Points Definition and 1000 Threads

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...

Homework Statement f(x,y)=2x^3+xy^2+5x^2+y^2 Homework EquationsThe Attempt at a Solution fx(x,y)=6x^2+y^2+25x fy(x,y)=2xy+2y fxx(x,y)=12x+25 fyy(x,y)=2y+2 fxy(x,y)=2y I found the partial derivatives from the equation. I am stuck at finding the critical points from the first two fx(x,y) and...

Homework Statement I'm plotting moving particles and I need a way to refresh the graph space with every loop. Meaning I want the points to NOT leave a trail of other points behind them . Basically I want to get rid of the old points as I plot new ones. Homework Equations N\A The Attempt at a...

I am trying to find the most efficient way to select points on a 2d plane from a set that maximizes the area of the of the shape they define when joined together. The points are all paired (sharing the same A->B vector), with these pairs also appearing mirrored about the origin. Here is an...

There are $9$ points in the interior of a cube of side $1$. a) Show that at least two of them are less than $\frac{1}{2}\sqrt{3}$ apart. b) Can $\frac{1}{2}\sqrt{3}$ be replaced by a smaller number?

Homework Statement I want to know the voltage between a and b in the drawing below.[/B] Homework Equations V= IR The Attempt at a Solution The resistors 5Ω and 5Ω are in series: (Req)1= 5+5=10Ω The resistors (Req)1, 5Ω and 10Ω are in parallel: 1/(Req)2= 1/10+1/5+1/10=2/5 (Req)2=2.5Ω The...

Homework Statement Find critical points and inflection points of: 1/[x(x-1)] Homework Equations 1/[x(x-1)] The Attempt at a Solution using quotient rule, we obtain (0-(2x-1)/(x^2-x)^2 set -2x+1=0 we get 1/2 for critical point. for second derivative, i get...

Homework Statement If d^2/dx^2 + ln(x)y = 0[/B]Homework Equations included in attempt The Attempt at a Solution I was confused as to whether I include the power series for ln(x) in the solution. It makes comparing coefficients very nasty though. Whenever I expand for m=0 for the a0 I end...

This space is homotopy equivalent to the complement of the three coordinate axes in ##R^3##. This is in the chapter about the Seifert-Van Kampen Theorem, so I'm expecting to invoke that theorem. The thing is, how should we choose our open sets such that the intersection is path connected and...

I have what at first seems like a very simple problem, yet I have no clue how to solve it. There is 1 point defined to have 0V, and another point has exactly 1V. Assume there is nothing else in the universe. https://i.imgur.com/iv9oL5j.png How do I find the electric potential and field at any...

edit: fixed typo's andrewkirk pointed out, oops I can cover the projective plane with 2 open sets U,V where each of these neighborhood contains the point that is missing, and the intersection of these two neighborhoods will be simply connected. I was then hoping to invoke the Seifert-Van-Kampen...

I was working on a centripetal question where it said that on glare ice, any car needs to travel 60 km/h to successfully make it through the banked highway, and in good road conditions, a car travels at 90 km/k, I had to calculate the coefficient of static friction. When drawing my FBD, I made...

Given is the function f: R2 -> R, with f(x,y)=x2+y2-6xy+8y. The level surface f(x,y)=1 contains infinitely much points (x,y) where x and y are integer. How can I prove this? I see that it is true with some examples, but how can I prove this. Do I need to use the gradient? Or tangent planes? Or...

Homework Statement An electron is trapped in a finite potential well that is deep enough to allow the electron to exist in a state with n=4. How many points of (a) zero probability and (b) maximum probability does its matter wave have within the well? Homework Equations For infinite potential...

Homework Statement Homework Equations https://answers.yahoo.com/question/index?qid=20120204205204AAEvo8V The Attempt at a Solution This is my attempt following the solution in the yahoo answer, yet it is incorrect... Can anyone tell me if I have made mistake in any of the manipulation? Any...

$\textsf{Find the area of the triangle determined by the points }$ \begin{align*}\displaystyle &P(1,1,1), \, Q(-2,-7,-1), \, R(-7,-1,4)\\ \end{align*} \begin{align*}\displaystyle \vec{PQ}&=(-2-1)i&+(-7-1)J&+(-1-1)k&=-3i-8j-2k\\ \vec{PR}&=(-7-1)i&+(-1-1)j&+(4-1) k&=-8i-2j-3k...

Homework Statement 2. Homework Equations [/B]The Attempt at a Solution so i was thinking i could take a look at small number of points and then generalize it but my method soon breaks down in the diagram i have denoted the resistance of the segment beside it if there is a bracket it means...

Homework Statement Homework EquationsThe Attempt at a Solution First part is easy . Area of the triangular loop is A = (1/2)(2R)(R) = R2 Induced EMF in loop ABC = Rate of change of flux = dΦ/dt = AdB/dt = R2(dB/dt) which is correct . Now the second part has stumped me . I would really...

Homework Statement Find the average y coordinate of the points on the semicircle parametrized by C:[0,##\pi##]-->##R^3##, ##\theta##-->(0, a*sin##\theta##, a*cos##\theta##); a>0 Homework EquationsThe Attempt at a Solution I think the answer should be an integral of the circle in the y...

Let $C$ be a smooth closed curve (no corners) in the plane with a convex interior, and $P$ a given point on $C$. Show that there are points $Q,R$ on $C$ such that the triangle $PQR$ is equilateral.

work done in taking positive charge from A to B in electric field E= potential energy at B - potential energy at A OR potential at A-potential at B Am i correct in both formula?

In the Classical Mechanics volume of The Theoretical Minimum, he writes a shorthand equation for a small change in a function. Please could someone explain exactly what it means and where it comes from?

Homework Statement Problem: Let ##A## be an infinite subset of a ##T_1## space, and let ##x## be a limit point of ##A##. Prove that every open neighborhood of ##x## contains infinitely many points of ##A##. Homework EquationsThe Attempt at a Solution First note that if ##\mathcal{O}## is an...

Hi all, I'm currently in the middle of performing an experiment for the final project of my MSc, and I have a question about how I should go about weighting the data when fitting a curve to it using the MATLAB fitting tool. Firstly, a bit of background about the problem. I am seeing how low...

Homework Statement find the shortest distance from (0,0) to the line passing A(2,3) and B(3,5) Homework Equations ## \frac{y-y1}{y2-y1} = \frac{x-x1}{x2-x1} ## y-y1 = m (x-x1) m1 * m2 = -1 (m1 perpendicular to m2) The Attempt at a Solution line passing A and B points ## \frac{y-3}{5-3} ## =...

Homework Statement A 90 μC point charge is at the origin. Find the electric field at the point x3 = -35 cm , y3 = 80 cm . Express your answers using two significant figures. Enter the x and y components of the electric field separated by a comma. Homework Equations E = kQ/r^2...

Homework Statement A transverse wave that is propagated through a wire, is described through this function: y(x,t) = 0.350sin(1.25x + 99.6t) SI Consider the point of the wire that is found at x= 0: a) What's the time difference between the two first arrivals of x = 0 at the height y =...

Homework Statement Homework EquationsThe Attempt at a Solution The direction of motion of all the three particles are changing w.r.t. lab frame. But , their relative velocity remains constant. relative velocity = vb - va And the distance between the two particles decreases from a to 0. So...

Homework Statement In the circuit shown, what is the potential difference VPQ? Homework Equations No relevant equations given in question The Attempt at a Solution Tried kirchhoffs law. Tried to find equivalent battery and resistance but that doesn't seem to be possible.

Hello Maths Help Board Users, I was hoping for some guidance on the following problem. Thanks in advance for your contributions and time. "A fish population grew according to the following quadratic model - the number of fish on day t is given by P (t) = 800t - t2" Q) Find the average growth...

Homework Statement Homework Equations y-y1 = m (x-x1) ---> line equation $$ (x - a)^2 + (y-b)^2 = r^2 $$ ---> circle equationThe Attempt at a Solution I tried to draw the triangles using, (1, 3) (2, 4) and (0, b) (0, b) is the tangent point to y-axisand used those points for making...

Hi Does anyone know what the straight line distances of L4 and L5 are from Earth? Many thanks.

The equation y = (x/2) + 1 is given. It forms a straight line going through the points A(x, 1.5) and B(x, 2.5). Find the x-coordinates of points A and B. Do I substitute the value of y for each point into the given equation and solve for x individually?

Homework Statement Homework Equations AV = AV P + 1/2*p*v^2 + pgh = P + 1/2*p*v^2 + pgh The Attempt at a Solution For a.) ... divide 3 by 0.1 because of (AV = AV) = 30 ms-1. answer is right. For b.) I am stuck on this one. I tried using the 2nd relevant equation above but i can't seem to...

Hello! Can someone explain to me, in real analysis, what is the difference in expanding a function as a Taylor series around 2 different point. So we have ##f(x)=\sum c_k (z-z_1)^k = \sum d_k (z-z_2)^k## and as ##k \to \infty## the series equals f in both cases, but why would one choose a point...

Homework Statement Homework EquationsThe Attempt at a Solution [/B] All the resistors are connected in parallel across A and B .The equivalent resistance is 1/Req= (1/R) +(1/2R) + (1/6R) + (1/12R) + ... I tried to work with few terms and it seems the effective resistance tends to zero as...

I'm reading a book on vortex methods and I came across the above mentioned terms, however, I don't understand what they mean in mathematical terms. The book seems to be quite valuable with its content and therefore I would like to understand what the author is trying to say using the above...

Homework Statement Points on an elliptical orbit where the speed is equal to that on a circular orbit? Homework EquationsThe Attempt at a Solution I have attempted this question and my calculations show that at points on minor and major axes, the radial component of velocity is zero. Hence at...

Homework Statement For an exam question i need to be able to sketch the root locus of a system, for example the following: g(S) = 200(S+3) / ((S+2)(S+4)(S+6)(S+8)(S+10) The Attempt at a Solution So i counted number of poles and zeroes and calculated no. of asymtodes: p-z = 4 and calculated the...

So I've been trying to wrap my head around this one for several hours now and it just has me stumped. I'm begging, someone, anyone, walk me through it before I swear off numbers for life hahah (Part b) Imgur: The most awesome images on the Internet Thanks in advance for any help anyone can...

How do you calculate the necessary points in a function to numerically integrate it using the Gaussian Quadrature? If I were to evaluate a function using two points, the Gaussian Quadrature needs the value of the function at ##\displaystyle{\pm \sqrt{\frac{1}{3}}}## with weights of unity. How...

Homework Statement Hello! I am at the topic on graphing trigonometric functions. Exercises are rather easy at this point, but I have a problem deciphering how authors of the book choose points for x values. Please, take a look at few examples (including screen shots I attach), and, please...

I just had a lab, and the results really aren't adding up to what i expected. And this is specifically about simple distillation, not fractional distillation. Lets say i have a solution of two liquids, one's boiling point is 90°C and the other is 110°C, a 20°C difference which is pretty close...

Homework Statement Question from OCR A Level Physics Exam 2014 (i) and (ii) = definitions (iii) = explanation (iv) = P.d. at 6Ohm Resistor = 0.48V (v) Suggest why the p.d. between X and Z is zeroHomework Equations I don't think there are any The Attempt at a Solution I couldn't understand...

Hi, I am trying to draw circles at the end points of a line but circle centre is not exactly on the end point of the line. Can somebody please guide me. import java.applet.Applet; import java.awt.*; import javax.swing.*; public class JCircle extends Applet{ int x1=30; int y1=30...

I wrote a Calc II midterm today. Things went quite well, except for one question. I left it blank, as I did not have sufficient knowledge to write anything that made any sense. The question was worth 10% of the exam mark. This question was about a part of a section we covered, but this part had...

Hi how can i plot a curve (red curve at this example) like this: