Points Definition and 1000 Threads

I was thinking of using Pythagoras here but it didn't get me far Any suggestions?

Hi. I have 2 questions regarding removable singular points. 1 - the residue at a removable singularity is always zero so by the residue theorem the integral around a closed simple contour is zero. Cauchy's theorem states the integral around a simple closed contour for an analytic function is...

I have computed a line from point A to point B by just subtracting the coordinates as below: line = np.array (x2-x1, y2-y1) I am not sure if I need to form the formula for this line first by computing the slope and intercept but I continued my code as below, slope being m and b being the...

I suck at geometry, but I have this intuitive notion that the points on the corners of a regular tetrahedron are all equidistant. How do I go about proving this true (or false, if I'm wrong)? Note that the highest geometry class I've taken is high school, but I'm okay with any undergraduate...

Farhan and Junhao had the same number of points in a game. After Farhan got another 470 points and Junhao got another 50 points, Farhan had 3 times as many points as Junhao. How many points did each of them have at first? My answer: Farhan = F Junhao = J We know F = H, F = F + 470 J = J + 50...

Dear Everybody, I am wanting to check the solution to this question: Sketch the set of points determined by the given conditions: a.) $\left| z-1+i \right|=1$ b.)$\left| z+i \right|\le3$ c.)$\left| z-4i \right|\ge4$ work: I know (a.) is a circle with radius 1 and its center at (-1,1) on the...

I have a hypothetical universe where the distance between two points in spacetime is defined as: $$ds^2 =−(\phi^2 t^2)dt^2+dx^2+dy^2+dz^2$$Where ##\phi## has units of ##km s^{-2}##. The space in this universe grows quadratically with time (and, as I understand it, probably isn’t Minkowski...

Pick a random set of N points from the unit disc. Calculate the distance between all pairs of points and call the smallest value r. Do this calculation for many such sets. Please give me a hint how to estimate what the average value of r is. I guess a computer program could quickly come up with...

This paper seems to claim, that there is found powerful observational evidence for some anomalies in the CMB that seems to suggest a conformal cyclic cosmology and so called Hawking points. As I understand it, it also claims, that these points, were present in the very early universe and that...

I have some experimental data, and I would like to plot a graph in MATLAB and also find the best fit line. I also want to find the distance between each point and the best fit line, and if the distance is greater than 1 unit, an error will be shown. For this, I have written a function. Here it...

I have 3 point on a perimeter of circle. How I prove/show between every the two point of them there is always short way that the way between the other points?

Hello PF, I have a question about comparing tensors at different points. Carroll says, “there is no natural way to uniquely move a vector from one tangent space to another; we can always parallel-transport it, but the result depends on the path, and there is no natural choice of which path to...

How do you find the equation of a plane in determined by say three or four points in $\mathbb{R}^4$? In $\mathbb{R}^{3}$ we would use the cross product to find normal vector, but that doesn't apply in $\mathbb{R}^4$.

Very recently, Roger Penrose, along with Daniel An and Krzystztof Meissner, have submitted a new paper to PRL. In the new paper they present new empirical findings which support CCC. It doesn't seem to be out yet though, I can't find it anywhere, but I will place the link here when it is out...

Homework Statement Moment of inertia of a metal plate (center at origin) which was a square before 1/4th of it was cut off (4th quadrant), about three points a)- top leftmost corner in 2nd quadrant b)- origin and c) (where the right-lowest corner used to be in 4th quadrant) ranked in decreasing...

in this link here you can see the hot exhaust temperature and cold exhaust temperature at different ratio (hot to cold) with input air/gas at different pressure level. I want to discuss the top here i.e. the data where the input air/gas is at 20 PSIG pressure. You can see that with a 80:20 ratio...

Homework Statement Homework EquationsThe Attempt at a Solution This problem belongs to the topic "calculus of variation ". The fundamental problem of “calculus of variation” is to find a function y(x) such that the integral ## I = \int_{x_i }^{ x_f} \phi (y’, y, x) ~d x ## is extremum...

This is my first time posting here so please forgive me any indiscretions... I'm actually not a student. I'm a general contractor. Part of what I do for a living is draw plans, and that quite often involves geometrical and trigonometrical type challenges. For the most part, I'm usually able...

I have no idea what to do please help me. although i did this for the second equation, x/2h+y/2k=1 this represents an elipse first equation is circle

Homework Statement {(x,y) ∈ ℝ^2 : (y-x)(y+x) = 0 } Homework EquationsThe Attempt at a Solution [/B] Is the reason the answer is the union of y = -x and y = x because if you divide (y-x)(y+x) = 0 by y-x you get y = -x and if you divide (y-x)(y+x) = 0 by y+x you get y = x? and if you...

I am trying to figure out how to calculate the resultant force between 4 anchor points. Basically I want to hang two kayaks on two ropes suspended across a room. Below I have some crudely drawn images of the set up: I found how to calculate the vector forces between two points as pictured...

Homework Statement Homework EquationsThe Attempt at a Solution From symmetry , C and D are at the same potential . So , resistance between them can be removed . This leaves us with three parallel branches between A and B i.e 45 Ω || 45 Ω || 15Ω . The net resistance will be 9 Ω . But this...

Homework Statement Let f be ##f:[0,\infty]\rightarrow \mathbb R \\ f(x):= \begin{cases} e^{-x}sin(x), \ if \ \ x\in[2k\pi,(2k+1)\pi] for \ a \ k \in \mathbb N_0 \\ 0 \ \ otherwise\\ \end{cases}## Exercise: Determine all inner points of the domain where f is also differentiable and determine...

Homework Statement if a beam fixed at two points is on an angle say 45 degrees from the x or y-axis instead of running parallel to x-axis in most questions does this effect calculations? The force acting upon it would be a load directly downwardsHomework Equations N/A The Attempt at a Solution...

Homework Statement Determine singular points of given DE. Classify as regular or irregular (x^3 -2x^2 + 3x)^2 y'' + x(x-3)^2 y' + (-x-1)y = 0 Homework EquationsThe Attempt at a Solution From the polynomial infront of y'' I get x^2 (x^2 -2x + 3)^2 right out of the bat I can see that x =...

Homework Statement Homework EquationsThe Attempt at a Solution [/B] The circuit is symmetric about AC and BD , but I am not sure how to use this to simplify the circuit . Could someone help me in solving this circuit using symmetry considerations .

Homework Statement Homework EquationsThe Attempt at a Solution I am trying to solve this question by symmetry .If I draw a line perpendicular to the line joining AB then points C and D are symmetric . Now I am unsure how to proceed further .

Homework Statement Homework EquationsThe Attempt at a Solution I will call the topmost node T , middle node M , bottommost left node L and bottommost right node Q . I tried to use symmetry arguments . If I connect a battery across AB , i1 flows through branch AT , i2 through AM , i3...

Homework Statement Homework Equations ##ΔV=Ed## The Attempt at a Solution ##V_A=E l## ##V_b=0## , because point B is perpendicular to the electric field ##ΔV = V_a + V_b## = El Is my answer correct ?

Homework Statement Homework EquationsThe Attempt at a Solution If we consider the bigger semicircular arc BD alone then potential difference between B and D will be 4BvR . If we consider smaller semicircular arc AC alone then potential difference between A and C will be 2BvR . If we...

Homework Statement I have to derive the Nodal and Principle points distance equations. Homework Equations Equations can be found here http://scienceworld.wolfram.com/physics/ThickLensFormula.html The Attempt at a Solution I have no clue about how to approach this problem. If...

Hi PF! I am trying to make a march madness (college basketball tournament) bracket with some friends. Last year we used common apps, but they all score each round exponentially (first round of 64 teams worth 1 point for a correct pick, second round of 32 teams worth 2 points, third round of 16...

I'm having a hard time putting together a formula. I have 2 points (x0, y0) and (x1, y1) and an angle (k). Using this information I need to calculate a third point that is k degrees from the previous 2 points. Is it possible to do that? Thank you for your attention.

Homework Statement The figure shown consists of two rods at right angles to each other and each is uniform of 2m length. D and E are the midpoints of AC and AD Draw the line of action of the weight of the arrangement relative to A, B,C, D and E when it is (a) Suspended from A and in...

Homework Statement Rank the vertical component of the velocity of each projectile at they moment they return to the ground, greatest first. Homework Equations n/a The Attempt at a Solution This is a conceptual homework, so there are no numbers involved. But looking at the picture i was...

Homework Statement Homework EquationsThe Attempt at a Solution [/B] y = 3sin^2x dy/dx = 3(2sinxcosx) dy/dx = 6sinxcosx For stationary points...

A person walked a distance of 10m from (0,0) to (10,0) - final distnation; prior to reaching final distancetion he stopped betwen 2 points (a,0) and (b,0). The distance between (a,0) and (b,0) is 2m. I need to know the distance between (10,0) and (b,0) Please check graph attached

I've been trying to wrap my head around equidistant points, like platonic solid vertices inside a sphere where the points touch the sphere surface. This led me to the strange and unusual world of mathematical degeneracy, henagons, dihedrons, and so on, along with the lingering question of...

Hi all, at the moment I am doing my Master Thesis and have the following problem. I am trying to measure Data and asign it a proper timestamp. My problem is, that the data is coming in bursts and the timestamps I assign with the software are wrong. The controller I am using for monitoring the...

I have some questions and refer you to the image below the caption of which states, "D-branes may be of exceptional importance in the explanation of elementary particles of the Standard Model. However, it still remains to find a solid connection between the M-theory and the Standard Model."...

Homework Statement Show that the sequence with two distinct accumulation points must diverge. (Hint: look at the proof of divergence for {##(-1)^k##}. Homework Equations Some definitions and propositions I'm trying to use: 2.2.3: A sequence cannot converge to two different numbers. If...

It's written in my book that if you have two points having the same voltage then you'll cancel the resistance between them ... how can I know if the voltages of the two points are equal ...( The resistances are given in the circuit .)

This is a well-known problem I think: take four arbitrary points on a sphere as the vertices of a tetrahedron. What is the probability that the centre of the sphere will be located within the tetrahedron? A friend gave me this puzzle to solve, and I came up with the answer P = 1/8. This is the...

Homework Statement A grid made of ropes is suspended by its four corners with strings tied to four different points on a building. Three of which are fixed and fourth is attached to a pulley which is in turn fixed to the building. Given data : Grid mass is 25 kilogram suspended at a height of...

<Moderator's note: Moved from a technical forum and thus no template.> The title isn't complete this is what I meant to say: Determine the values of aa and bb where the function has inflection points (x2+ax+b)(ex) I made the second derivative $$f''(x) = 2 e^x + 2 a e^x + b e^x + 4 e^x x + a...

$\tiny\textit{243.12.7.12}$ $\textsf{Write the equation for the plane through points}$ $$A(-3,8,1),\, B(5,-7,-18),\, C(-1,-5,24)$$ ok, tried to follow an example of cross product but.. $$\displaystyle\vec{AB}\times \vec{AC} = \begin{bmatrix} \textbf{i} & \textbf{j} & \textbf{k}\\ \, 5 &-7...

Homework Statement Homework Equations First derivative=maxima/minima/vertical tangent/rising/falling When f'(x)>0 ? the function rises The Attempt at a Solution Deriving relative to x: $$10x-6(yy'+x)+10yy'=0~\rightarrow~y'=-\frac{x}{y}$$ What do i do with that?

1. The problem statement, all variables, and given/known data Find and categorize extremes of the following function: $$F(y)=\int_{y}^{y^{2}}\frac{1}{\ln^{2}x}dx$$ for ##y>1##. Homework Equations $$\frac{d}{dx}\int_{a}^{b}f(x,y)dy=\int_{a}^{b}\frac{\partial}{\partial x}\left(f(x,y)\right)dy$$...

Statement Four point charges, Q, -Q, Q, -Q, are placed at the four ends of a horizontal square of side a as shown in the figure above. What are the neutral points? The attempt at a solution The square is not exactly aligned parallel in its plane, say XY. So, the center is not a neutral point...

Hello all, Below there is a problem: There are five points inside an equilateral triangle of side length 2. Show that at least two of the points are within 1 unit distance from each other. I have plotted such a triangle using "Geogebra", and attaching the picture. I know that if I create...