Positive Definition and 963 Threads

Given that a, b, c are positive reals and not all equal, show that $\dfrac{a^3 + b^3 + c^3}{a^3b^3c^3}\ge\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c}$

Homework Statement So as I understand, a negative Corona discharge happens between an electrode/pin/rod and a plane electrode. When the sharper electrode is connected to the negative (DC) plug, electrons concentrate on the tip, when sufficient breakthrough voltage is achieved a discharge...

Usually when we calculate the kinetic energy acquired by a positive charge as it moves in the direction of the electric field produced by another positive charge, we assume that the source charge remains stationary and so the loss in potential energy for the moving charge is equal to its gain in...

Good morning, How do we prove that the number zero is a negative or positive number?

Homework Statement A positive point charge q is located off-center inside a conducting spherical shell.We know from Gauss’s law that the total charge on the inner surface of the shell is −q. Is the surface charge density negative over the entire inner surface? Or can it be positive on the far...

I am aware of what positive and negative polarities are but what specifically causes the distinction between positive and negative polarity?

Hello! I want to prove that the probability current is a continuous entity at the boundaries of the square for the situation of 0< E< Vo in the problem where V is zero except a finite region in space where it is +Vo and we consider an incoming particle from the left(for example). I thought that...

This references a specific problem in my Physics class in relations to electrical potential and electrical fields, but I kind of want a more general answer in terms of physics. So obviously, I know that distance is always positive. However, when I was given a problem to solve, there were 3...

Homework Statement I am trying to prove the following: if ##A\in C^{m\ \text{x}\ m}## is hermitian with positive definite eigenvalues, then A is positive definite. This was a fairly easy proof. The next part wants me to prove if A is positive definite, then ##\Delta_k##=\begin{bmatrix} a_{11} &...

Problem: Prove that any positive fraction plus its inverse is greater than or equal to two. Proof: $$\frac{a}{b}+\frac{b}{a}\ge2$$ $$\frac{a^2+b^2}{ab}\ge2$$ $${a^2+b^2}\ge2ab$$ $$a^2+b^2 - 2ab\ge0$$ $$a^2 - 2ab + b^2\ge0$$ $$(a-b)^2\ge0$$ This is true for all a and b: Case 1...

Homework Statement Calculate the acceleration of a 1400kg car if it can stop from 35km/h (9.72m/s) on a dime (diameter= 1.7cm) (0.017m). What is the force felt by the 68kg occupant of the car? Homework Equations v^2=v0^2+2a(x-x0) F=ma The Attempt at a Solution ok after solving for a in that...

Homework Statement A 14.0kg bucket is lowered vertically by a rope in which there is 163N of tension at a given instant. What is the acceleration of the bucket. Homework Equations ƩF = may The Attempt at a Solution I know how to solve this but I got it wrong because of the signs. Since the...

Prove $$\frac{ab}{a+b+ab}+\frac{bc}{b+c+bc}+\frac{ca}{c+a+ca}\le \frac{a^2+b^2+c^2+6}{9}$$ for all positive real $a,\,b$ and $c$ and $a,\,b,\,c\ne 0$.

Homework Statement In the diagram below, each division on the horizontal axis (the displacement s) is 0.10 m while each division on the vertical axis (the electric potential V) is 1.0 V. What is the electric field component along the displacement axis s in each of the regions specified below...

So this is something that troubled me a bit- in Shankar's PQM, there's an exercise that asks you to find the position expectation value for the harmonic oscillator in a state \psi such that \psi=\frac{1}{\sqrt{2}}(|0\rangle+|1\rangle) Where |n\rangle is the n^{th} energy eigenstate of...

Hello, I'm sure most of you are already familiar with the book "Mechanics" by Landau and Lifshitz. There's a section that I do not understand. In section 4 towards the end they mentions that "It is easy to see that the mass of the particle cannot be negative." They then give the argument that...

Physicists have observed the cosmic radiation background to conclude that the universe is flat (or within the margin of error of being flat). This means that the Universe contains the critical density needed to keep it flat, which is a mix of ordinary matter, dark matter and dark energy (I...

Homework Statement It says that a horse gallops 116m away from its trainer in 14.0s and then abruptly turns and gallops halfway back in 4.8s. I need to calculate average velocity . displacement/ time elapsed. displacement is xf-xi. Homework Equations avg velocity= displacement/ time...

What happens when negative plate of a charged capacitor is connected to positive plate of another charged capacitor and vice versa. ?

Determine all triples of positive integers $x,\,y,\,z$ such that $z\ge y\ge x$ and $x+y+z+xy+yz+xz=xyz+1$.

I'm a little confused over what constitutes negative and positive energy. I've heard it said that we have a zero energy universe because the mass of the galaxies, etc. counts as positive energy which is exactly balanced out by gravity, or the gravitational potential, which counts as negative...

Three identical point charges, each of mass m 0.10kg and charge q, hang from three strings, as pictured below. The lengths of the left and right strings are L 30.0cm and the angle is 45.0o. Just on looking at the picture I think the charge is positive since there is tension separation the...

For positive real numbers $a,\,b,\,c$, prove the inequality: $$a + b + c ≥ \frac{a(b + 1)}{a + 1} + \frac{b(c + 1)}{b + 1}+ \frac{c(a + 1)}{c + 1}$$

The book I'm reading is discussing the physics of semiconductors. I'm having a hard time understanding a passage in section introducing n-type semiconductors. (Phosphorus is used as the impurity) The book says: "At normal operating temperatures, this extra electron breaks its bond with the...

If $a$ and $b$ are two positive real, and that $a^3+b^3=a-b$, prove that $2\left(\sqrt{2}-1\right)a^2-b^2\lt 1$.

How would we define positive and negative work in terms of energy? When the force and displacement are in opposite directions, we say the work done by the force is negative. When the force and displacement are in the same direction, we say the work done by the force is positive. However, how we...

Find all positive integer solutions to: $xyzt-2xyz-xyt+2xy+zt-2z-t=12$

Hi everyone, and happy new year! A colleague at work came up with this problem today, which I find very interesting. We are both chemists, so our ability to solve it is limited - here I am asking for your help! In a target discovery campaign that we run, we have two separate tests, let's call...

Homework Statement Write a program that will square the input positive integer represented as a string. Homework Equations 3. The Attempt at a Solution [/B] Is there another way of squaring a string number instead of multiplying it by itself? Something like a pow() function for strings? If...

The problem gives you a function describing the position of a particle moving along an x axis: x(t) = 12t2 - 2t3 With this function, one must determine the maximum positive coordinate reached by a particle and the maximum positive velocity. The first step to the problem is to take the...

Homework Statement I was just wondering whether the following notes I took on work in physics are accurate? Or have I got my understanding wrong? Note on friction Following from the example of the dragging object above… The object stops because it loses kinetic energy due to friction. How...

Exercise 2.24 on page 71 of Nielsen and Chuang's Quantum Computation and Quantum Information asks the reader to show that a positive operator is necessarily Hermitian. There is a hint given; namely, that you first show an arbitrary operator can be written $A=B+iC$, where $B$ and $C$ are...

Hello! (Wave) We have that $q(x) \geq q_0>0, x \in [0,1], h>0$. Suppose that we have this $(N+1) \times (N+1) matrix$: $\begin{bmatrix} \frac{1}{h^2}+\frac{1}{h}+\frac{q(x_0)}{2} & -\frac{1}{h^2} & 0 & \cdots & 0 \\ -\frac{1}{h^2} & \frac{2}{h^2}+q(x_1) & -\frac{1}{h^2} & \cdots &0 \\ 0 &...

Hey all. I know that A^TA is positive semidefinite. Is it possible to achieve a positive definite matrix from such a matrix multiplication (taking into account that A is NOT necessarily a square matrix)?

Hey all! Let me get right to it! It is given that $$A \succeq 0$$ I need the following to hold for M: $$M^TAM\succeq 0$$ What are the constraints or conditions on M for M^TAM\succeq 0 to hold? Anything would help at this point... I am open to discussion. Note: It may be worth mentioning that...

Solve for positive integers $x$ and $y$ where $x^2+x=y^3+y^2+y$.

For all positive integers $n$, $r$, and $s$, if $rs \le n$ then $r \le\sqrt{n}$ or $s \le \sqrt{n}$ Proof: Suppose $r$ , $s$ and $n$, are integers and $r > \sqrt{n}$ and $ s > \sqrt{e}$. Multiply both sides of the first inequality by $s$. I get $sr > s\sqrt{n} $, but the book gives $rs >...

Given a Positive Definite Matrix ## A \in {\mathbb{R}}^{2 \times 2} ## given by: $$ A = \begin{bmatrix} {A}_{11} & {A}_{12} \\ {A}_{12} & {A}_{22} \end{bmatrix} $$ And a Matrix ## B ## Given by: $$ B = \begin{bmatrix} \frac{1}{\sqrt{{A}_{11}}} & 0 \\ 0 & \frac{1}{\sqrt{{A}_{22}}}...

Homework Statement https://www.google.se/search?q=f%C3%A4ltlinje&rlz=1C1_____enSE665SE665&espv=2&biw=1366&bih=643&source=lnms&tbm=isch&sa=X&ved=0CAYQ_AUoAWoVChMI9dTNgquLyQIVhJIsCh1NxQZU#tbm=isch&q=physics+field+lines&imgrc=rKecBAfLOMsOoM%3A Why are the field lines on the positive atom pointed...

Homework Statement Homework EquationsThe Attempt at a Solution I was able to do the second part of part a using integration by parts. But I am having no luck for the first part, proving that the inner product is positive definite. Pointers are appreciated!

How can I prove that the entropy change is intrinsically positive? Given two systems with both of the heat capacities are independent of temperature.

Let ##u,v## be vectors in the same Euclidean space, and define the symmetric matrix ##M = uv'+vu'##, the sum of their two outer products. I'm interested in whether or not ##M## is positive (semi)definite. Does anybody know of any equivalent conditions that I might phrase "directly" in terms of...

Find all the positive integers $x$ such that $\dfrac{1}{4}<\dfrac{1}{x+1}+\dfrac{1}{x+2}+\dfrac{1}{x+3}<\dfrac{1}{2}$.

For part number 5, it says to make sure that each ΔT is positive. Why is this? Couldn't it be a negative? Or does it have to be positive since if it wasn't you would be getting heat going in the wrong direction? Like the one substance would be gaining instead of losing the heat? Which would...

Homework Statement An amount of work equal to 1.5 J is required to compress the spring in a spring gun. ? Homework Equations Wtotal = change of KE[/B] The Attempt at a Solution W=ΔKE=(1/2)m(Vf² - Vi²) It sounds like the Vf >0 and would be maximum after the spring is compressed hard and...

Homework Statement Consider the feedback loop involving Clouds, Rainfall and forest area. All the relationships represented in this figure show positive couplings between the components: Forest area is positively coupled to rainfall, plant evapotranspiration is positively coupled to forest...

Hi, I was always told that positive acceleration means that an object is always speeding up. However, I am starting to question this. I know that if an object is speeding up in the positive direction, the acceleration is positive. However, if an object is slowing down in the negative direction...

Homework Statement [/B] Show that the statement holds for all positive integers n 2n ≤ 2^n Homework Equations Axiom of induction: 1 ∈ S and k ∈ S ⇒ k + 1 ∈ S The Attempt at a Solution Let S be set of integers 2(1) ≤ 2^1, so S contains 1 k ∈ S, 2k ≤ 2^k I want to show k + 1 ∈ S, 2k +...

Why potential at a point can only be obtained by supposing/assuming a positive test charge there? For example There was a question In figure two points A and B are located in a region of electric field.,The potential difference ##VB##-##VA## is 1-positive 2-Negative 3-zero 4-none of the...

Find the positive integer numbers $a$ and $b$ such that $65(a^3b^3 + a^2 + b^2) = 81(ab^3 + 1)$.