What is Terms: Definition and 1000 Discussions

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  1. anemone

    MHB Solving $x$ in Terms of $a$: $x^4-3ax^3+3a^3x+a^4=0$

    Solve for $x$ in terms of $a$ in the equation $x^4-3ax^3+3a^3x+a^4=0$.
  2. R

    Calculation boundary terms of a functional

    Dear all, I am stuck with the problem which is given below; In this problem the equilibrium equations of the given functional must be derived in u, v, and w directions from which the boundary terms must be found. I think that i have derived the equilibrium equations( 5 equations), but i...
  3. S

    Source terms in Maxwell's Equations and retarded positions

    Hi All, Thanks again to all the great mentors and contributors to this forum. I wanted to ask a question about the Gauss's law/Ampere's law equations in Maxwell's Equations: \nabla \bullet \textbf{E} = \frac{\rho}{\epsilon_0} \\ \\ \nabla \times \textbf{B} = \mu \left( \textbf{J} + \epsilon...
  4. W

    Rewrite Indefinite Integral in Terms of Elliptic Coordinates

    Problem: Rewrite the indefinite integral ## \iint\limits_R\, (x+y) dx \ dy ## in terms of elliptic coordinates ##(u,v)##, where ## x=acosh(u)cos(v) ## and ## y=asinh(u)sin(v) ##. Attempt at a Solution: So would it be something like, ## \iint\limits_R\, (x+y) dx \ dy =...
  5. N

    How do you express a vector in terms of I,J,&K?

    Express the vector <1,0,0> in terms of I,J,&k. (a)*I + (b)*J + (c)*K You have to find a,b, and c. I know that I,J,&K are unit vectors and so I thought that a = 1, b = 0, c = 0. But the answer has radicals and fractions in it. I don't understand how to arrive at the solution.
  6. S

    What do you think of the terms used in this article?

    The article is about something spinning at an incredibly high rate, with a blurb from the scientist saying that the spin rate is so high that the angular acceleration is compared to gravity - which makes no sense since gravity is a linear acceleration, and as well, if it were the tangential...
  7. T

    Confirmation of some chemistry terms.

    What is the difference between: Atomic mass Relative atomic mass Atomic weight Relative atomic weight People misuse these so many times that I've confused myself. Somebody please confirm their definitions please, thanks.
  8. B

    MHB Area of a triangle in terms of the tangent function

    Hi there, the problem says, an n-gon is circumscribed around a circle so the mid point of each side is tangent to the circle. Prove the triangle consisting of one side of the n-gon and the sides from the end points to the middle of the circle has area tan(pi/n) Cheers!
  9. F

    MHB In the simplest qualitative terms what is a differential equation?

    I'm going to be taking a course in differential equations and I'm nervous. From previous calculus courses I know the derivative is the ratio of how one quantity changes with respect to another the integral is the area under the curve So what's a differential equation? According to here "A...
  10. T

    Metric expansion in terms of planck pixels

    what if the evolution of the universe over time and the expansion of space a series of binary events such that the same quantity of energy is divided geometrically from one into two, four, eight, sixteen pieces, such that each Planck time is equivalent to one such split and each Planck length is...
  11. B

    How scientific terms become established

    I am a bit curious about how pedagogical terminology, say what you found at the glossary of your science (or non-science) textbook gets established. My guess is that you have a pioneer in the field come up with some concepts, write articles etc. on those concepts and gives it a name, and then...
  12. karush

    MHB Find vector w in terms of i and j

    The vectors $\vec{i}$ , $\vec{j}$ are unit vectors along the x-axis and y-axis respectively. The vectors $ \vec{u}= –\vec{i} +2\vec{j}$ and $\vec{v} = 3\vec{i} + 5 \vec{j}$ are given. (a) Find $\vec{u}+ 2\vec{v}$ in terms of $\vec{i}$ and $\vec{j}$ . $–\vec{i} +2\vec{j} +...
  13. D

    Expressing q in Terms of a_1,b_1,a_2,b_2

    Homework Statement A tangent line at point A with coordinate (a,f(a)) of function f(x) intersects f(x) at point B coordinate (b,f(b)) . A vertical line is drawn from point p (a<p<b) and intersects f(x) at C. From C a perpendicular line to the tangent line is drawn which intersect the tangent...
  14. O

    Quadratic Air Drag and Bullet Motion: Solving for v^2 in Terms of x

    Homework Statement A gun is shoot straight up. Assuming that the air drag on the bullet varies quadratically with speed, and the equation of motion for the bullet is (m/2)(dv^2/dx)= -mg-(cv^2). Find for the downward motion , v^2 in terms of x. Taking that upward direction is positive...
  15. M

    Archived Simple roulette in terms of circular motion

    Homework Statement I am trying to understand game of roulette through kinematic equations of circular motion. Roulette is game where a ball spins in circular motion. Initially it is accelerated such that velocity of ball increases with time however after reaching its peak value it starts to...
  16. J

    Integral in terms of summation?

    So i realize that the integral of [f(x)dx] is pretty much the height of the rectangle f(x), multiplied by the width dx. But that is the area of 1 infinitesimally skinny rectangle. How does the integral sign add up an infinite amount of rectangles? I've taken cal 2 so if you could show what the...
  17. J

    MHB Geometric Sequences help - (3 given terms, find the rest)

    I need to find the value of the first term for this geometric series. Sn = 33 tn = 48 r = -2 I know that I have to take the formulas tn = t1 x r^(n-1), and Sn = [t1 x (r^n) - 1] / (r - 1), and isolate t1 for the first formula and then input that into the second, but I don't know the actual...
  18. S

    Defining functions in terms of differential equations

    I have set myself the task of teaching my Freshman in high school brother Calculus, and today while reviewing some topics I saw something I didn't see before. To start out, I let y = ln[x] => x = e^y Obviously, we know that y' = 1/x = e^-y So, I "discovered" that one can define the...
  19. V

    Want to know what is the best in terms of friction

    i want to use a 100 cm diameter piston witch will have 4000 kg of pressure on it. Questions -how thick does the piston have to be to hold that much weight if it is made of metal? -what material should i use to make a seal to the cylinder wall and should the cylinder wall be another material then...
  20. L

    Can matter be defined strictly in terms of mass and energy?

    I was reading some articles and discussions on the topic and got confused when I read that conventionally photons and all other massless particles aren't considered a form of matter. The Wiki article on matter begins with the statement that the term itself is poorly defined. I was thinking...
  21. M

    Solving for n in a Summation Series

    Homework Statement How many terms of the AP, 12, 16, 20, 24 . . . . . must be taken for the sum to equal 408? Solution For this series, a = 12, d = 4 and Sn = 408. its asking me to solve for n and gives me the answer to n as 12 at the end but when i try to calculate it myself i don't get 12...
  22. I

    Describing system in terms of 2 variables vs natural variables

    Realised I probably posted this in the wrong forum before, should've been here.. I often see a function's differential expressed in terms of convenient partial derivatives eg dU=(dU/dT) dT + (dU/dV) dV And I've seen it written that "any system is uniquely specified by two parameters, such...
  23. S

    I need the definition of a few basic physics terms. Can anyone help?

    So, I know this stuff is probably very elementary for most of the people on this site, but I have never had physics before, and I just started physics I at college. The professor has asked us to learn a few basic physics terms and I am having a hard time finding clear definitions for some of...
  24. W

    What is Discrete Math (in layman's terms)?

    Wikipedia says it deals with distinct objects and is differentiated from continuous math, which has objects that "vary smoothly." For a layman, can someone explain what this means? And is all math discrete or continuous? No other options?
  25. Lebombo

    Difference between 2 Sum of n terms of geometric series formulas

    Difference between 2 "Sum of n terms of geometric series" formulas Notation A) S_{n}= \sum_{k=0}^{n - 1} ar^{k} = ar^{0} + ar^{1} + ar^{2} +...+ ar^{n-1} = \frac{a(1-r^{n})}{1-r} Proof: S_{n}= ar^{0} + ar^{1} + ar^{2} +...+ ar^{n-1} - r*S_{n}= ar^{1} + ar^{2} + ar^{3} +...+ ar^{n}...
  26. J

    Writing parameters in terms of given vectors

    Homework Statement Four 3-vectors a, b, c, and d are related by the equation ax + by + cz = d; where x, y, and z are real parameters. Using a suitable combination of scalar and vector products, findd x, y, and z in terms of the vectors Homework Equations The Attempt at a...
  27. A

    Write a complex valued function in terms of z

    Is there a general way of writing a complex valued function f(z)=u(x,y)+iv(x,y) in terms of z? For example, suppose that I know f(x,y)=(x/(x^2+y^2))-i*y/(x^2+y^2) How do I know that it is actually f(z)=1/z?
  28. E

    Solving for Vo in terms of Vs/Vx

    http://imgur.com/xe52P30 2. Vx= Vs(R1/R1+R2), V=IR 3. I combined the 1k Ω and 5k Ω resistors then used voltage division to find Vx. I used Vx to find Vo which I found to be (5/18)Vx. I don't know where I can do KCL or KVL to solve for Vx.
  29. A

    Solve Summation of Terms Upto n: Urgent Help

    Find the sum upto n terms: 1.3.5+3.5.7+5.7.9....tn I solve it this way: tn=(2n-1)(2n+1)(2n+3) Now can I take summation on both sides? How? I mean when I add 2 on both sides the resultant is 0(2-2=0).Similarly the resultant summation will be zero? And if I take summation I get...
  30. Mandelbroth

    Trying to understand derivatives in terms of differential forms

    Suppose we have a curve, formed by a function f that maps real numbers to real numbers, such that f is everywhere smooth over a subset D of its domain. Let's suppose that, for all x in D, there is a vector space that contains all vectors tangent to the curve at that point, called the tangent...
  31. H

    Expressing a symmetric matrix in terms on eigenvalues/vectors

    Homework Statement Generate a random 10 x 10 symmetric matrix A (already done in MATLAB) . Express A in the formHomework Equations ## A = ## \displaystyle \sum_{j=1}^{10}λ_j(A)v_jv^T_j\ for some real vectors ##v_j, j = 1, 2, . . . , 10.## The Attempt at a Solution I'm pretty sure the...
  32. M

    Equivalence of differential operator terms in action

    Hi guys, I'm sure I'm being very stupid here but I'm reading through notes which contain various actions for fields, most of which are very similar, however there is some discrepancies with the way differential operators are shown acting on the fields and I can't for the life of me work out...
  33. X

    Explanation of some nuclear terms.

    Hi everyone, I was reading the report about the Fukushima incident and I do not understand some concepts because of my limited understanding. Could you please help me? Combustible Gas Control. <----- can you explain this concept in simpler language The NRC regulations in 10 CFR 50.44...
  34. B

    How to define light in laymans terms

    So I've got to give a speech for a class soon with the informative topic of what is light. Light is just what we call the visible portion of the spectrum. How can i go about defining this to a group of college kids in a way they can understand? thanks
  35. D

    Can quantum operators be pictured in terms of wave packets?

    I've found the wave-packet picture quite useful as I work my way through the very basics of quantum mechanics. But I'm having trouble finding a wave-mechanical picture of operators. For example, at least in terms of a free particle, using the wave mechanics treatment (as opposed to the matrix...
  36. H

    Upwinding method for convection terms 2nd order PDE

    I'm trying to solve the equation $$ \frac{\partial u}{\partial t} + \frac{\partial}{\partial x}\left(Cu\right) - \frac{\partial}{\partial x}\left(D\frac{\partial u}{\partial x}\right) = f(x,t) $$ where C and D allow for linearity. I'm using a discontinuous Galerkin method in space and...
  37. D

    How to drop terms in a Lagrangian?

    Hi guys, So textbooks have it that: "Two Lagrangians differing by a total time-derivative of a function of the coordinates are equivalent". I have no idea what that means or how to use it; so I don't know which terms I can drop from Lagrangians, which is a bit of a problem. For example...
  38. Logan Land

    MHB Calculating Terms of Sequence: a1,a2,a3,a4

    write the terms a1,a2,a3,a4 of the following sequence. an+1=0.4an+330, a0=550 everytime I get 550 for a1 a2 a3 and a4 is that correct or am I doing it wrong.
  39. S

    Group Velocity in terms of Wavlength and velocity

    Homework Statement Show that the group velocity vg=dω/dk can be written as vg=v-λ*dv/dλ where v = phase velocity Homework Equations n=n(k)=c/v k=2∏/λ ω=2∏f=kv fλ=c The Attempt at a Solution dω/dk = d(kv)/dk= v+k(dv/dk)= v+ck(d(n^-1)/dk) =v-(ck/n^2)(dn/dk)...
  40. S

    Kahler potental terms linear in visible sector fields

    Hello, I have a question regarding the expansion of the Kahler potential in visible sector fields C^{\alpha} : It is usually said that the Kahler potential can be expanded as follows: K = K_{hid}(\phi,\phi^*) + K_{\bar{\alpha} \beta}(\phi,\phi^*) C^{*\bar{\alpha}} C^{\beta} + \frac{1}{2}...
  41. C

    Can Lead-lag Controllers be Converted to PID Controllers?

    Homework Statement I'm curently designing a controller, I have calculated the desired controller in terms of phase lead and phase lag, however I'm designing the controller on labview FPGA, which can only cope with a PID controller, I'm just wondering if anyone could help me by pointing me in...
  42. D

    Period of circular orbit with in terms of varying speeds and radius.

    Homework Statement A particle of unknown mass moves in a circular orbit of radius R under the influence of a central force centred at some point inside the orbit. The minimum and maximum speeds of the particle are vmin and vmax respectively. Find the orbital period T in terms of these speeds...
  43. M

    Expanding an f(x) in terms of Legendre Polynomials

    Homework Statement Expand f(x) = 1 - x2 on -1 < x < +1 in terms of Legendre polynomials. Homework Equations The Attempt at a Solution Unfortunately, I missed the class where this was explained and I have other classes during my professor's office hours. I have no idea how to begin this...
  44. T

    Can Beauty be described in terms of mathematics?

    This is Dr. Stephen Marquadt. http://img404.imageshack.us/img404/1373/stephenmarquardt.jpg When he was a young child, his mother was horribly disfigured in a car crash. So he eventually took the route of becoming a reconstructive plastic surgeon. As a plastic surgeon, he had to work out...
  45. N

    Potential energy of pendulum in terms of displacement.

    Hi guys, I'm having troubles finding how to write the potential energy of a 1D pendulum down. In terms of displacement however. This should be easy and it is, but my professor had this nice "clean" solution whereas mine is really dreadfull, any help? :) edit: Ok nvm guys. I was thinking I went...
  46. M

    Find the resolving power of a microscope in terms of its diameter

    Find the resolving power of a microscope lens in terms of its diameter Homework Statement In this problem, we will find the ultimate resolving power of a microscope. First of all, in order to obtain a large magnification, we want an objective lens with a very short focal length. Second, in...
  47. G

    Factoring in terms of a variable

    Homework Statement ((1/3)(y^3))+(1/y)=.5*ln((x^2)+1) Solve in terms of y Homework Equations The Attempt at a Solution I am in college differential equations, and i just can't solve in terms of y. y teacher wants that...i tried wolfram alpha, etc. How on Earth do you factor this...
  48. G

    Nth term of alternating series with two positive terms at beginning

    (I hope this is the right subforum) I'm talking about the series 1, 1, -1, 1, -1, 1, -1... I thought about it for a long time but I have no idea. If that first term were gone it would just be (-1)^(n+1), but...it's there...
  49. M

    Compact linear operator in simple terms?

    Hi, I'm struggling to understand this concept. I think the term probably comes from functional analysis and I don't know any of the terms in that field so I'm having trouble understanding the meaning of what a compact linear operator is. I posted this in linear algebra because I'm reading...
  50. B

    MHB How do I isolate y in terms of x?

    I feel like I should know this already, but I need to isolate y in the equation: x= 6y-y^2 I was thinking of using the quadratic formula, but that would keep the equation in terms of x. No matter how I seem to slice it, I can't figure out what to do... Which is kinda sad that I'm doing good on...
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