Points Definition and 1000 Threads

a) At what point do the curves r1(t) = (t, 2 − t, 35 + t2) and r2(s) = (7 − s, s − 5, s2) intersect? (x,y,z) = b) Find their angle of intersection, θ, correct to the nearest degree.

circle: (x+2)^2+y^2=1/2 line: x+2 iv been able to find one point but can't find the other work: 2(x+2)^2 =1/2 divide by 2 on both sides (x+2)^2=1/4 square both sides x+2=.5 subtract 2 x=-3/2 i used that to find the y but that only gives me one point please help

I feel like this should be a super easy problem, but I'm not understanding something about it. The graph of y = f(x) passes through the points (0, 1), (1, 2), and (2, 3). Find the corresponding points on he graph y = f(x + 2) - 1. I graphed the (x + 2) - 1, but what does it mean by...

If there is a bijection between R and R2, then why can't a point on a plane be represented by one real number instead of two?

Homework Statement Member BC exerts on Member AC a force P directed along line knowing that P must have a 325 N horizontal component, determine (a) the magnitude of the force P, Homework Equations Trig I suppose The Attempt at a Solution So I'm not sure if this correct I found two angles...

Two compressed air(A, B) at 100 PSIG: Air A - Compressed with -70C dew point. Air B - Compressed without entering an air dryer. If this two compressed air is distributed into a tank together, would the the air mix to form Air C (same pressure with dew point between air A and B)? I have read a...

Hi been a while, but you guys always square me away. I've recently noticed that when a night time photo is taken with the aperture closed down, (higher f number) seen in the resultant image is a starburst radiating from points of light. The general wisdom is that it is cased by diffraction...

Q6c) Why is the phase difference between two points in a stationary wave equals to zero? I understand that a stationary wave is formed by two progressive waves which have the same amplitude, frequency, wavelength and speed, but traveling in opposite directions.

I know that 1) when eccentricity is less than 1 then it is an ellipse 2) locus of points making sum of the distance from two fixed points(foci) with that point a constant, creates ellipse. Here comes the question, I understand that locus made according to number 2, is ellipsoidal. But how can...

Homework Statement...

##f(z)=z^{\frac{1}{2}}## has brancing point at ##z=0##. ##z=re^{i\varphi}=re^{i(\varphi+2n\pi)}## From that z^{\frac{1}{2}}=r^{\frac{1}{2}}e^{i (\frac{\varphi}{2}+n\pi)} For ##n=0##, ##z^{\frac{1}{2}}=e^{i \frac{\varphi}{2}}## For ##n=1##, ##z^{\frac{1}{2}}=e^{i (\frac{\varphi}{2}+\pi)}=-e^{i...

Circle $\omega$ is described on $ABC$. The tangents to the $\omega$ at points $B$ and $C$ intersect at $T$. Point $S$ lies on the line $BC$ and $AS \perp AT$. Points $B_1$ and $C_1$ are points of intersection of the circle with a radius of $TB$ and center at the $T$ with a line $ST$. Let...

1. Homework Statement ##x^{2}y'' + (x^{2} + 1/4)y=0## 3. The Attempt at a Solution First I found the limits of a and b, which came out to be values of a = 0, and b = 1/4 then I composed an equation to solve for the roots: ##r^{2} - r + 1/4 = 0## ##r=1/2## The roots didn't differ by an...

Homework Statement Hi I'm suppose to find the critical point and minimun or maximum of f(x)=(4/5) Homework Equations [/B] I have a question regarding how to interprete the results The Attempt at a Solution1) we start by finding f'(x)=4/(5*x^1/5) Now my first question is this: we cannot...

Is there a way to know the points if I only have the vector coordinates and I can't use the origin as one of the points? For example, if I have vec(PQ) <-1,4,-5> . Is there a way to know the points of this vector?

Hi... I want to know why charge density is higher at sharp points in a conductor? I have gone through the analogy of two spheres connected by a wire... But is there any other explanation which is not specific to spheres...?

Just for fun, I tried enumerating the topologies on n points, for small n. I found that if the space X consists of 1 point, there is only one topology, and for n = 2, there are four topologies, although two are "isomorphic" in some sense. For n = 3, I I found 26 topologies, of 7 types. For n...

I am wondering how can I solve following problem. I would like to see how can it be solved.

Homework Statement The figure shows a plot of potential energy U versus position x of a 0.220 kg particle that can travel only along an x axis under the influence of a conservative force. The graph has these values: UA = 9 J, UC = 20 J and UD = 24 J. The particle is released at the point where...

A have the set consisting of the complex numbers ##1 + 3r \cos \theta - i r \sin \theta##, where ## r \in [0,1]## and ##\theta## may vary between ##0## and ##2 \pi##. This is my first encounter with mathematica, and am having difficulty discerning between the methods I have found online which...

Determine the singular points of each function: f(z) = (z^3+i)/(z^2-3z+2) So it is my understanding that a singular point is one that makes the denominator 0 in this case. We see that (z-2)(z-1) is the denominator and we thus conclude that z =2, z=1 are singular points. f(z) =...

Hi, What is the physical meaning of zero probability of finding a particle in the square of the Quantum SHO wave function? the particle is supposed to oscillate about the equilibrium position, how would it go from an end point to the other end point without passing by certain points? Could the...

How do I derive an expression or algorithm that determines the existence of a point or set of points within k distance of an N number of other fixed, given points? In application, I expect to only need to determine that this region exists for three to five points. This is part of a greater...

I have an optimization algorithm running 50 full trials with up to 10,000 iterations each (it breaks off if the error goal is reached before that). I want to export the iteration number and the best function value at each iteration to an excel file, then after each trial completes move to the...

I was reading about the tangent vector at a point on a curve. It is formulated as r' = Lim Δt→0 [r(t+Δt) - r(t)] / Δt (sorry for the misrepresentation of the 'Lim Δt→0 ') where r(t) is a position vector to the curve and t is a parameter and r' is the derivative of r(t). All I can...

Hello I have a doubt with the least squares fitting (linear fitting). The low-level statistics textbooks only take into account the statistical error of fitting, but not the error of the fitted points. How is the error of the fitted points taken into account, and included in the total error...

Hello again, I have a small problem. I am looking for local minimum and maximum points of the function: \[f(x,y)=3x^{2}y+y^{3}-3x^{2}-3y^{2}+2\] The first question was how many stationary points are there. I have found the derivatives by x and y: \[f_{x}=6xy-6x\] \[f_{y}=3x^{2}+3y^{2}-6y\]...

apologies if this has been asked before: I'm trying to understand the expansion of the universe and i was wondering. . . . as the universe expands, are new points of space (or is it spacetime) being created? if the answer is 'yes', what are the ramifications of this? my understanding...

Hey! :o The velocity field $u=ax^2, v=bxy$ ($a, b=\text{ constant }$) represents a flow field of an incompressible fluid. Construct the streamlines and find the cutoff points of the flow ($\overrightarrow{u}=(u,v)=0$). From the fact the fluid is incompressible we have that $$div u=0...

Homework Statement [/B] Find points P,Q which are closest possible with P lying on the line x=8+1t y=8+1t z=7−3t and Q lying on the line x=231−6t y=−10−17t z=71−13t 3. Attempt at solution Hi, I am at loss as to how to do this. I know that from the equations I can get point (8,8,7) and...

Can someone rephrase the title question into something more meaningful in terms of Calculus/Analysis?

Hi, What's the surface joining two points in a family of concentric spheres? Shown below is the general idea; it's actually optical. Two rays meet at P from P1 and P2, respectively, where each point comes from a different sphere. How do I find surface S if I know the coordinates of P1 and P2...

I have a question about horizontal axis of energy band. In band structure of FCC lattice, like Si, GaAs, the horizontal axis have discontinuous at U point and K point. But other region have continuous like from Gamma to X or to L. I cannot hit on an idea about this discontinuous. Would anyone...

Hey all 1. Two speakers emit sound in phase with the frequency of 13.2 kHz, the sound from the loudspeakers directed at points A , B and C. Rank the volume of the three points with the weakest first. speed of sound 340m/s 2. 3. I think I need to use Pythagoras says to calculate the path...

Hi! I'm struggling in identifying the lattice points and atom basis. As I understand in a cube, there are 8 lattice points, on on each corner of a cube. But in 2d it is any square between 4 points which are the lattice points. Is this correct? So if the points on the corners are the lattice...

Figure: 1. Homework Statement We know system is in equilibrium and we are given the mass m, and the distances d, r1, and r2. We assume that the rotational inertia of the bar is negligible. What are the forces at points a and b? Homework Equations Torque = radius × Force Force = mass *...

Hi I am attempting a question on moments and beams. I have attached the question and my solutions so far. But having trouble completing d) and e) Can someone show how to work out bending moments and the point of contraflexure? [PLAIN]http:// any help is appreciated thanks

I have two a convex set: {(x1, x2): 1≤ ∣x1∣ ≤2, ∣x2−3∣ ≤ 2} I have to find two points in the set for which the line segment joining the points goes outside the set. I have graphed the function and found my convex set. My question is, how do I find these two points? I have found various points...

Hi guys, I'm new to this site and it seems like it will be a great resource when I'm stuck on a problem. I'll firstly set out the question and then add in my working so far. Question: I was firstly asked to graph the trigonometric functions y=sinx, y=cosx and y=tanx in the interval where x is...

Homework Statement Find the points on the ellipse 4x2+y2=4 that are furthest from the point (1,0) on the ellipse. Homework Equations Ellipse: y=±√(4-4x2) Distance Formula: d=√[(x2-x1)2+(y2-y1)2] The Attempt at a Solution The distance from (1,0) for any point on the ellipse should be...

Homework Statement a) Suppose that A,B,C,D are four "points" in a projective plane, no three of which are on a "line." Consider the "lines" AB, BC, CD, DA. Show that if AB and BC have a common point E, then E = B. b) From a) deduce that the three lines AB, BC, CD have no common point , and the...

Homework Statement Homework Equations V=IR (Voltage = Current x Resistance) Possibly Kirchoff's Loop Rule but I'm not really sure how to use it The Attempt at a Solution I looked at something else on line and ended up doing 9 - 0.7(3) - 6 - 2(3) which got me the right answer for the first...

Homework Statement Find the points on the curve xy^2+x^2y=16 when the tangent line is horizontal The attempt at a solution I found the derivative of the curve -(y(2x+y))/(x(x+2y)) then I found what values of y make the derivative equal 0 y=0,-2x Then I went to plug into the original curve to...

Let $PQR$ be a triangle and let $A$ be an interior point such that $\angle QAR=90^{\circ}$, $\angle QBA=\angle QRA$. Let $B,\,C$ be the midpoints of $PR,\,QR$ respectively. Suppose $QA=2AB$, prove that $P,\,A,\,C$ are collinear.

Hey! :o I am taking the course computability and at the end of the semester I will have a presentation about the Ackermann's function. Should the structure of the presentation be the following? -History -Definition -Proof that the definition is well defined -Table of values -Proof that...

Homework Statement A rectangular region of 125,000 sq ft is fenced off. A type of fencing costing $20 per foot was used along the back and front of the region. A fence costing $10 per foot was used for the other sides. What were the dimensions of the region that minimized the cost of the...

Do you guys know of any program that can give me the radius of a circumference, if I input the cartesian coordinates of some points?

Hi, I am in the process of deleting some services ( or at least stopping them from being loaded upon starting up), but I don't want to delete my restore points. Which services will have the effect that their removal will delete restore points? WWGD: What Would Gauss Do? ( If he knew about...

Question: A cube ABCD, has been placed somewhere in space and is cut by the xy plane. The z-axis indicates the height of the cube. We know that A = <10,7,4> and C = <9,5,6>, find B, D, A', B', C', D' (Where A', B', C', D' are the points which intersect with the xy plane. B and D have the same Z...

Hi there! Just say I have large square piece of some homogeneous resistive material like graphite. How would I go about determining the resistance between any two given points? Further, just say I supply a voltage across two arbitrary points, can I determine the voltage difference between any...