Point Definition and 1000 Threads

Homework Statement Find the local max, min, and saddle point for the function: f(x,y) = 2x^2+3xy+4y^2-5x+2yHomework EquationsThe Attempt at a Solution I've taken the two partial derivatives Fx = 4x + 3y - 5 Fy = 3x + 8y + 2 I know that the critical points will sit where both of theses partial...

Homework Statement Point with mass is moving along the positive direction of x axis, its velocity is described by (A-Bx^2)^(1/2). Show that its equation of motion describes dynamic harmonic oscillation and find period (T) of this oscillation. Homework Equations v=(A-Bx^2)^(1/2) A and B is...

At the very basic level, I understand this notion of discontinuity. But I am looking to understand this better, at a deeper level. Because I know I will need to know this well as I start to explore piece-wise functions. Why do we bother drawing graphs? I want to be able to tell if a function...

I understand that the derivative of a function ##f## at a point ##x=x_{0}## is defined as the limit $$f'(x_{0})=\lim_{\Delta x\rightarrow 0}\frac{f(x_{0}+\Delta x)-f(x_{0})}{\Delta x}$$ where ##\Delta x## is a small change in the argument ##x## as we "move" from ##x=x_{0}## to a neighbouring...

Conventionally we have the following equation of a plane ax+by+cz=d where d = ax0+by0+cz0. Where (x0,y0,z0) is a known point on the plane. Now if we try to find the distance between a point P and a plane we take any point on the plane Q (x,y,z) and find the vector from Q to P and project on...

As the name of the thread says, I am wondering what would the amount and the direction of the electric field at some point in the uniformly charged ball of radius R(it has a constant charge volume density) be at the distance r from the centre of the ball. Does anyone know what would they be? I...

Homework Statement In a wire passes the current I=21A. A part of the wire is bent to form three consecutive sides of a square with sides 40 cm. Find the induction of the magnetic field in the point O which is the center of the square. Homework Equations B=I*μ0*/2*pi*d The Attempt at a Solution...

If moving inside the event horizon of a super-massive black hole and theoretically surviving we could see the universe pass by at millions of years per second relative to someone on earth, where could we go where time passes at a much faster rate than someone on earth? For example where 2...

Homework Statement ≈ What is a 3D representation of voltage using Kq/r assuming a positive point charge and what is the equation in cartesian and cylindrical form2. Relavent equations Kq/r 3. Attempt at solution[/B] I was trying to get a better understanding of Voltage, to really FEEL...

Homework Statement A magnifier has a magnification of 9× How far from the lens should an object be held so that its image is seen at the near-point distance of 25 cm? Assume that your eye is immediately behind the lens. Express your answer to two significant figures and include the...

Hello! (Wave) Suppose that a parallelogram $ABCD$ has vertices $A=(0,0)$ and $B=(1,0)$. In terms of $C=(x,y)$, find the position of $D$ and where the two diagonals will intersect. Then we will have something like that: How can we find the coordinates of $M$, i.e. the point at which the two...

Hello! Suppose that a point has cylindrical coordinates $(r, \theta, z)$ where $r$ is not zero. Describe all other cylindrical coordinates of that point. Suppose $(R, \theta_1, \phi)$ and $(R, \theta_2, \phi)$ are two representations of the same point in spherical coordinates. Is it true that...

I'm finding it difficult to find the exact value of epsilon on python? Moreover, I am also supposed to find the smallest floating point number as well. Wikipedia tells me that the machine epsilon is 2−52 ≈ 2.22e-16 for 64-bit IEEE 754 - 2008? Is this the exact value on Python? Outside of...

This is a really abstract question, and I'm absolutely clueless on how to approach it. I know W= F*d, where F=force and d=distance, as well as W= PEa-PEb. The question reads: The diagram shows an isolated point charge. Marked are four paths (A, B, C, and D) from a point (P1) to point (P2). The...

Hi, I'm trying to work out how many time a particle going on a random walk starting at the origin would pass a particular point or points for a given total number of steps. I've simulated the problem and get approximately the same answer every time, however I'm struggling to know where to even...

For the following question I am given a plane: x + 2y + 3z = 12. I want to find the equation of a line normal to the plane and going through the point (4,6,8). I am trying to use the formula N . (r - r0) = 0 however seem to be getting the incorrect answer :(

Let $P = (1,2,-1)$ and $Q = (3,1,0)$. A point $B$ lies on the line segment between $P$ and $Q$. Given that its distance from $P$ is twice its distance from $Q$. Find the position vector of $B$.

Hello I have to prove that the intensity of seidel point is equal to ##I_{sp}=\frac{8}{\pi^2} I_o## I didn't get any other information only that there is an integration in this prove. Hope you can help me. It is enough for me if you only give me link or the name of this prove.

Homework Statement I have seen Earth and ground used interchangeably. However, there appears to be some distinction with regards to reference point ground and Earth ground. My textbook used an example of a loaded voltage divider and examined how the voltage across certain resistors can be...

Homework Statement Take the expression 21.11 (pictured below, specifically the bottom one) for the electric field above the center of a uniformly charged disk with radius R and surface charge density σ, and show that when one is very far from the disk, the field decreases with the same square...

Hey everyone, So I've been learning about electric fields and all that good stuff. So now the question arises, what is the electric field at a point P away from an object (say a rod or a ring) at a distance D away? So we know E=Kq/r2 or E=KQ/r2 . The difference between q and Q: q the charge for...

Hi. I'm currently learning about magnetism, however the course I'm in doesn't combine special relativity with E&M so I just wanted to do some personal exploring. The magnetic field for a point charge is proportional to V1 x R of the charge. Then, the magnetic force is proportional to V2 x B...

Hello! I'm currently teaching an advanced course in mathematics at high school. The first half treats discrete mathematics, e.g. combinatorics, set theory for finite sets, and some parts of number theory. Next year I would like to change some of the subjects in the course. My question is: Are...

Homework Statement If a charge of +2 µC and mass 2 g is taken to (0,0,4) in the presence of an electric field due to a ring {R : x2 + y2 = 25,z = 0} of uniform charge density ρL = +3µ C/m, and then released, find the maximum velocity it gains. Given in the problem: You solve the equation 1/2...

Homework Statement [/B] Three point charges each of 4 µC are situated at the three corners of an equilateral triangle of side 4 m. Find the work done in moving one of them to a point mid-way between the other two. Solution: The Potential difference VAB between two points A and B is the work...

Homework Statement [/B] Consider 2 radio antennas placed on a 2 dimensional grid at points x1 = (300,0) and x2 = (-300, 0). If the antennas are out of phase such that ϕ2-ϕ1 = π/4 and both are emitting waves of frequency 2.59 MHz. What will the amplitude of the resultant wave be at the point...

Homework Statement A point charge q1 = 4.40 μC is at the origin and a point charge q2 = 6.00 μC is on the x axis at x = 2.49 m. i) Find the electric force on charge q2 ii) Find the electric force on charge q1 Homework Equations Coulomb's law F = k (q1q2)/d^2 The Attempt at a Solution Part...

Homework Statement Recently I have conducted an experiment using a gamma source (22Na) and a scintillation detector (NaI), at the start of the experiment one of the desired outcomes was to see that the intensity of the source fell off as 1/r^2. Seeing as the detector is not point like (I am...

If you want to show that a propagator of a heavy particle reduces to a point interaction at distances large compared to the inverse mass of the particle by Taylor expanding the propagator (for simplicity take 1-dimension): $$G(x)=\int^\infty_{-\infty} \frac{dk}{2\pi} \frac{e^{-ikx}}{k^2+M^2}=...

I am not a scientist, but as a hobby I am summarizing different initial condition theories, specifically, eternal inflation, LGC, cyclic, and bounce theories. I need a completion time ATB where all theories produce an identical plasma. The plasma then enters the big bang process of expansion...

Homework Statement A line charge with a uniform linear charge density Lambda lies along the x-axis and extends from -∞ to 0. Determine the X-component, and Y-component of the E-field at a point P, a distance 'a' from the origin on the positive y-axis. Homework Equations dE= (k*dq/r^2)* r(hat)...

How would 2 photons with the same starting point& time and same end point view each other's positions, time and distance from start to end point. I recognize this is likely a bad question, so any input would be helpful.

here from time 0:53 to 0:58 velocity at center would be more than or approximately equal to zero .I want to ask why approximately zero why not zero?

Homework Statement When an object is placed at the proper distance to the left of a converging lens, the image is focused on a screen 30.0 cm to the right of the lens. A diverging lens is now placed 15.0 cm to the right of the converging lens, and it is found that the screen must be moved 19.2...

I've done a question similar to this, however this one has no complete equations i can solve for. Determine the equation of the plane that passes through (1,3,8) and is perpendicular to the line of intersection of the planes 3x−2z+1=0 and 4x+3y+7=0. I know to take the cross product of the two...

There's this question, A conducting sphere of radius R and charge Q is placed near a uniformly charged non conducting infinitely large thin plate having surface charge density σ. The potential at point A on sphere due to charge on sphere is? I have uploaded the picture. Now I know the net field...

Homework Statement Consider two equal point charges q, separated by a distance 2a. Construct the plane equidistant from the two charges. By integrating Maxwell’s stress tensor over this plane, determine the force of one charge on the other. I have the full solution, but I'm confused on one...

Simple as that, I've uploaded the image. I don't really care about the exact value, I would prefer just to know the method. So how would I find the equivalent resistance between A and B? Note the component in the middle is a constant current source.

Homework Statement hello, i want to calculate the inertia tensor of the combination of a point mass and a sphere in the object's frame, the center of mass is at the origin. The point mass remains at the surface of the phere The sphere is uniform, radius r and mass M, and the point mass has mass...

Homework Statement Consider the motion of a point mass m in the potential V(r)=-k/r , k>0 Show that there is a solution x(t) of the equations of motion which is a circular motion with constant circular frequency ω. Determine the relation between ω and the radius of the circular motion. Show...

first of all i simply don't want to give up learning numerical methods ... i am trying to follow fixed point iteration method from this link ... http://www.ce.utexas.edu/prof/mckinney/ce311k/Overheads/14-NonlinearEquations_1_FixedPoint.pdf fixed point iteration can be used to solve...

Hello, I've been trying to answering this question but my answer is always wrong. Two point charges, -9.10 μC and 21.29 μC, are placed at x = 0 cm and x = 8.00 cm, respectively. (a) At what point along the x-axis is the electric field zero? What i did: i figured that the point should be on the...

Hi everyone. Can someone please explain me how a two or three points test can be made, in the field of genetics? I've read of it in many books, but I'm looking for an explanation as clear as possible. Thanks in advance :)

It has been made clear to me that any velocity can be seen as rest mass, meaning that if I observe someone else experiencing time more slowly than me due to general relativity, so long as they do not change velocities, they will see me as experiencing time more slowly than them. I have also...

Note: Post edited by moderator: 1. Homework Statement Homework Equations I can't use voltage, nor polar coordinates (got to stick with cartesian). Cartesian vector form of Coulomb's Law The Attempt at a Solution

Homework Statement Find parametric equation of the line through the point ##(4,0,-4)## that is parallel to the planes ##x-8y+7z=0## and ##4x+3y-z+4=0##. Homework Equations ## \vec r = \vec r_0 + t\vec v ## (for orthogonal vectors) ## v \bullet w = 0 ##[/B] The Attempt at a Solution So I...

I'm playing a game, From the Depths, that let's you build your own helicopter blades (and put them on ships that you build) and program in LUA. I did some searching and found: Calculating the Center of Thrust on Multirotors | Flite Test Currently, there is no way to tell how much lift a given...

Homework Statement Of the following compounds, which has the highest boiling point? (A) CH3—CH3(B) CH3—CH2OH(C) CH3—COOH(D) CH3—COH(E) H2S Homework Equations - The Attempt at a Solution Chose C because is more polar with the 2 oxygens, however, the answer has conflicting answer. It...

I've come to understand that intermolecular forces cause the boiling point of hydrochloric acid solutions below 20% to be higher than the boiling point of water. I also understand that dissolving hcl in water is an exothermic reaction. But, what about those intermolecular forces. I assume they...

Given a parametrized curve ##X(t):I\to\mathbb{R}^2## I am trying to show given a fixed point ##p##, and the closest point on ##X## to ##p##, ##X(t_0)##, the line between the point and the curve is perpendicular to the curve. My only idea so far is to show that...