Points Definition and 1000 Threads

The graph of y = x - 1 CUTS the x-axis at x = 1 while the graph of y = x2- 1 TOUCHES the x-axis at x = 1. The point at which the tangent touches the curve is shown mathematically by having two solutions of x, i.e. x = 1 (twice). Is there some deeper meaning to these two identical solutions for x?

Homework Statement in the formula of shear stress, t is the width of member's cross sectional area calculated about neutral axis. for τc , why t is 6.4 ? Why not 102.1 ? second question, why we have to consider that specific area? Cant we consider the (red) area? Homework EquationsThe Attempt...

When we talk about differentiability on a Set X, the set has to be open. And if a set X is open there exists epsilon> 0 where epsilon is in R. Then if x is in X, y=x+ or - epsilon and y is also in X But this contradicts to what i was taught in high school; end points are excluded in the open...

Hi, I'm currently reading Calc III by Marsden & Weinstein. One of the examples shows a plane being drawn through three points. While I understand their solutiom, I'm very curious as to why my solutiom doesn't work. 1. Homework Statement Write the equatiom for a plane through A = (1, 1, 1), B...

Homework Statement The position vector of a particle at time t is R=(1-t^2)i+(3t-5t^2)j. Find the time at which P is moving (a) towards the origin (b) away from the origin.[/B] Homework EquationsThe Attempt at a Solution I've thought about this for a while but I've come to the conclusion...

I'm trying to find out if Mars has any Lagrange Points - L1 and L2 specifically. A lengthy trawl through Google's webpages suggest that they may exist, although if so they would be extremely close to Mars, being gravitationally bound by Phobos and Deimos. Is this true? PS. Should Mars indeed...

I have this really noisy data and I'm wanting to plot Temperature v. Time. I used this function to calculate a moving average. Here's some sample code. BA1='ANP-Heat-BA1.csv' #Time Trial 1 time1=pd.read_csv(BA1,skiprows=0) time1=time1['Time(s)'] #Temperature tmp1=pd.read_csv(BA1,skiprows=0)...

My question involves the discussion in this thread, which I contributed to back in 2009. https://www.physicsforums.com/threads/point-of-inflection.350149/ My question involves the function f(x) = x^(2n) for n greater than 1. Take f(x) = x^4 for example. You differentiate twice and you get...

Homework Statement A 60kg object placed 1m from B is drawn across a beam laid down across two support points. Support point A can only withstand 600N of force before giving way. Support point B is assumed to be capable of withstanding any amount of force. The beam is 6m in length and weighs...

A source that is orbiting close to a singularity of a black hole is transmitting a radio frequency signal that lasts 60 seconds and is repeated infinitely. The signal is being transmitted using the amplitude modulation method (AM Radio). Let suppose that each minute passing in the transmitting...

The other day I was wondering if as the universe is infinite and you can say that every single point in it is the centre of the universe, or that there is no centre for the same matter. Since you are not able to set up a centre in Earth's surface. Is then Earth's surface infinite? When you talk...

The Wiki article shows 5 Lagrange points. I can “see” how the points L1, L4 and L5 points would be balanced by the gravitation of the two bodies, but not the L2 and L3. For L2 and L3, it looks to me like the combination of the Sun’s and Earth’s gravity increase pull and make less stable. So...

Given that the resistance of each resistor is 1.0 ohm, find the effective resistance between P and Q. I do not know how to simplify the circuit. A little help on how to redraw the circuit such that the Reff can be calculated is appreciated.

Homework Statement Q. With the switch closed, what is the voltage difference, VA-VB ? Homework Equations Junction rule: I3 = I1 + I2 Loop rule(s) The Attempt at a Solution I solved for the currents in this circuit when the switch is closed. Top loop(clockwise): +10V1 - 15*I1 - 47*I1 +...

If I a pump with a main suction header and 4 smaller branch connections of difference sizes. Let's say for this example we have (2) 3", (1) 1", and (1) 2". Also let's say our pump is requiring 20 gal/min. The flow rate of each branch would be proportional to the area of the pipe correct? flow =...

Let ##\vec{a}## be the gravitational acceleration along the curve. Then ##|\vec{a}|=a=-g\sin\theta## and ##\vec{a}=a_x\,\vec{i}+a_y\,\vec{j}=-g\sin\theta\cos\theta\,\vec{i}-g\sin^2\theta\,\vec{j}## My question is why does the solution below ignore the direction of ##\vec{a}## and calculate...

Homework Statement For the system: \frac{dx}{dt}=x\cos{xy} \: \: \frac{dy}{dt}=-y\cos{xy} (a) is Hamiltonian with the function: H(x,y)=\sin{xy} (b) Sketch the level sets of H, and (c) sketch the phase portrait of the system. Include a description of all equilibrium points and any saddle...

Hello! (Wave) Let a particle be forced to move over the sphere $x^2+y^2+z^2=1$, that is subject to gravitational forces while also to an additional "dynamic" $V(x,y,z)=x+y$. Find the stable equilibrium points , if they exist.I have found a similar example: Let $\vec{F}$ be the gravity field...

The function g is defined by g(x,y) = 3 + x^3 - x^2 - y^2 on the domain D given by points in the xy-plane satisfying x^2 + y^2 <=1 and x >= 0. So I need to find and classify the stationary points of g, and find the global extreme points of g in D. Do I start with taking partial derivatives and...

$$f(x,y) = \frac{1}{2}{x}^{2}{e}^{y}-\frac{1}{3}{x}^{3}-y{e}^{3y}$$ To start off I found the partial derivatives of $$x: {e}^{y}x - {x}^{2}$$ $$y: \frac{{e}^{y}{x}^{2}}{2}-{e}^{3y}-3{e}^{3y}y$$ Then solved simultaneously for each equation equal to 0. $$y = \ln(x) = -\frac{1}{6}$$ $$x =...

Homework Statement Let P(x) be a polynomial of least degree whose graph has three points of inflection (-1,-1) ; (1,1) and a point with abscissa 0 at which the curve is inclined to the axis of abscissa at an angle of ## \frac {\pi}{3} , Then \int_0^1 P(x) \,dx = ? ## Homework...

In Charles Murray's book Real Smart: Four Simple Truths For Bringing America's Schools Back To Reality, Murray writes about the postmodernists in literary criticism. His description really gets my interest. I think it would be interesting and perhaps amusing (I have a strange sense of humor)...

Hi PF! I used NDSolve to find the solution to a differential equation. I then plotted the solution in mathematica. However, I would like to be able to plot this in LaTex, specifically in TikZ. Can anyone help me here? Thanks so much!

Homework Statement Let ##E'## be the set of all limit points of a set ##E##. Prove that ##E'## is closed. Prove that ##E## and ##\bar E = E \cup E'## have the same limit points. Do ##E## and ##E'## always have the same limit points? Homework Equations Theorem: (i) ##\bar E## is closed (ii)...

Homework Statement The method that we are taught on how to determine the equation of a plane is as follows when given 3 coplanar points: 1. Determine the vectors 2. Find the cross product of the two vectors. 3. Substitute one point into the Cartesian equation to solve for d.Homework...

MENTOR Note: Moved this thread from a math forum hence no template Is it possible to find this? Really only need the semi major axis or even it's orientation. In the image below, elements in red are known.

Homework Statement Need to find the pressure difference between the two water pipes. Specific gravity of water = 1000 kg/m^3, specific gravity of oil = 800 kg/m^3[/B] Homework Equations pressure = height * specific gravity * gravitational acceleration The Attempt at a Solution I think that is...

If $(m_r,\frac{1}{m_r})$ for r from 1 to 4 are 4 points that lie on a circle show that $m_1m_2m_3m_4= 1$

Homework Statement The circuit is shown as above. If ε = 3 volt and each resistor has 2 ohm resistance, then what's the potential difference between point B and point D ? A. 4 B. 3 C. 2 D. 1 E. 0 Homework Equations V = I R R series = R1 + R2 + .. 1/ R parallel = 1/R1 + 1/R2 + ... The...

Homework Statement find the inflection points of x^2-4√x Homework EquationsThe Attempt at a Solution Okay, I started with finding the derivatives; f'(x)=2x-2/√x f''(x)=2+1/√x^3 and made the second derivative =0 (2+1/√x^3=0)(√x^3) 2√x^3+1=0 (√x^3=-1/2)^2 x^3=1/4 x=cube root(1/4) x=0.63 But when...

Homework Statement U = Ax2 - Bx3 Homework Equations du/dx = 2Ax - 3Bx2 The Attempt at a Solution If I was given a potential energy function U = Ax2 - Bx3 and am asked to find: 1) The expression for the force as a function of x. 2) The equilibrium points and determine if are they stable or...

Hello! I've read on several pages that plane mirrors have an infinite amount of focal points. I don't understand? I thought plane mirrors have no focal points because the rays are parallel and don't focus in the first place. Why does a plane mirror have infinity focal points and what does it mean?

Homework Statement Homework Equations The voltage between any two points due to the field from a point charge q is: Kirchoff's voltage laws, which states that the total voltage around a closed loop must be zero, i.e.: The Attempt at a Solution To find V(e<-d) I used Kirchoff's...

What do we mean by break points in band structure ? and what that sentence means : "if the band index were chosen in such a way that the energies are indexed in ascending order for any k then break points would appear in the εnk vs. k plot (with n fixed) wherever two lines intersect." ...

Homework Statement Find the equation of all planes containing the points P(2, -1, 1) and Q(1, 0, 0) Homework EquationsThe Attempt at a Solution I use PQ to get a vector, (-1, -1, 1). I some how need to use another vector so I can use the cross product to find the planes. So i let another...

Homework Statement This is a silly question... but I know that a lens has two focal points but one focal length. If each focal point is at 5cm from the lens, would the focal length be 5cm, or 10cm (adding the position of each focal point together)? Homework Equations N/A The Attempt at a...

Hello! (Wave) How can we find what section of the cylinder $x^2+y^2=1$ corresponds to cylindrical points $(1,\theta,z)$ in the range $\theta$ in $[0,\pi]$ and $z$ in $[ -1,1]$ ? We have that the cylindrical points are of the form $(r, \theta, z)$ where the following relations hold: $$x=r...

Homework Statement Let S \subset \mathbb{R} be bounded above. Prove that s \in \mathbb{R} is the supremum of S iff. s is an upper bound of S and for all \epsilon > 0 , there exists x \in S such that |s - x| < \epsilon . Homework Equations **Assume I have only the basic proof...

Homework Statement The problem includes a graph. All I have is a current to external resistance graph, with 20 A coming at 10R of external resistance. I am to find the EMF and internal resistance of the battery. Here is the problem and my two attempts. http://1drv.ms/1LKbu5H Homework...

Hi! I have a real problem in understanding the use of symmetry for finding equal potential points in nasty electric circuits. There are lots of problems were the solution simply says: "due to symmetry reasons, nodes X and Y have equal potential", but I rarely really understand the so called...

Homework Statement I am only currently in multivariate calculus, so i haven't even touched differential geometry yet, but a question that i had while learning about gradients came up and it led me to the topic of geodesics and differential geometry, so here goes: Class problem: Find the...

If the line passing through the points $p = (1,2,-1)$ and $q = (3,1,0)$ contains the point $(a, 4,-3)$ then what's the value of $a$? I think $a = -3$. but I'm not sure. $(1,2,-1)x+(3,1,0)y = (a,4,-3)$ $(x,2x,-x)+(3y,y,0) = (a,4,-3)$ $(x+3y, 2x+y, -x) = (a, 4,-3)$ so $x = -3$, $y = -2$ and...

Homework Statement Find the potential difference between points a & b. Diagrams attached below. I have doubts in part (b) and (c). Homework Equations Q = CV, kirchhoff's laws The Attempt at a Solution I honestly don't get how the current can flow in opposite directions in part(b). if we...

I'm trying to understand the concept of vectors. Vectors have magnitude and a direction. When I read vector with some values \textbf{x} = \left(\begin{array}{c}x_1\\x_2\\x_3\end{array}\right) = \left(\begin{array}{c}1\\2\\3\end{array}\right) I'm not sure what these values are. Are the values...

Homework Statement isn't that p1 and [2 at the same point ? why shouldn't the P1 = P2 , which is ρg(h1 +h2 +h3) ? Homework EquationsThe Attempt at a Solution

Hi, Suppose I have a data structure that models a polygon, by storing all the nodes of the given polygon, and their connections (i.e. edges). I understand that sorting a set of nodes that may form a concave hull is ill-defined, as there could be many polygons that can be formed with those. But...

Hi, I'm working on some coursework for which I have been modelling a curve to a set of points, and for the final section I am wanting to calculate how close each point is to the curve as a method of comparison between the curves I have calculated. Some of the curves are quadratic, and others are...

Homework Statement "Determine the set of points at which the function is continuous" ƒ(x,y,z) = √y/(√(x2-y2-z2)) Homework Equations ƒ(x,y,z) = √y/(√(x2-y2-z2)) The Attempt at a Solution If y is zero this function would be discontinuous or if the denominator became zero. As much detail as you...

Homework Statement A dipole is centered at the origin, with its axis along the y axis, so that at locations on the y axis, the electric field due to the dipole is given by E vector = 0, 1/4πε0 * 2qs/y^3, 0 V/m The charges making up the dipole are q1 = +6 nC and q2 = -6 nC and the dipole...

Why does light (or indeed any object) travel the shortest path between two points (whether for flat or curved space/space-time) ?