Points Definition and 1000 Threads

Hello, I am trying to solve a problem and I would like to ask for help. I have 3 points (A, B, C) in 3D space that are assumed to be on a circle. EXAMPLE 1 EXAMPLE 2 My goal is to create an algebraic formula to calculate the coordinates for 10 points on a circle composed of ABC points at...

Yesterday I found a playlist of videos by a youtuber "Dialect" who made a distinction between what he called Tier 1 and Tier 2 arguments of Relativity. Tier 2 promoted a view that acceleration was an observer dependent phenomena. In particular he was discussing the Twin Paradox, and he said...

a. I solved a but I don't fully understand how it works. $$z = f_x'(1, -1)(x -1) + f_y'(1, -1)(y+1) = 2(x-1) + 3(y+1)$$ Eitherway it's b that's my issue. I can find the gradient of both plane and surface, but trying to do "dot-product of both normals = 1" will give an equation involving two...

I tried using hamilton method but i don't think that's correct

I tried the following proof and got -2 < x < -1 and y = 0 but my prof said that there should be something else I am missing. I have no idea what that is. Thank you.

Hi there, experts on three-D space! while thinking about (physical) space, I have come up with the following (geometry) question: Is it possible to define five points (A, B, C, D, E) in Euclidian space, so that all distances (AB, AC, AD, AE, BC, BD, BE, CD, CE, DE) can be expressed in rational...

For this question i tried to reason with my self that C was the fastest and A was the second fastest. B would be the third fastest and D would be the least fastest since the ball has to go up. I looked up the answer and it says that C is the fastest , B and D are equal, and A is the slowest. How...

I am familiar with Cantor's work on the concept of infinity and his use of the set theory to explain various types of infinities. Having said that my intuition never seems truly grasp/accept it. Is there a way to train my mind to see this seemingly contradictory situation as a fact? This is...

What is the delta-v requirements from each of the Earth-Moon lagrange points to landing on the lunar surface? What would be the best software I could use to visualise and calculate that kind of thing? Thanks.

Fuel oil like heavy fuel oil consists of multiple different Carbon and Hydrogen molecule strains. This means that there are a multiple of different boiling points with in the same oil. Cavitation in pumps and valves happen when due to the acceleration of the fluid the pressure drop causing the...

I would like to check my understanding of this problem. There are the following possibilities: a. Isolated points where the gradient is 0. b. The level curves of height 0 c. The level curves of height 1. d. The level curves of height -1. e. None of the above. I would choose a, c, d. Where...

is this method accepted? 2V is split equally between the 2 5kohms resistor because they are of equal resistance. 2V=5kohms 2kohms= 0.8V 3kohms=1.2V. p.d across P and Q= 1V-0.8V=0.2V

Are there "nice" ( without heavy machinery) proofs that ## X:=R^2 - \{p,q\} ## is connected? All I can think is using that path-connectedness implies connectedness. So we consider x,y in X and show there is a path joining them. I am looking for an argument at undergrad level, so that I would not...

Hi everybody We can't differentiate ##x^x## neither like a power function nor an exponential function. But ##x^x=e^{x\mbox{ln}x}##. So ##\dfrac{d}{dx}x^x=\dfrac{d}{dx}e^{x\mbox{ln}x}=x^x(\mbox{ln}x+1)## And here comes the doubt: prove the domain of ##x^x## is ##(0, +\infty)## Why is only...

I want to understand bettew what this statement says. Maybe later we could try to put it mathematically, but for while i want to know if my interpretation is right. When we lie outside the light cone, the physics regarding the limit of the velocity is break, and technically we could go faster...

Chapter 1, Section 1.1 Collinear Points 59. Three or more points are collinear when they all lie on the same line. Use the steps below to determine whether the set of points {A(2, 3), B(2, 6),C(6, 3)} and the set of points {A(8, 3), B(5, 2), C(2, 1)} are collinear. (a) For each set of points...

Hi everyone, for a lab I need to determine the position of the cardinal points of a telephoto lens. The focal points were determined experimentally, and the focal length given on the lens is 200mm. The principal points should be determined with f=PF. In all the textbooks, the principal points...

Q: See f(t) in graph below. Does the graph of g have a point of inflection at x=4? There is a corner at x=4, so I don't think there is a point of inflection. Does a point of inflection exist where f''(x) does not exist? The solution says there is a point of inflection, could anyone explain why...

Problem statement : The function ##y = f(x)## is given above. Question 1 : Locate the points at which the ##\text{first derivative}## of ##y## with respect to ##x## is ##\text{non-zero}##.##\\[5pt]## At points of extrema, like A, C and D, the derivative is zero. Hence the derivative is non...

Hey! :giggle: We have the function $$f(x,y)=(x-3)^2+y^2+(x-y)^2$$ and I have shown that at $(2,1)$ we have a minimum and so $f(2,1)\leq f(x,y)$ for all $(x,y\in \mathbb{R}^2$. I did that in this way: I calculated the gradient and set this equal to zero and found that the only critical point...

Hi there. I'm having some trouble wrapping my head around some ideas of inflection points as they relate to the second derivative. I know that an inflection point occurs when f''(x)=0 in most cases. This makes sense to me because at this inflection point the slopes of the tangent change from...

As they are in engineering and manufacturing? I ask because during a very deep, post stroke marbles census in came to light that I had an extraordinarily high level of pattern recognition such that the department head said I was in the top .003 percent of the population. I ran the numbers...

A 3d printer that could print metal and other materials would revolutionize everything. The only problem is that metals have a really high melting point, so if you try to get a metal hot enough to bind to the other metals in its vicinity it would probably destroy the bonds of the neighboring...

Hi. I'm not sure about something related to the equilibrium points (or fixed points) of a non linear ode system solution. As far as I know, to check if an equilibrium point exists, I need to put the function of my ode system equal to zero. Then once the point is found, I can use it to evaluate...

In hockey, the points a player scores is the sum of the goals scored and he assists. In one session, Ryan scored 83 points. Ryan scored 21 fewer goals than assists. a) Write a system of equations to represents the situation. State your variables. b) How many goals and assists Ryan scored in...

Table boiling point (°C) melting point (°C) TiF4 284 N/A TiCl4 -24 136.5 TiBr4 38 233.5 TiI4 155 377 The solution says that TiF4 is an ionic compound, while TiCl4, TiBr4, and TiI4 are covalent compounds. How would I determine this from the problem without prior...

If the sign on the sign diagram of f" changes from positive to negative or from negative to positive, this means the critical points of f" is non-horizontal inflection of f But what about if the sign does not change? Let say f"(x) = 0 when ##x = a## and from sign diagram of f", the sign on the...

The solutions used the spend of the wheel and its radius to find the angular velocity. I’m confused because I thought to find angular velocity you use the speed at the points of the radius not the translation speed of the wheel itself. Can someone explain this to me please

Why does the isomer C-C-C-N have the highest boiling point, rather than CC(N)C (where the N is attached to the second carbon)? Isn't N able to form 3 H-bonds in both cases? Thanks.

I was recently studying the pressure gradient force, and I found it interesting (though this may be incorrect) that you can use a Taylor expansion to pretend that the value of the internal pressure of the fluid does not matter at all, because the internal pressure forces that are a part of the...

Say I have phi starting at 0 and ending at 360 degrees. Theta starts at 0 and ends at 360, and I input 10 points for phi and theta. I am trying to 3d plot phi * theta number of points around a center point. I can plot a coordinate around a sphere using the following, which I think is correct...

Hello everyone. I have two points in space (on the surface of the earth) represented using spherical coordinates (in this case there is no z axis since both are assumed to be at the same height). These points have an associated standard deviation in lambda and in phi, which are longitude and...

Hi PF! I have the given data points here data = {{1.92, 0.74}, {2.32, 1.36}, {2.44, 1.88}, {2.52, 2.08}, {2.68, 1.92}, {2.64, 1.4}, {2.46, 0.78}}; and the following plots the correct interpolation Show[{ListLinePlot[{data}, InterpolationOrder -> 3], ListPlot[\[Lambda]cplx1]}] but...

How do I distinguish between a point of local maxima or minima, when the second derivative in that point is equal to zero?

Given the equation : ##|y| x = x##. Two conditions are possible : (1) ##\underline{y\geq 0}## : ##xy = x\Rightarrow \boxed{y = 1}\; (x \neq 0)##. We note that except for zero, ##-\infty<x<+\infty## for this case. (2) ##\underline{y < 0}## : ##-xy = x\Rightarrow \boxed{y = -1}\; (x \neq 0)##...

We can write the equation given as ##y+|y| = x+|x|## This has a few conditions. (1) If ##\underline{y\geq 0\; \text{and}\; x\geq 0}##, we obtain ##2y = 2x \Rightarrow \boxed{y = x}##. (2) If ##\underline{y\geq 0\; \text{and}\; x < 0}##, we obtain ##2y = 0 \Rightarrow \boxed{y = 0}##. (3) If...

I calculated the derivative of this function as: $$\frac{6x^3-4x}{3\sqrt[3]{(x^3-x)^2}}$$ Now, in order to find and later study non-differentiable points, I must find the values which make the argument of the root equal to zero: $$x^3-x=0 \rightarrow x=0 \vee x=\pm 1$$ and then find the left and...

re: https://www.physicsforums.com/threads/is-it-possible-to-solve-for-t.996132/post-6421205 https://www.physicsforums.com/threads/is-it-possible-to-solve-for-t.996132/post-6421230 Would it be possible to find t and r via the exact same equations as found in posts #4 and #10, and then find the...

Find where increasing/decreasing, concavity, local extrema and inflection points for f(x)=ln/x So here is what I have so far: The derivative is 1-ln(x)/x^2 Critical points are (e,1/e) No concavity Local max is also (e,1/e) (no local min) no inflection points Increase on (0, e) and...

Hi everyone, I need help with this exercise becouse I don't know how to calculate the equilibrium points of a circuit. The original exersice is the following: Assume that the open loop dynamic response of the OVA-opamp gets captured by Fig. 1(a) and consider the circuit of Fig. 1(b). Consider...

zx = 2xy + y2 -3y = 0 and zy = 2xy + x2 - 3x = 0 Subtracting one equation from the other gives y2 - 3y = x2- 3x ⇒ y (y-3) = x (x-3) This leads to the following solutions ( 0 , 0) , (0 ,3) , (3 , 0) but the answer also gives ( 1, 1) as a solution. What have i done wrong to not get this...

I want to find the probability that the two points ($x_1, y_1$) and ($x_2, y_2$) lie on the opposite sides of a line passing through the origin $o = (0, 0)$ and makes an angle $\psi$ that is uniformly distributed in $ [0, \pi]$ with the $x$ axis when the angle is measured in clockwise direction...

Greetings, could you commend or correct the following: A dense subset ##X## of a set ##Y## is a set such that in each environment of ##y\in Y##, there is at least one element ##x\in X##. In other words, the elements of ##Y## can be approximated arbitrarily well by elements in ##X##. A set...

I’m struggling with questions c, e and f. I don’t think I understand how to find stationary points.

I know this is the equation I have to use a(x - h) 2 + k, but don't know what points to use and how to covert to vertex form

proof: Assume instead that every point of ℤxℤ is a cluster point. Note that (0,0)∈ℤxℤ. So by assumption, (0,0) is a cluster point of ℤxℤ. ⇒ every neighborhood of (0,0) contains at least one point ℤxℤ different from (0,0). Consider the open ball with center (0,0) and r =1/2, denoted by A. We...

I have two answers and somehow the answers have the decimal point in different place. 2445859.873 with the answer of 2.44x106 and 254777070.1 with the answer of 254.6x106 why the teacher do that ?

This is a problem in two dimensions. Consider an obstacle (in the form of a line segment) placed at ##x=1##, ##0 \leq y \leq 1##. Now consider the circle of radius ##1## and center at ##(x_0,1)## [initially at time ##t=0##] moving towards right with a combination of: (i) Angular speed of ##2...

I'm reading a section on the derivative of a vector in a manifold. Quoting (the notation ##A^{\alpha}_{\beta'}## means ##\partial x^{\alpha}/\partial x^{\beta'}## - instead of using primed and unprimed variables, we use primed/unprimed indices to distinguish different bases): Now this "we know...

From points A to B at sea, the angles of elevation to the top of the mountain T are 37 degrees and 41 degrees, respectively. The distance between points A to B is 80 meters. 1. Find height of the mountain. 2. Find the distance from point A to the bottom of the mountain. I think making two...