Sign Definition and 596 Threads

Given is the diagram shown in the context: My solution: However, the correct solution is I am confused with the direction and signs of the system. How would I derive the solution? Thank you for your help.

I understand the approximation statement but he divide the |delta t| in the left but only delta t on the right. Is it true because delta phi would have the same sign as delta t ?

For this problem, I am confused how they get all their negative definite, positive definite, and negative semidefinite domains. I agree that ##V_2## is positive definite by definition. However, for ##V_3## I think they made a mistake since by definition, ##V_3## is negative simi-definite. I'm...

For this problem, However, I'm confused how their got their solution. My solution is, using set builder notation, ##[ (x,y) \in \mathbf{R} : 1 - \cos x + y^4 ≥ 0 ]## which implies that ##V(0,0) = 0## so it satisfies the first condition for being sign definite, sign semidefinite, and sign...

Hello Forum, I have read about an interesting example of multiple linear regression (https://online.stat.psu.edu/stat501/lesson/12/12.3). There are two highly correlated predictors, ##X_1## as territory population and ##X_2## as per capita income with Sales as the ##Y## variable. My...

Im so confused on these solutions here for the shear stresses. Why is Tau_V sometimes negative and sometimes positive? Can someone please explain this and maybe illustrate? Here for example. Heres the solution for problem b): Here Tau_V (talking about F_xQ/(Ir) ) is negative, so how im...

Shouldn't work be minus when the man climbing up and force on him is down? shouldn't the power be also in minus? Can someone explain to me why is it positive please!

From the picture, the particle experiences upwards force. But how to determine the direction of motion? I think there are two possibilities: if the particle is positive, it moves from Q to P and if it is negative it moves from P to Q. Thanks

Is it generally the case even with light like paths that ##\dot t>0##?

Trying to model friction of a linear motor in the process of creating a state space model of my system. I've found it easy to model friction solely as viscous friction in the form b * x_dot, where b is the coefficient of viscous friction (N/m/s) and x_dot represents the motor linear velocity...

And have all molecules or even atoms negative energies? So when a molecule have energy let's say -70 Ha and the other -75 Ha, does it mean that the second molecule has a lower energy?

I recently submitted a self-authored article with no affiliation to a peer reviewed journal, which then got desk rejected. The email however wasn't a generic one; the editor made a comment about its content that clearly indicates he read the whole thing, but he didn't correct me or say anything...

Attempted creating equations for zeros of torque and components of forces in x and y as seen in picture. Got lost with having only variables and the d & 2L for the length of the beam. Not sure how to do the question with two points of contact between the beam and the sign. Is the center center...

Part -B $$\sum \tau_{cw} = \sum\tau_{ccw}$$ $$\tau_B=\ torque\ of\ the\ beam $$ $$\tau_S =\ torque\ of\ the\ sign\ board$$ $$\tau_C = \ torque\ of\ the \ cable$$ $$\tau_B+\tau_S = \tau_C$$ $$F_B\cdot d_1 + F_S\cdot d_2 = F_C \cdot d_3$$ Since the tension in the left and right chains are evenly...

If there are two charges positive and negative and their electric field point in the same direction then the total electric field would be their sum of magnitudes. Why don't we consider the sign of the charges? For example, a parallel plate capacitor is inside the region where both the positive...

Considering the FLWR metric in cartesian coordinates: ##ds^2=-dt^2+a^2(t)(dx^2+dy^2+dz^2)## With ##a(t)=t##, the trace of the extrinsic curvature tensor is ##-3t##. But why is it negative if it's describing an expanding universe, not a contracting one?

When a spinor is rotated through 360◦, it is returned to its original direction, but it also picks up an overall sign change. This sign has no consequence when spinors are examined one at a time, but it can be relevant when one spinor is compared with another. Is there an experiment to make an...

Hello everyone. I use Bio Savar's law to determine the intensity of the magnetic induction vector. I use this formula R is distance of wire from point in which I calculate intensity of the magnetic induction. How can I known which angle is positive and which angle is negative from this two...

Summary:: Figure b also shows that there is no negative sign in Faraday's Law. How do I know when to include the negative sign?

So for the transmissibility ratio equation, after doing a lot of questions when damping is zero and I have to take the square root of the denominator. Some questions take the positive root (1-r^2) while for other questions the solution takes the negative root (r^2-1). Can someone explain when we...

Let ##f:[0;1)\to\mathbb{R}## and ##f\in C^1([0;1))## and ##\lim_{x\to1^-}f(x)=+\infty## and ##\forall_{x\in[0;1)}-\infty<f(x)<+\infty##. Define $$A:=\int_0^1f(x)\, dx\,.$$ Assuming ##A## exists and is finite, is it possible that ##\text{sgn}(A)=-1##?

Could I please ask for help with the following question: The last part follows easily from the first part. Answer from back of book for first part is: 2/(3u') <= tan(Ɵ) <= 2u What I have done is the following: Here's my diagram (I have separated the components to show the internal forces...

Hello everyone, I've been struggling with this problem for 1 hour so far. homework-and-exerciseselectric-cir

Adopt the speed of light equals one. Calls ##cos = c##, ##sin = s## $$ux' = \frac{v-uc}{1-uvc}$$ $$uy' = \frac{us}{\gamma(1-uvc)}$$ $$tan \theta' = uy' / ux' = \frac{us}{\gamma(v-uc)}$$ So that's basically my solution. The problem is: The answer is ##\frac{us}{\gamma(v+uc)}##. Now, i can't...

I have just met linearized gravity where we decompose the metric into a flat Minkowski plus a small perturbation$$g_{\mu\nu}=\eta_{\mu\nu}+h_{\mu\nu},\ \ \left|h_{\mu\nu}\ll1\right|$$from which we 'immediately' obtain $$g^{\mu\nu}=\eta^{\mu\nu}-h^{\mu\nu}$$I don't obtain that. In my rule book...

In Chandrasekhar's book, The Mathematical Theory of Black Holes. The sign of Einstein equations is minus "-" , Eq. (1-236). However, the sign of Riemann and Ricci tensor are the same as MTW's book. The sign of Einstein equations in MTW's book are "+"! Is there a error?

So I know that E = -ΔV/Δs. If I wanted to solve for change in potential I could rearrange this equation and get Δ = -E*ds. With that information I believe I can solve the problem below. But in both solutions provided below, the negative sign goes away. Now I know I can pull the E out because it...

In orbital mechanics, the effective potential is given by ##\frac {1} {2} m r^2 w^2##, which can be expressed in terms of angular momentum ##L## which is conserved. Yet, https://web.njit.edu/~gary/321/Lecture17.html apparently shows the centrifugal potential as the negative of the above...

Hi everyone :smile: . I had came across a simplified simplified rocket lateral dynamics model :https://github.com/build-week/hover-jet/blob/feature/start-design-scripts/design-scripts/jet_vane_speed.ipynb . It has vanes at the exit which generate lift force and can control the rocket...

In a video, a person discussed how to solve modulus problems with a negative sign. This is the link of that video lecture. He showed two methods to solve the problem. The first method is commonly used. Later he showed another method where he used a number line and a graph. Unfortunately, I...

It's about problem 106 and 107 in Gauge Fields, Knots & Gravity. There's a wormhole of topology ##\mathbf{R} \times S^2## on which has been defined a spherical metric ##g = \mathrm{d}r^2 + f(r)^2 (\mathrm{d} \phi^2 + \sin^2{\phi} \mathrm{d} \theta^2)## as well as a 1-form ##E =...

First i calculated the sign Force which was 4*9.81 = 39.24N which meant that the force already exceeds the traction force. What i don t understand in the question is how the distance h will avoid this?

I have heard many times that it does not matter where you put the zero to calculate the potential energy and then ##L=T-V##. But mostly what we are doing is taking potential energy negative like in an atom for electron or a mass in gravitational field and then effectively adding it to kinetic...

Hello: I was looking for a widespread convention (akin to Hibbeler's, Beer's, etc) that deals with the sign convention of a vertical bar for bending moments. For example, without knowing in advance, how do I draw the bending moment at a cut passing through point E in the figure attached? Beam...

Hi, I have recently learned the technique of integration using differentiation under the integral sign, which Feynman mentioned in his “Surely You’re Joking, Mr. Feynman”. So, I decided to try it on the Gaussian Integral (I do know the standard method of computing it by squaring it and changing...

Since the index of the root is odd, the domain is going to be ##R##, and I can calculate the second derivative to be: $$y''=\frac{1}{3}\times \frac{e^x(e^x-3)}{3(e^x-1)^{\frac{5}{3}}}$$ Studying the sign of this function, it results positive for ##x<0 \vee x>ln(3)##, so the main function will be...

Question: Solution: Issue: I would like to know why ##\Delta m=-\Delta M## rather than ##=\Delta M## if minus signs have been used in the second equation. Thank you.

I am able to simplify/evaluate the above equations correctly, however I end up with an incorrect sign for each answer (i.e positive when it should be negative) and I can't see where the error is. I feel I am clearly missing something but having checked my working including with a calculator for...

I am not sure how to determine the sign of this derivatives. (a) first we can pass a plane by (1,2) parallel to XZ (y fixed) and see how the curve belongs to the plane will vary with x, but what about the next partial derivative, with respect to y?

I realize that this is to be solved by breaking up the object into simple objects and using their known center of mass to find the center of mass of the entire object. 1. In the solution the circular gap is also considered in the calculations with a negative center of mass, why is this done? 2...

I am a bit confused on the definition/convention of work. In some books I see statements that say : "If work is done on the system, its sign is positive. If work is done by the system, its sign is negative." And in other books I see things like: "By convention, work is regarded as positive...

Could it be said that since ##a=A(f(x))\sqrt{f(x)}##, with ##A(x)\in\{1,-1\}## then ##a^2=f(x)##,, that ##a## is the square root of ##f(x)## ? In other words could the sign of the root depend on the argument inside it ? Else it would have to be chosen by human free will and to be blocked for...

Hello, everyone. I know that it is feasible to exchange the order of one variation sign and one integral sign. But there gives a proof of this in one book. I wonder about a step in it. As below marked in the red rectangle: How can ##\delta y## and ##\delta y^\prime## be moved into the integral...

A common definition seems to be that emf is an electrical action produced from a non-electrical source. So, for instance, a voltage might develop across a resistor due to a gradient of electric charge across the resistor, however this isn't an emf since the source is electrostatic in nature. As...

Just to clarify, I'm aware of the two equivalent expressions of the first law ##\Delta U = Q + W## and ##\Delta U = Q - W## when applied to a certain system, though my question is primarily about ##Q## - for which, as far as I am aware, the convention is almost universally that ##Q > 0## if heat...

I note the general Taylor series for ##a(t)## as: \begin{equation} \begin{split} a(t)&\approx a(t_0) + a'(t_0) (t-t_0) + \frac{1}{2!} a''(t_0) (t-t_0)^2 ... \end{split} \end{equation} which I rewrite as: \begin{equation} \begin{split} a(t)&\approx a(t_0)\left(1 +...

In electrochemistry, we define ##E_{cell} = E_{cat} - E_{an}##, the difference between the electrode potentials of the cathode and the anode. This has the effect that if the reaction is spontaneous, we obtain a positive ##E_{cell}## and if it is not - i.e. we need an external driving voltage...

For passive electrical components, I can understand the need for the passive sign convention - i.e. taking the voltage to be the potential on the side where the current enters (higher potential, for a passive component) minus the potential on the other side. For a resistor, this means the change...