Points Definition and 1000 Threads

Hello MHB, I am doing some old exam and got less knowledge for this problem. consider the graph of the function $$g(x)=\frac{1}{x}, \ x\neq 0$$ the point $$\left(3,-1 \right)$$ lies on two tangents to the graph. Decide tangents equation. My progress well I derivate and find the slope...

This is a tiny part of a presentation I am giving Friday, any and all help is appreciated. Homework Statement Suppose we have a circle centered on O. We are looking for the distribution of the points generated by the following method: We choose a random radius of the circle, and then choose...

Homework Statement Find the coordinates of α, β, and γ rel. to u, p, q (unit vectors) of x = 1/9( 2i + 62j - 11k )( (Note there orthogonal to each other) Question 2 : The position vectors of two points A, B has position vectors a = < 2, 1, 7> and b = <1, 4,-1> Find the parametric vector...

Homework Statement (see attachment, ignore those marks done with the pen) Homework Equations The Attempt at a Solution I think this has to do with calculating torques and forces but I don't know about which point to calculate torque about. I know this is a very less attempt...

This is more of a hypothetical "it doesn't work, but WHY?", but what stops something from being at point A now, then moving to a different point an instant later without traveling through the space in-between? What makes it so that the motion we observe is always (nearly) contiguous? Is there...

Is there a way to find all points of intersection in a polar co ordinate graph without the need to draw the graph. i/e USing algebra? If so, how?

Homework Statement I'm told to find the 2 points the two curves P and Q will intersect on and the parametric equations are: P (x=t, y=2t-1) Q (x=3t-t^2, y=t+1) The Attempt at a Solution I know I'm supposed to set x-equations and y-equations equal to each and solve so that...

How do you find average acceleration given a table with points of velocity (ft/sec)? t (sec): 0 15 30 45 60 v(t) (ft/sec):0 40 60 70 75 the question asks: Find the average acceleration of Rocket A over t=[0,60] seconds. I used change in v(t)/change in time to find 4...

Hey folks, I'm trying to obtain the melting points of several materials in a vacuum. It's pretty straightforward to look up the melting point in 1 atm, but I'm having difficulty doing this in a vacuum. One material in particular I'm looking at is Teflon. If anyone can provide any...

Find the value of m such that the sum of the squares of the vertical distances from each of the points (1,1) , (2,2) , and (3,2) to the line y=mx is minimized. Hint: Find the sum as a function of m (no x in the expression) and then minimize it. Distance equation...

Homework Statement Find dy/dx on the curve 1/3*y^3 + y*sin(x) = 1 - x^6 At which points on the curve does this derivative does not exist? Find the slope of the line tangent to the curve at the point (0,3^(1/3)). Homework Equations dy/dx = - Fx/Fy The Attempt at a Solution I solved dy/dx...

Find the ellipse centered at the origin that runs through the points (1,2), (2,2), and (3, I). Write your equation in the form $$ ax^2 + bxy + cy^2 = 1 $$ I understand the $$ ax^2 $$ and $$ cy^2 $$ in the equation because the equation of an ellipse centered at origin is $$ (x/a)^2 + (y/b)^2 = 1...

I have a group of 8 3-D points which all sit on an arbitrary plane (The points were generated by projecting the corners of a axis aligned cube, box, onto the plane) I wish to group all the points in a rectangle with the smallest surface area - so a tight fit rectangle. What I am doing at...

This is a prediction that is made every day. If I do a back test assemble a curve composed of each days' prediction, I get fair results. However, if I smooth this backtest curve, I get fantastic results. So what I need to do is take today's prediction and the prediction time history...

Homework Statement Let A, B, C, D be distinct points on a circle with centre O. If there exists non zero real numbers x and y such that ##|x\vec{OA}+y\vec{OB}|=|x\vec{OB}+y\vec{OC}|=|x\vec{OC}+y\vec{OD}|=|x \vec{OD}+y\vec{OA}|##, then which of the following is always true? A)ABCD is a trapezium...

Homework Statement 7 Find the points on the ellipse x^2 + 2y^2 = 1 where the tangent line has slope 1 Homework Equations The Attempt at a Solution I got the correct X and Y values but this gives me four possibilities and the answer key says there are two points. I got x...

Hi Folks,I have come across some text where f(x,y)=c_1+c_2x+c_3y+c_4xy is used to define the corner pointsf_1=f(0,0)=c_1 f_2=f(a,0)=c_1+c_2a f_3=f(a,b)=c_1+c_2a+c_3b+c_4ab f_4=f(0,b)=c_1+c_3bHow are these equations determined? F_1 to F_4 starts at bottom left hand corner and rotates counter...

Hello everyone, I am currently reading 'Geometrical Methods of Mathematical Physics' by Bernard Schutz and I have some questions about manifolds. I'm fairly new to Differential Geometry so bear with me! On P33 he states that 'manifolds need have no distance relation between points, we...

Homework Statement \dot{x} = -pxy + qx, \dot{y} = rxy - sy where p,q,r and s are positive constants (p does not equal r) Question is : Determine all the equilibrium points for the system of differential equations given above, expressing your answers in terms of p,q,r and s The...

I have a practical application which relies upon the generation of evenly distributed points on a sphere. When I first considered this problem, I learned that some number of polyhedrons (Platonic polyhedrons) had each vertex lying evenly spaced from the others within the surface of a sphere...

1. Given. F(x) = 4x/(x^2+1) 2. Problem Find all points (x,y) where the function has a horiztonal tangent line 3. Attempt I took the derivative of F(x) and came to (-4x^2+4)/(x^2+1)^2 I set it equal to zero and found an x value of 1. I used that x value and plugged it into...

I'm supposed to identify the points of inflection in the following graph: I know the point of inflection is where concavity changes, and I keep getting stuck on one answer that is apparently not correct. I believe that the following points are points of inflection: ABCDEFHJKL A -...

I find it surprising that China has found a way to measure intelligence! Let's kill all diversity and raise a new generation that are good at taking IQ tests.

Homework Statement A long metal cylinder of radius R is carrying a current ##I_C## into the page and the current in a second wire a distance 2R from the cylinder is set so that the magnetic field at point P is zero. Calculate: 1. the current in the second wire, 2. the magnetic field at the...

This sort of came up the other day: Given a sequence of monotonically decreasing points, a_n, such that a_n \rightarrow 0 does there exist an analytic f on ℝ such that f(n) = a_n ? I figured there should be some sort interpolation theory on this, but I haven't found anything...

1. Homework Statement [/b] So I found this problem online, and I really do not know how to go about solving it! My professor has done similar problems in class, but it's still a little confusing. A current of 1.2 A flows from A to B. Therefore, the magnitude of the potential difference...

1. A submerged scuba diver hears the sound of a boat horn directly above her on the surface of the lake. At the same time, a friend on dry land 22.0 m from the boat also hears the horn (Figure 1). The horn is 1.2 m above the surface of the water. What is the distance (labelled by"?" in Figure 1)...

Why does it write all that stuff about fxy2? Isn't it unnecessary? I mean, isn't the following true? If in a point (a,b): fx=fy=0 and fxxfyy>0, then the partial derivatives must be either both negative or positive, and thus point (a,b) is a local minima or maxima. And if fxxfyy<0 => (a,b) is a...

[FONT=Georgia]Look at this page and the Proof part, Fermat's theorem (stationary points) - Wikipedia, the free encyclopedia [FONT=Georgia]How to change the proof 2 into a proof of higher dimensions or can you give a proof of Fermat's theorem of higher dimensions?

Homework Statement At what points on the curve y = (x^2)/(2x+5) is the tangent line horizontal? Homework Equations Quotient rule The Attempt at a Solution I figured out the derivative which is 2x(2x+5) - 2x^2 ----------------- (2x+5)^2 I also know that for the equation of...

Hi gang, I am hoping you can clear something up for me. When evaluating the potential of a solid sphere, I find myself confused about the volumes used such that, \phi = Q \int_{\infty}^R \frac{1}{V_1} r^2 \sin(\theta) \, dr \, d\theta \, d\phi + Q \int_R^r \frac{1}{V_2} r^2 \sin(\theta) \...

in the picture below http://tinypic.com/view.php?pic=9riq9l&s=6 if we know the angular velocity of the gear on the left, as well as their current distance from contact point, what can we say about the velocity of the right rod at the contact point at anytime t? we know it is not...

Homework Statement Plot the following point: B(-2,3,5) The Attempt at a Solution If I were to plot (-2,3,5), when I make my first movement of -2, it does not move anywhere on the y-axis correct and when I am moving on my Y axis, There is no movement in the z axis?

Hello, I have come across this sentence in a paper: "For a metal, the introduction of a finite temperature T can be of a more technical use: the Fermi surface of the system is no longer a sharp feature in the Brillouin zone, and the number of electronic wave vectors "k points" needed to...

Homework Statement Find the maximums, minimums, and saddle points (if any) of Z = 4Y3 + X2 - 12Y2 - 36Y +2 Homework Equations The partial derivatives with respect to X , and Y. The Attempt at a Solution I took the two partials, and set them equal to zero. The problem is...

Is there a formal way to measure the error between some arbitrary points and a non-linear curve in order to minimize it?

Homework Statement Find critical points. f(x,y) = (x-1)^4 + (x-y)^4 The Attempt at a Solution \frac{\partial f}{\partial x} = 4(x-1)^3 + 4(x-y)^3 \frac{\partial f}{\partial y} = - 4(x-y)^3 \frac{\partial f}{\partial x} = 0 , \frac{\partial f}{\partial y} = 0 , -...

If I specify the latitudes and longitudes of both point A and B on the surface of a unit sphere, how can I find the great circle angle between the two points? Say if Latitude and longitude of A is ##\epsilon_1 \;\hbox { and }\;\tau_1## respectively. Latitude and longitude of B is ##\epsilon_2...

Hello, I'm working on a design for an architectural structure, and I am choosing the material for the design. Are there any resources that will tell me the breaking point for like "1-inch" of material X. I need something that can support the weight of a car. Thanks! Carpetfizz

Homework Statement Determine the set of points at which the function is continuous. F(x,y) = arctan(x + √y) Homework Equations Perhaps the chain rule? The Attempt at a Solution I derived it, but the solution in the back of the book is nothing like what I expected. It involves e and...

Jordan writes:

U=kqoq/r ? Please look at the attachments. I was wondering if someone could please check my work. That is all. Thank you for your time!

Given a circle centered at the origin, how can one prove that the limit of the quotient of the number of lattice points on the circle over the radius goes to zero as radius goes to infinity?

for cos y the critical points are n*pi - 0.5*pi for cos 2x, the critical points should be n/2 * pi - 0.25*pi because if I set y=2x = n*pi - 0.5*pi , I get the eq in red for x. However if I do it graphically, I just get n*pi - 0.25*pi. The question: why algebraically I am constrained to use...

Homework Statement In the figure below, determine the point (other than infinity) at which the electric field is zero. (Let q1 = -2.45 µC and q2 = 6.50 µC.) Homework Equations The Attempt at a Solution Here is a little commentary my author gives on this problem: Each...

Homework Statement There are two parallel plates. The plate on the left has an electric potential of +60 Volts. The right plate has an electric potential of 0 Volts. The plates are 8.0mm apart. Between the two plates lies a point P 2.0mm from the left plate with a charge -3.5pC. Point R lies a...

I model arterial baroreflex data that I have collected in humans using the Kent equation which is: y=p1/(1+exp((x-p3)*p2))+p4; where Y=heart rate, X= estimated carotid sinus pressure, p1=range of Y, p2=slope coeff, p3=centerpoint on X, p4 = minimum Y. I use Sigma Plot to do a best fit line...

Homework Statement I was looking at the following tutorial http://mathworld.wolfram.com/Circle.html Homework Equations equations 31-34 o the link The Attempt at a Solution My question is just whether this means that for 31-34, the answers are determinants of 3x3 matricies...

Homework Statement How to find equilibrium points between four point charges? How do you determine whether these equilibrium points are stable, unstable, or neutral? I know the sum of the forces should equal zero, but that's it. How do you determine the stability of the equilibrium...