\diamond 8)\square 2= [(4(3)+4(8))^2 +2^2]=1940$ ok just want to see if this is correct before i run thru the ribbon :unsure:
  23. G

    To find the forces on a composite object

    Could I please ask for help with the following: Here's a diagram: (in what follows, for clarity, I write L to represent the lower case L of the diagram). My diagram wrongly shows u (the coefficient of friction) to be the same at both points of contact. Since this image was taken I have...
  24. G

    To calculate the forces on a composite body

    Can I please ask for help regarding the following: A uniform rod AB of length 3L is freely hinged to level ground at A. The rod rests inclined at and angle of 30 degrees to the ground resting against a uniform solid cube of edge L. Contact between the rod and the cube is smooth and contact...
  25. J

    Just found out there is strontium in composite dental fillings

    I have like 5 composite dental fillings, two placed when I was nursing my babies. Found out they have strontium, barium and zirconium in them to make them radiopaque on the X-rays. Now worried I am radioactive since I have that stuff in me, worried for my kids as I was pregnant and nursing them...
  26. antonov

    Moment of inertia composite body

    I have this moment of inertia problem and is a little confused on the semicircle part and if the rest is really right? I get over 10 if I calculate it in crew CAD but by hand I get 7,568032142. What is right and what am I doing wrong?
  27. L

    Engineering Heat transfer from composite pipe -- Is my answer right?

    Im practicing the questions in the problem book and seem to be getting different answers to the book can somebody check cheers. [Answers: 57.99 W/m: 1739.7 W: 84.9ºC] textbook answers A water pipe of bore 65 mm bore and 6mm wall thickness, carrying water at 85ºC is insulated with one layer of...
  28. T

    Engineering Why is it expensive to recycle composite materials?

    I have read a document where it says that composite materials are expensive to recycle but did not explain why. However, I am searching and find only a few papers and answers.
  29. A

    Poisson ratios for Orthotropic materials (composites)

    I'm new to composite materials. I've studied mechanical engineering but I am actually usually involved in hydrodynamics (in which I've done my masters). However for a project we do fluid structure interaction with composites, and as these things go, you cannot get away with the 'black box'...
  30. anemone

    MHB Is a Always Composite Given the Integer Condition?

    Positive integers $a$ and $b$ are such that $\dfrac{5a^4+a^2}{b^4+3b^2+4}$ is an integer. Prove that $a$ is composite.
  31. S

    Solution of inequality of composite function involving inverse

    I can solve (i), I got x = -1.6 For (ii), I did like this: $$(f^{-1} o ~g)(x)<1$$ $$g(x)<f(1)$$ But it is wrong, the correct one should be ##g(x) > f(1)##. Why? Thanks
  32. greg_rack

    Solving an immediate indefinite integral of a composite function

    That's my attempt: $$\int (\frac{1}{cos^2x\cdot tan^3x})dx = \int (\frac{1}{cos^2x}\cdot tan^{-3}x) dx$$ Now, being ##\frac{1}{cos^2x}## the derivative of ##tanx##, the integral gets: $$-\frac{1}{2tan^2x}+c$$ But there is something wrong... what?
  33. Urika

    Engineering Composite Manufacturing Question

    Hello. My question is related to Materials & Manufacturing. I have attached the question plus my solution. Pls guide me if its okay
  34. anemone

    MHB Prove that the sum of 6 positive integers is a composite number

    Let $a,\,b,\,c,\,d,\,e,\,f$ be positive integers and $S=a+b+c+d+e+f$. Suppose that the number $S$ divides $abc+def$ and $ab+bc+ca-de-ef-df$, prove that $S$ is composite.
  35. anemone

    MHB Prove 9999999+1999000 is Composite Number

    Prove that the number $9999999+1999000$ is composite.
  36. AN630078

    Composite and Inverse Functions Problem

    1. a. fg(x)=2(1/2(x-1))+1 fg(x)=2(x/2-1/2)+1 fg(x)=x-1+1 fg(x)=x gf(x)=1/2((2x+1)-1) gf(x)=1/2(2x+1-1) gf(x)=x+1/2-1/2 gf(x)=x The functions functions f(x) and g(x) are inverses of each other. This can be demonstarted by f(x)=2x+1 y=2x+1 x=2y+1 x-1=2y (x-1)/2=y Thus, y=1/2(x-1) = g(x) And...
  37. M

    Mass moment of inertia of a composite shape

    My thought process was to get the mass moment of inertia of the rectangle and then subtract the mass moment of inertia of the quartercircle from it. The MMoI of the rectangle is: (1/3)(0.005*7850*.6*.3)(.3^2)= 0.212 meters The MMoI of the quartercircle is: (1/4)(0.005*7850*¼π 0.3^2)(.3^2) + ? My...
  38. S

    B Domain of a composite function

    ##f(x)=-x^2 + 3## so ##f^{-1} (x)=- \sqrt{3-x} ~, x \leq 3## ##ff^{-1} = - (- \sqrt{3-x})^2 + 3 = x## and the domain will be ##x \leq 3## ##f^{-1} f = - \sqrt{3-(-x^2+3)} = -x ## and the domain will be ##x \leq 0## My question: ##ff^{-1} (x)## or ##f^{-1} f(x) ## is not always equal to...
  39. srfriggen

    Comparing the domains of composite functions

    Hello, I have attached my question and the work. I believe the answer is correct. Looking for verification. Thank you!
  40. rxh140630

    Formulas for computing composite function

    h(x) = 0 for x ≤ 0 h(x) = x^2 for x>0 But my book says h(x) = 0 for x<0 h(x) = x^2 for x≥0 Can my solution (the first one) work as well? Because the actual function value at x = 0 is zero. I feel like my solution is more elegant.
  41. anemone

    MHB Solving 8 Roots: Can 3 Quadratic Polynomials Fulfill $f(g(h(x)))=0$?

    Is it possible to find three quadratic polynomials $f(x),\,g(x)$ and $h(x)$ such that the equation $f(g(h(x)))=0$ has the eight roots 1, 2, 3, 4, 5, 6, 7 and 8?
  42. cwill53

    How much ice is needed to cool 31055.04J of water from 42°C to 0°C?

    My answer: a. $$H=\frac{dQ}{dt}$$ $$H_{brass}=H_{copper}$$ $$(109\frac{W}{m\cdot K})(0.005m^2)\frac{100^{\circ}C-T_{c}}{0.3m}=(385\frac{W}{m\cdot K})(0.005m^2)\frac{T_{H}-0^{\circ}C}{0.8m}$$ $$T_{H,Cu}=T_{C,brass}=T_{2}$$ $$-1.8166667T_{2}+181.666667^{\circ}C=2.40625T_{2}\Rightarrow...
  43. Janosh89

    B Possible factor(s) of 2^(12n+9)+1

    It seems to hold true .. n factor(s) of (24n+19) (24n+19) divides 2(12n+9)+1 ? 0 19 YES 1 43 YES 2 67 YES 3 7, 13 NO 4 23, 5 NO 5 139 YES 6 163 YES 7 11, 17 NO 8 211 YES 9 47, 5 NO 10 7, 37 NO 11 283 YES
  44. S

    Correct statement about composite and inverse functions

    f-1(f(A)) = A and f-1(f(B)) = B so options (a) and (c) are wrong. For (b), I get A ⊆ A For (d), I get B ⊆ B For (e), I get A ⊆ A So there are three correct statements? Thanks
  45. A

    Introductory application of the Newton Euler equations to a composite body

    α is the second derivative of angle and w is the first derivative In the free body diagrams the only force on A is the normal force since it is only constrained not to move vertically. Have I drawn the free body diagram and kinetic diagram correctly? By relating the accelerations of the...
  46. M_Abubakr

    Micromechanical Vibration Analysis of Composite Materials

    This project is stressing me out along with other workload and I'm in panic mode right now. The brief of the project is in the attachment. I can interpret 4 objectives out of this: (1) Analysing the relation of the physical parameters in the composite material with the characteristics of wave...
  47. J

    Engineering What is the formula for calculating the density of a composite material?

    Does anyone have an equation for the resultant density of the composite materials? Having a look around the internet and I can't find anything, there was this one website that gave me a step-by-step but the answers did not match (sciencing.com)
  48. FutureEngineer1720

    Micromechanics of High Strain Rate Loaded Composite Media

    I would like to know some guidelines regarding this topic. The characteristics of wave propagation depend highly on the orientation of fibre (unidirectional and warp & weft arrangement), fibre volumetric fraction, relative fibre modulli etc. What is the relation of wave propagation and these...
  49. S

    I Generating samples on a 2-D composite binomial distribution

    I would like to generate (X,Y) pairs such that they would follow a distribution something like this: This is the sum of three normal distributions. Each distribution could have a different taper along the X and the Y, plus an offset along X and/or Y. So the parameters of these three...
  50. Adgorn

    Limit of the remainder of Taylor polynomial of composite functions

    Since $$\lim_{x \rightarrow 0} \frac {R_{n,0,f}(x)} {x^n}=0,$$ ##P_{n,0,g}(x)## contains only terms of degree ##\geq 1## and ##R_{n,0,g}## approaches ##0## as quickly as ##x^n##, I can most likely prove this using ##\epsilon - \delta## arguments, but that seems overly complicated. I also can't...
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