Zero Definition and 1000 Threads

Homework Statement Find a function, strictly increasing, whose derivative equals zero at TWO places. Find another such function whose derivative equals zero at infinitely many places. These should not be piecewise and should be continuous on all reals. Homework Equations f(x)=x^3 has one...

Hello. An open differential works by the principle of distributing torque equally to both wheels, no matter what. And I think I understand how that works, so no problem with that. Consider the case of one of the wheels on ice, and therefore having a very low traction limit. Almost every...

I am working on a physics problem from a calc-based E&M (intro) course, and I came up with the following equation: E = 0 = 10 / (1 - x)2 + 5 / x2 - 10 / (1 + x)2 I got here and worried it was a dead end, so I checked the solutions manual, and they have the exact same thing, and then say "...

if b >> a ,Ex and Hy are zero .why ? hello friends...in schaum series book on Electromagnetic field theory , its shown that if b>> a then Ex and Hy are zero , and only components present will be Ey , Hx, Hz... can you please tell me the reson for that...what happened when we made b >> a... (...

Can a square matrix with a column of all zero's be invertible?

Homework Statement \lim_{t\to0}\frac{1}{t}-\frac{1}{t^2+t}Homework Equations Limit Laws, et al.The Attempt at a Solution \lim_{t\to0}\frac{1}{t}-\frac{1}{t^2+t} I didn't feel this would work, too much division by zero, so I found a common den...

By definition, superconductors are conductors with zero resistance at low temperatures. Do superconductors exist ideally, i mean whether zero resistance is practically possible?

Gday, I was wondering if someone could tell what the nullity of an nxn zero matrix is? I can't decide if its zero or n. Could someone knowledgeable please enlighten me?Thanks

Hi, Today in school I performed an experiment that went like this: We had a capillary tube with trapped air on the bottom, the top part was open to the atmosphere and, in between, there was some sulphuric acid. We heated the capillary tube and recorded the increase in volume of the trapped...

A) If the moon of mass mM has radius RM and the distance between the centers of the Earth and the moon is REM, find the total gravitational potential energy of the particle-earth and particle-moon systems when a particle with mass m is between the Earth and the moon, and a distance r from the...

If \int_{-\infty}^{\infty} f(k) e^{i\mathbf{k}.\mathbf{r}} d\mathbf{k} =0 then is \ f(k)=0 ? Is it correct to say that this is an expansion in an orthonormal basis, \ e^{ik.r} , and so linear independence demands that f(k) be zero for all k?

If I understand correctly: "Time does not evolve for a photon." However, a photon has a frequency (which is cycles/time). Question: how can a photon have a frequency that is preserved while it travels despite the photon not experiencing any elapsing of time?

Semester is over but still want to figure this out Prob 8 on here: http://www.math.uic.edu/~akers/310PracticeFinal.pdf When trying to SVD that matrix one of the U or V matrix turns out to be zero but the answer key has just the general formula for SVD can anyone explain thanks

(Apologies for ascii art math, I don't know latex. Also apologies if this is in the wrong forum.) Homework Statement Why, in this lemma, must there be a vector v in V? That is, why must V be nonempty? An isomorphism maps a zero vector to a zero vector. Where f:V->W is an isomorphism, fix any...

Whyyyyyy??! Whhhhhy?!?

Homework Statement A charge of +6.0µC at point A is separated 10.0 cm from a charge of -2.0µC at point B. At what locations on the line that passes through the two charges will the total electric potential be 0? The Attempt at a Solution[(+) A] ------------------------------ [(-) B]I know that...

Homework Statement Find all zero divisors of the ring Z17 Homework Equations Are there any zero divisors of the ring Z17? The Attempt at a Solution I multiplied 17*17=289...that is only divisible by 17, so I do not think there are any zero divisors...am I missing something?

This is highly theoertical and I came up with it taking a standerized test. So without further adoo, What would happen if you to a cyrogenic chamber froze something to ablsolute zero and put it on a spacecraft moving at exactly the same velocity as the universe is. Thus canceling out...

When something is frozen fully, and the temperature is absolute zero -there is no entropy - but does that mean the "quantum jitters" are not occurring?

Homework Statement I am trying to prove that if f is continuous almost everywhere on [a,b], and if g is cont a.e. on [c,d], with f[a,b] contained in [c,d], then g composite f is cont. a.e. The Attempt at a Solution ------ Originally, my proof went something like this: f is cont...

What is the proper term to use when you end up with a divide by zero answer? I never what to write out when I run into this situation. I've heard; singularity, undefined, infinity, and of course divide by zero. What are you guys using when you have to explain this phenomenon? Or does it...

Homework Statement a closed wire loop with current I is in a uniform magnetic field B show that the total magnetic force on the loop is zero Homework Equations The Attempt at a Solution everywhere that I've looked just states it without explaining why

I was just wondering. With the Twin Theory, with the person traveling at the speed of light causes them to age slower. So I wondered, does that mean that something would age faster if at absolute zero? Because I've heard that motion is relative to temperature, and time is relative to velocity...

According to Charles' law, volume decreases with temperature. Extrapolating down towards absolute zero, and the volume of the gas will be zero. How can this be possible? Surely any amount of gas will still have to take up some volume in space. Can multiple gas molecules really occupy zero volume?

For example,K is a triangulation of S^2 ;H_1 (K ) = Z_1 (K )/B_1 (K ).And Z_1 (K ) = B_1 (K ) .Then I think H_1(K)=[z],z is any element of Z_1(K),[z] is the equivalent class of z .But why is it zero?Thank you!

What is the definition of a zero set and what exactly does it mean? I have come across different responses on the internet, but none of them explain really what it means or give good examples, I am having a rough time with this concept in real analysis. For example, how would I determine...

I was looking at a situation where a fridge in the back of a truck is just about to tip back due to the truck's acceleration. I am looking at the moment just before it tips. The net torque here is 0 since it is not yet tipping back. I thought I was allowed to pick any axis I wished and so picked...

Homework Statement http://www.electron.rmutphysics.com/physics/charud/scibook/Physics-for-Scientists-and-Engineers-Serway-Beichne%206edr-4/29%20-%20Magnetic%20Fields.pdf Go to page 17 to 18 (it cuts off there), in the picture the vectorial sum of the forces are CLEARLY 0 (they even took...

I understand how he got -120 and 360 as zeros, but then there is another zero 240, how did he get that? Check the diagram i have posted (which was done by the teacher) for simpler version A bit of background: we are working with sine functions the equation being y=2sin(x-30)+1 so we re...

My applied maths teacher proposed this question while we were having a discussion about gravitational effects. We do not know the answer. Given a hollow cylinder with a mass large enough to have its own gravitational effects, placed in zero gravity. If you propel an object into to an...

Homework Statement I know that the field inside a conductor is zero but what if there was a charged object in the cylinder I mean in some examples I see infinite charged wire inside an infinite hollow conduction cylinder with radius a but if we take a cylindrical gaussian surface with r <a...

if we take a liquid to agravity free space then is the bouyant force is 0 ?

I have a particular scenario that has been bothering me lately, which I can't quite figure out: Suppose scientists are somehow able to create a room where the force of gravity is equal to 0, however this room still contained atmosphere (ie. the room is not a vacuum). Would friction still...

1. The Problem: An elevator is hoisted by its cables at a constant speed is the total work zero, negative, or positive? 2. Homework Equations : g= -9.81m/s2 3. The Attempt at a Solution I'm thinking that since the weight of the elevator is in downward direction along with the acceleration of...

My teacher recently docked me 6% on a test because I failed to put units on two values that ended up being zero. For as long as I can remember an answer that is zero does not need units. I looked up examples in our textbook and they left units off answers with values of zero as well. I was...

Homework Statement A 13.0 nC charge is at x= 0 cm and a -1.2 nC charge is at 6 cm. At what point or points on the x-axis is the electric potential zero? Homework Equations V=kq/r The Attempt at a Solution 0=13K/r + 1.2K/(r-0.06) 13(r-0.06)=-1.2r r=5.5 cm There is another...

If the separation between two objects (say, me and my chair) is zero, shouldn't the gravitational force between those two objects be infinite because in the equation for force you divide by r? And I understand that the centers of my atoms are not literally touching the chair, so maybe the...

I am confused as to exactly what a local base at zero (l.b.z.) tells us about a topology. The definition given in Rudin is the following: "An l.b.z. is a collection G of open sets containing zero such that if O is any open set containing zero, there is an element of G contained in O". Ok, great...

Hello to all. I'm having a few problems and would love to know how to do the following. 1. f(x) = 3x^2-8 2. Find the function's zeros, local max/min and the function's behaviour 3. My attempt at drawing the function ended with a downward curve intercepting at y=-8, x=0 But a...

hello fine people, ohm law is V=IR. suppose V is a constant value, as say 5. then it is I=5/R. when R is zero current is infinite. me thinks this is case with superconductors. me have been telled that limit of I=5/R does not exist. what did it mean in this real world problem? will this mean...

Is it zero divided by zero even a division? According to some, it is not, because division would have three requirements: 1) That any quotient must be a number. 2) That any quotient multiplied by a divisor must give us a dividend, which presupposes that any quotient is a number. 3) That no...

Dividing any number by zero truly consists in two different mathematical operations: 1) Dividing zero by zero, which has any quotient, since the product of any number by zero is again zero -- so mathematicians call that quotient indeterminate. 2) Dividing any other (than zero) number by...

Reworded version: I think I need to re-word as follow: Can a nonempty set X with P(X)=0? Suppose F to be a non-empty set with P(F)\neq 0. Call its closure be F'. Now let set theoretic different F'\F be A. Clearly, A could be non-empty. Is this the case where P(A)=0? Is not, how do you...

hello all the people, in the formula V=IR where V is voltage, I is current and R is resistance. suppose the value of R slowly decreases to "0". in real world, i have been said, it is impossible to have some conductor with zero resistance. which means R tends toward zero without ever reaching...

If we ask whether dividing zero by zero equals one, then we must answer yes, because if we multiply one by zero then we recover zero. However, if we ask whether it equals two rather than one, then we must still answer yes, because if we multiply two by zero then we also recover zero. Likewise...

Homework Statement Suppose F: Rn --> R has first order partial derivatives and that x in Rn is a local minimizer of F, that is, there exists an r>0 such that f(x+h) \geq f(x) if dist(x, x+h) < r. Prove that \nabla f(x)=0. Homework Equations We want to show that fxi(x) =0 for i = 1,...,n So...

Let R be a commutative ring. If an doesn't equal 0 and a0+a1x+a2x^2+...+anx^n is a zero divisor in R[x], prove that an is a zero divisor in R. What I did was say if the polynomial is a zero divisor in R[x] then let that polynomial equal p(x) and any other polynomial be q(x) with...

Let R be a commutative ring. If an doesn't equal 0 and a0+a1x+a2x^2+...+anx^n is a zero divisor in R[x], prove that an is a zero divisor in R. What I did was say if the polynomial is a zero divisor in R[x] then let that polynomial equal p(x) and any other polynomial be q(x) with...

Hi, I'm looking for some help on how the sum of a certain number of vectors can equal zero. I know that the sum of 2 vectors with equal magnitudes but opposite directions will equal zero; 2 vectors of unequal magnitude can never have a sum equal zero; and that three vectors of unequal...

If we have a linear system(it could be a RLC circuit) with the following differential equation: d2y/dt2+7*dy/dt+12*y=dx/dt+5*x So H(s) = (s+5)/((s+4)*(s+3)) = -1/(s+4)+2/(s+3)--> h(t) = (-e^(-4*t)+2*e^(-3*t))*u(t) (Please calculate the unit impulse response by Laplace transform and verify the...