Relationships Definition and 167 Threads

Hello all, I'm doing some major review for a upcoming final and am making sure to fill in some arithmetic gaps. I am trying study using only my equation sheet given for my course. I am having a hard time understanding the relationships between some of the equations that are given...

This is just basic algebra for the energy-momentum relationship, but the calculations confuse me. May I ask what is wrong with my concept or calculation causing the following problem. Maybe it's because I'm getting older, my ability to think and calculate has declined...

PHOTOGRAPHIC REDUCTION OR ENLARGEMENT The proportions of a circle never change. But... Question: If a circle is always a circle, then how is it possible that the S/L and {[S/L]/R} ratios of a circle can vary as a function of the radius size?

I have a number, the high, that could be positive, negative or zero and can be a fraction. I have another number, the low, that could also be positive, negative or zero and can be a fraction. I have another number, the variable that is between the high and the low. It is safe to say that the...

Hello, I am studying geometry with an app on my phone. There was a difficult problem, which had two different explanations for solving. I correctly understood one explanation. I reviewed later without memory of the problem at all. There was an obvious attempt from what was learned previously...

Homework Statement:: Not a homework problem. I need a conceptual explanation. Relevant Equations:: ##p_2 = p_1 + \rho g(y_1 - y_2)## (1) ## p = p_0 + \rho gh## (2) When deriving equation (1) we use the example of a submerged cylinder in static equilibrium with its top at position ##y_1## and...

If propositions ##p,q\in{\mathscr L}_{\mathcal H}## (i.e., the lattice of subspaces of ##\mathcal H##) are incompatible, then ##\hat p\hat q\neq\hat q\hat p##. But since it's a lattice, there exists a unique glb ##p\wedge q=q\wedge p##. How are they mathematically related? In particular, I...

Homework Statement Here's a derivation of the adiabatic PVT relationships. QUESTION: When solving adiabatic PVT homework problems I found that I needed to express temperature in Kelvin, rather than Celsius, to get the right answers. Where in this derivation should this be specified, and how...

I am trying to understand how a blazed diffraction grating works and came across a deduction I don't understand. I believe that you don't need to know much about optics to answer this question as it is more geometry related. I have the diagram below of a diffraction grating with all the relevant...

Hi there - it has been quite a long time since I took Calculus. I am trying to brush up and understand where to start with this question: Starting with the identity a^x = e^xlna, derive the relationships between (a) e^x and 10^x; (b) ln x and log x. Note: log x = log10 x unless otherwise...

f(\vec{x}+\epsilon \vec{y})-f(\vec{x})=\epsilon \mbox{d}f_{\vec{x}}(\vec{y})+O(\epsilon^2). Is ##\mbox{d}f_{\vec{x}}(\vec{y})## dual vector and why? Is it because ##\mbox{d}## is linear transformation? Also why equality f(\vec{x}+\epsilon \vec{y})-f(\vec{x})=\epsilon...

Are there any relationships between the speed of light and the virtual particles in the vacuum? I mean that, Can I call it as a medium of propagation of a light beam?

[SOLVED] Okay so I have an assignment to do with only 1 question left incomplete because we have not covered this section yet, non the less it is due soon and I can't find any helpful resources on how to do this question. I know it has something to do with graphs but I'm still lost. So if...

Homework Statement Refer to this pic https://www2.southeastern.edu/Academics/Faculty/rallain/plab193/page1/page37/page37.htmlor I was wondering how increasing the mass at the bottom would influence the time taken for the object to complete 10 revolutions, my hypothesis was that it would...

So, my pre-algebra class is learning about linear relationships, but can anyone help explain it to me a little more? I tried google, but honestly, I want to hear other people before jumping to conclusions. So, my question is, what is a linear relationship?

Homework Statement After plotting a graph with frequency (f) of a wire on the y-axis and tension (C-Clamps) on the x-axis, a root curve was obtained. If the trend of the line is maintained, does it pass through the origin? Should it? Note: graph attached Homework Equations f is proportional...

Homework Statement An experiment was conducted to determine the relationship between metre-stick projection from a table (L) on the vertical depression of the free end (y). Using the collected data, graphs had to be plotted until a linear relation was found, and the equation of the line had to...

Homework Statement [/B] Given a a log-log graph with 8 lines, you must determine the equation of each line in its original relationship. The slope of the graph (m) gives the power of the original relationship. Examples: if m = 2, 3; then y ∝ x^2, x^3, etc. if m = -1, -2; then y ∝ 1/x...

What will be the graph of v=Vmsin(wt+theta) and v= Vmsin(wt-theta) and why?:oldconfused:

The question I am asking comes from a side issue in another thread. I am seeking an explanation that will explain my wrong understanding of the physics. https://www.physicsforums.com/threads/q-re-wiki-equation-for-t-x-t-2.903984 In post #19 of the above thread I describe my uncertainty about my...

Homework Statement I have ## f(t) = \sum\limits^{\infty}_0 a_{n} e^{2 \pi i n t} ## [1] and ## g(t) = \sum\limits^{\infty}_0 b_{n} e^{ \pi i n t} ## [2] I want to show that ##b_n = a _{2n} ## Homework Equations see above. The Attempt at a Solution [/B] So obviously you want to use the...

Homework Statement 2. Homework Equations 3. The Attempt at a Solution [/B] For part (c), should the phasor diagram just have everything on a straight line, save for the Rt and Vrt? Honestly not sure how to attempt part (d) as we never really covered phase relationships in lectures, just...

Homework Statement Prove that ##\int _0^a\left(\frac{f\left((sin(ln(c))x\right)+\sqrt{\cos \left(e-\pi ^2\right)}}{\ln \left(\pi ^2-e\right)+\pi ^2\sqrt{\cos \left(e-\pi ^2\right)}}\right)dx## is a probability density function (when ##a=\frac{1}{\pi ^2}##) given that ##\int _0^{\pi...

Can someone explain to me the relationships with this equation (and probably any other equation). For example i don't fully understand how the ΔX is inversely related to the d. I have an idea of how this is so, however i can't really picture it with numbers. If you could explain the...

I'm confused about in phase and definite phase relationships. Please correct me if I am wrong. 1. Two waves of 360 degree phase difference are in phase. 2. Two waves that are 180 degree out of phase are classified as having definite phase relationships.

Hi Everyone, I will try to keep this short as I can and to the point, there is a bit of a back story, so bear with me. For the last 18 months (on and off as life allows), I have been trying to develop an induction heating assisted machine for 2 reasons. 1 - To learn as much as I can by doing...

Can some please explain to me how to solve these two questions? Let A, B and C be any sets, prove that: (a) A-B ⊂ A (b) (A∩B) complement = A complement ∪ B and (A∪B) complement = A complement∩ B complement.

I know everyone here must know this but it is a new revelation to me and very interesting. But I have a question about the reason behind the following... Take ##x^2+10x+10## for example. Any coefficient of ##x^2## modifies the "zoom" of the parabola, for lack of a better word, and determines...

A quadratic equation in this format x² - 2 A x + B² = 0 can be modified and expressed like: x² - 2 (u) x + (u² - v²) = 0. The roots x1 and x2 are therefore: x_1 = x_1(u,v) = u + v x_2 = x_2(u,v) = u - v Or: x_1 = x_1(a, b) = \frac{a+b}{2} + \frac{|a-b|}{2} x_2 = x_2(a, b) = \frac{a+b}{2} -...

in particular f=Gm1m2/r^2?sorry if my question sounds very irrelevant.if f is proportional to m1m2 it implies f=some constant times m1m2.okay.at the same time f is inversely proportional to r^2 .so force = some other constant times 1/r^2.okay.but in most places i see that what is done is they...

Hi, I saw a derivation in a book and I don't see the logical connection. Suppose 1.\ \ a=b \text{ and } 2.\ \ x=y Then 3.\ \ a-b= \lambda (x-y) makes sense to me since 0=\text{Anything}⋅0 However they said "similarly" 4.\ \ a+b= \mu (x+y) , and this I don't understand. To me a+b= 2a...

Hi All, The "best practices" in RDB on 1:1 relations between entities are that the two entities E1, E2 should be merged into a single one by default, i.e., unless there is an overwhelming reason to keep them separated. Can someone provide illustrating examples of when the two entities...

Homework Statement Using the given equations prove that Homework Equations , ,[/B] + (it won't render together in Maple for whatever reason) The Attempt at a Solution So I started with expanding the Jacobi Identity (the third relevant equation) and through tedious algebra arrived at...

What are the mathematical relationships (if any) between the particles as described by Quantum Mechanics and the particles described by Quantum Field Theory? A specific question related to the general question above arose in post #14 of the thread: How can a particle be a combination of other...

So I have been looking around throughout the physics forum and other sources and still can't seem to find a good general explanation of how Life, and energy are related. First let me propose some definitions to help further our discussion and clarify what i mean. Life, in the way it concerns us...

this is the gyroscope I am talking about: the variables are: -the angular velocity of the disk -the angular velocity of precession -the amount of force "applied" by the disk upward or downward

It seems to be implied, but I can't find it explicitly - the order in which linear operators are applied makes a difference. IE given linear operators A,B then AB is NOT necessarily the same as BA ? I thought it was only with rotation operators that the order made a difference? I noticed this...

A couple of times I have come across the suggestion that numerically evaluating a recursive relation in reverse can be a valuable approach. I can see this where, for example, the boundary conditions at one 'end' are inaccurate or undiscoverable. However, while the arithmetic of manipulating...

Many physical laws involve relationships between time derivatives to space derivatives of one or more quantities. For example, thermal conduction relates the thermal energy time rate of change [dQ/dt] to temperature space rate of change [dT/dx]. In fluid flow, the Navier-Stokes Theorem relates...

Homework Statement Homework EquationsThe Attempt at a Solution a) I am having some trouble understanding the notation. I'm uncertain whether it should be $$ \langle {f} | \hat {O_{2}} | g \rangle = \int_{-\infty}^{\infty} f^{*}g \frac {dg}{dx} dx $$ or $$ \langle {f} | \hat {O_{2}} | g...

Why is gravitational potential energy directly related to the distance of between two objects (mgh, so as distance increases, potential energy increases) while electric potential energy is inversely related (kq1q2/r,distance increases, electric potential energy decreases)?

I'm hoping for some help finding an alternative forum for this search. As a non-physicist pathologically curious about admittedly philosophical questions regarding physical concepts, I often come to PF for clarification of ideas that I'm chasing. Unfortunately, these ideas almost always boil...

I don't understand the relationships between the integration limits of Maxwell Equations (specifically the ones in integral form in matter) Is this related to Stokes/Gauss' Theorems? or something else?

The following are some good references that I recommend on building and maintain relationships: Dating: Every person should read about attachment theory. An understanding of attachment theory allows one to not only understand his or her self, but it will also help understand partners...

Homework Statement Explain in details in one paragraph (without using formulas) what effect the weight of a block has on the normal force, frictional force, and coefficient of friction. How would you increase or decrease the coefficient of friction? Homework Equations Give me any...

How does weight affect air resistance? [i.e A heavy feather falling v.s a light one}Please be simple

I'm trying to come up with an expression for \partial y / \partial x where z = f(x,y). By observation (i.e. evaluating several sample functions), the following appears to be true: \begin{equation*} \frac{\partial z}{\partial x} + \frac{\partial z}{\partial y} \cdot \frac{\partial y}{\partial...

I'm having trouble understanding the relationships between various variables at play in diffraction. Say you have diffraction with one slit, two slits, and a grating as shown below. So 1) The Amplitude of each peak is directly proportional to the intensity of the incoming waves. This makes...

Hello, I'm trying to get a hang of the defintion presented in Arfken - Mathematical Methods for Physicists for 3 dimensional rotations (a setup for an introduction to tensors). That being said I'm a Physicist and I'd like a component approach if possible to the explanation. They give: A_i ' =...

can you help me how to formally present a solution to this problem show that $j^2=-1$, $j^3=-j$, $j^4=1$ and $\frac{1}{j}=-j$, $\frac{1}{j^2}=-1$, $\frac{1}{j^3}=-j$, $\frac{1}{j^4}=1$. From the result of these, evaluate $j^{2312}$ and its reciprocal. sure I can solve for $j^{2312}$ and its...