Points Definition and 1000 Threads

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...

So I have a cube in 3d space and this cube is made out of 8 coordinate points at each corner. Now I have a temperature reading at each point of these corner points. Inside the box I have another point, I want to be able to use the information from the 8 points surrounding the the one middle...

AB, AB, AD are Ld, that is, the three vectors lie on the same plane, so, "yes, the points lie on the same plane" However, AB CB and AD are Li, that is, the three vectors span the space R3, and don't lie in the same plane, so, how can four points that lie on the same plane, that can generate only...

Summary:: I have a upwards opening parabola where I know the Y vertex point = 0. I also know 2 arbitrary points separated by a step size on the parabola. How can I solve for x at the vertex point? X=horizontal plane Y=vertical plane I have a upwards opening parabola where I know the Y vertex...

Hello! I need to make a straight line fit to 8 points, with errors on them. The data is like this ##x = [1,2,3,4,5,6,7,8]##, ##y=[377.488 691.191 , 1030.319, 1428.801, 1753.884, 2113.065 , 2398.642, 2797.664]##, ##y_{err}=[97.145, 131.452, 160.492, 188.997, 209.397, 229.840, 244.879...

Hello everyone, I've been struggling quite a bit with this problem, since I'm not sure how to approach it correctly. The inequality form reminds me of the equation of a circle (x^2 + y^2 = r^2), but I have no idea how to be sure about it. Would it help just to simplify the inequality in terms...

are the points where the derivative is undefined ##x=-4,-2,0, 4##?

Since the answer wants x values only, will my answer be ##x=-\frac{1}{\sqrt{2}}, 0, and \frac{1}{\sqrt{2}}##?

Is my work right?

Hi all, I have recently faced some problem about distances between two curves, and (re?)"discovered" an interesting point that I would like to share with you. In the following, we consider a function of two variables ##f(x,y)##, but it should be clear that the definitions and the result is...

https://www.physicsforums.com/attachments/9838 well not sure why we need 3 different coins other than confusion also each toss at least 2 coins have to have the same face frankly not sure how any of these choices work didn't want to surf online better to stumble thru it here and learn it better...

Might be I am asking a silly question but really want to clarify that would critical points and roots are same terms use interchangeably? I mean we can use critical point as value of x and root also as value of x then what is the difference between?

I have a vector field which is originallly written as $$ \mathbf A = \frac{\mu_0~n~I~r}{2} ~\hat \phi$$ and I translated it like this $$\mathbf A = 0 ~\hat{r},~~ \frac{\mu_0 ~n~I~r}{2} ~\hat{\phi} , ~~0 ~\hat{\theta}$$(##r## is the distance from origin, ##\phi## is azimuthal angle and ##\theta##...

The first thing I want to do is reconcile the two definitions of 4-velocities ##\tilde{U} = \frac{d \tilde{R}}{d \tau} = c \frac{ d \tilde{R}}{ds}##Start off with the usual definition of 4-velocity##\tilde{U} = \frac{d \tilde{R}}{d \tau}##we know that d \tau^2 = \frac{ds^2}{c^2} \Rightarrow d...

How do I algebraically prove how many times the line y=-5 intersects the circle (x-3)^2 + (y+2)^2 =25?

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Hello! I have some data points obtained from a measurement and one of them is defined as the reference point. I need to compute the difference between that reference point and all the others (including itself) and plot the difference as a function of another variable (which doesn't have an error...

Unsure about this, but here is my attempt: B from the first wire: ##\dfrac {\mu _{0}I}{2\pi r} ## B from the second wire: ##\dfrac {\mu _{0}I}{2\pi r} ## Let the point be (x,y) Can I state that: ##\dfrac {\mu _{0}I}{2\pi y}+\dfrac {\mu _{i}\left( I/3\right) }{2\pi x}=0## Hence the magnetic...

I have tried this question and have gotten to an answer from the following steps So my angular separation is 2.85 millidegrees. Have I done this right with the formula I have made use of? Any help would be great, thanks!

I am reading Tej Bahadur Singh: Elements of Topology, CRC Press, 2013 ... ... and am currently focused on Chapter 1, Section 1.2: Topological Spaces ... I need help in order to fully understand Singh's proof of Theorem 1.3.7 ... (using only the definitions and results Singh has established to...

I started noticing some numbers next to each person's profile: Reaction Score and Points. I tried searching for the meaning of these values. Either it is hidden in plain sight, or I'm a bad searcher ?:) My guess is that Reaction Score has to do with the number of likes (or the other positive...

So to do this problem I need the relevant formula for phase difference which is this: I first need to find wavelength and this is lambda = velocity/frequency So lambda = 257/641 = 0.40093603744 m Hence phase difference (in radians) = 2pi * (2/0.40093603744) = 31.3 rads My concern is that...

Hello, I have recently gotten ahold of a hygrometer and was wondering if there were any interesting topics I could research with measured dew points and relative humidities. Thanks in advance.

Hello, I have a question about period doubling and fixed points in the logistic map. Let's say I have a basic logistic map, ##f(x) = 4\lambda x(1-x)##. Let me then compare 1,2 and 4 iterations of this map on fixed points. I assume that ##\lambda## is large enough such that two period doublings...

Summary:: The set of values of ##b## for which the origin and the point ##(1, 1)## lie on the same side of the straight line ##a^2x+aby+1=0## ##\forall~a\in\mathbb{R},~b>0##.(a) ##a\geq1## or ##a\leq-3## (b) ##a\in~(-3,~0)\cup(\frac13,~1)## (c) ##a\in~(0,~1)## (d) ##a\in~(-\infty,~0)## I tried...

First I try to visualize it: w = Surface 1, is a spheroid w_2 = Surface 2 is a cone stretching up the z axisThen I calculate their gradients: $$∇w = (8x, 2y, 2z)$$ $$∇w_2 = (2x, 18y, 2z)$$ The points where they intersect at 90 degrees is when dot product is zero. $$∇w \cdot ∇w_2 = 0$$ $$16x^2 +...

The components of the energy tensor are defined sometimes as the flux of the ith component of the momentum vector across some component jth of constant surface. But isn't the tensor a function of points of spacetime just as the metric? How can you evaluate a surface of j when the tensor is a...

First I find the normal vector given any position: $$w(x, y, z) = x^2 + y^2 + z^2$$ $$∇w(x, y, z) = (2x, 2y, 2z)$$ Normal vector of plane: $$w_2 = x - 2y + 3z$$ $$∇w_2 = (1, -2, 3)$$ ##∇w = ∇w2## => point where planes are parallel = (1/2, -1, 3/2) This is completely off, but I can't find any...

Having made/modified my own distributors for years, I was surprised to see MSD (Multiple Spark Discharge) company show their graph using Points, HEI, and Performance HEI comparisons, with little difference in Horse Power made, up to about 6000 RPM. I know a points mechanical system makes a...

In a closed circuit the battery sets up a potential difference which causes charge to flow. I understand potential difference as the measure of electric potential energy per unit charge, the amount of energy required to move a charge from one point to another per charge. for example when a...

Summary: I need to translate points on coordinate axes as part of a calculation process Hello everyone, I've created the diagram below to try and explain what I am trying to do as part of an existing software app that's used to generate profiles and programs to drive a CNC machine to grind...

Let E, F be such points inside the ABCD square that | ∢AEF | = | ∢EFC | = 90∘ and | AE | = 2, | CF | = 6 and | EF | = 6. Calculate the surface of ABCD.

Suppose we have a function which looks like this: It seems like it meets criteria of probability density functions: this function is asymptotic to zero as x approaches infinity and also it is not negative. My question is: if at some points this function reaches zero (as I have shown above)...

I have ##3x^{2/3}## as an even function although there is some debate as to this in another thread I started but the (5-x) factor means the function is neither odd or even. I also see the domain as all real numbers. Hopefully this is right ? To find the critical points I differentiate f(x) to...

Is there a way to calculate the average linear speed of all points in the volume of a sphere rotating on a single axis? Since points closer to the axis of rotation and the poles move slower than points further out, would the average speed be a simple function of r/2 and pi? It would seem that...

A sketch of the setup and the equivalent circuit are attached. I believe the correct way to solve this is to redraw the circuit as shown in Fig. 3 and then remove the connections between evidently equipotential points, which reduces the problem to a familiar setup of in parallel and in series...

My school recently got an industrial robot arm with a precision turntable. I was thinking how to use this with some cameras/lasers to make a 3d scanner. Where would you folks recommend I start looking?

Hi all, Sorry, in my first message, I posted this question in the Basic Probability section, and so I moved it to this section. I have a surface (for example, a blank paper). In this surface, I have some elements of the set "A" randomly distributed. In this surface, I also have some elements...

Summary: Given three points on a positive definite quadratic line, I need to prove that the middle point is never higher than at least one of the other two. I am struggling to write a proof down for something. It's obvious when looking at it graphically, but I don't know how to write the...

The only restrictions are: -There are N points randomly distributed over an X-Y plane and it is necesary to pass every point at least 1 time, in order to get the path of the minimun distance throught all of them. -If does not matter how many times you pass any of this points. -You have to pass...

I find λ first and I get λ = 3/10 m phase difference = ##\dfrac{2 \pi (1) }{\dfrac{3}{10}} = 6.7 \pi## Answer key = B What is my mistake? Thanks

https://www.freemathhelp.com/forum/attachments/1568726293258-png.13677/ solution] https://www.freemathhelp.com/forum/attachments/1568726452915-png.13678/ take the C-Ordinates of A,B use the formula TO FIND OUT THE SLOPE Of A,Band then compare it to the c-ordinates that you already have for CD Am...

Thanks in advance to anyone that can help me solve this problem, its causing me a real headache. I need to transport a rather large frame that supports a large heavy item. The weight is not evenly distributed along its length. I know the various distances between the supports, the total weight...

Hey, this is a problem given to me by my prof for an assignment, and the TAs at my tutorials haven't been much help. Was wondering where to go with this question. Also, I'm a uni freshman who isn't used to the whole concept of proofs, and a lot of what my profs say seem to be a slew of...

Why would the pressure at points 1 and 2 be the same? I understand they are at the same elevation and due to Pascal's law should have the same pressure, but isn't water denser than air? So in turn, wouldn't it exert more pressure than air? So then how come despite all the water pushing down on...

You and I each choose an undisclosed real number from 0 to 1. Then we compare them to see if we chose the same number. p(a)=0, p(b)=0 -> p(a=b)>0 ? I seem to recall that the probability of one instance of choosing a particular number should be zero, but if two people are doing so and the...

The above screen shot is from, @ the 1:43 mark. Which set of points is random? Answer below. The right set of points.

Let's say you were proctoring some test that required proofs of Jordan canonical forms and rational canonical forms. Would you dock points from a lazy student abbreviating the former as "J-canonical forms" and the latter as "##\mathbb{Q}##-canonical forms" in their proofs?