Intersection Definition and 712 Threads

Homework Statement Hi I'm trying to find where these two graphs intersect I would like it to be exact but it isn't quite working. If I have y = tan(x) and y = x^1/3 how can I solve exactly? Homework Equations tan(x) = x^1/3 ? Hmm. I'm not sure. I don't want arctan popping up on the...

Homework Statement Prove: ##A \cup \varnothing = A## ##A \cap \varnothing = \varnothing## The Attempt at a Solution Intuitively both are true. The first is true because union with nothing will eventually return the original set. The second is true because there is no element that can be in a...

Homework Statement identify the point on the line of intersection of the two planes that is nearest to the point (2,1,1) not on this line p1: x + 2y - z - 1 = 0 p2: x + y + z - 3 = 0 Homework Equations The Attempt at a Solution I think I can find the line of intersection by...

Homework Statement Show that if the two lines ##\frac{x - c_1}{d_1} = \frac{y - c_2}{d_2} = \frac{z - c_3}{d_3}## and ##\frac{x - d_1}{c_1} = \frac{x - d_2}{c_2} = \frac{x - d_3}{c_3}## intersect, they lie in the plane ##r.(c \times d) = 0## where c = c1i + c2j + c3k and d = d1i +...

1. Homework Statement . Parametrize a circumference contained in the plane x+y+z=1, centered at (2,-2,1), and of radius 40.2. The attempt at a solution. At first I thought I could intersect the plane x+y+z=1 with the sphere (x-2)^2+(y+2)^2+(z-1)^2=40^2, but then I realized that this is wrong...

If A and B are two independent events then P(A intersection B) = P(A).P(B) I don't refute this but it confuses me. What is the sample space in this? For eg: - If A is the event that we get Head while tossing a coin and B is the event that we get 2 while throwing a die, then what will we be the...

Its been a while since I've done this stuff, and I don't have a text handy. I know that for sets, intersection distributes over union, I don't remember if the same will hold for vector spaces over addition? for example does A \cap (B + C) = A \cap B + A \cap C

Hi, I would very much like someone to help me solve the area of intersection between to intersecting circles (one with the radius r, and one with the radius 1). Tangents at the intersecting point form a 120 degree outer angle. 1. Homework Statement , 2 Relevent equations Here is a...

In the Principles of Mathematical analysis by Rudin we have the following theorem If \mathbb{K}_{\alpha} is a collection of compact subsets of a metric space X such that the intersection of every finite sub collection of \mathbb{K}_{\alpha} is nonempty , then \cap\, \mathbb{K}_{\alpha} is...

Hi, I've attached the problem and the solution. I understand the solution except for one thing. I've circled the part I'm having problems with. How do I decide if the circled part should be f2(x,y,z)=x2-y2-z or f2(x,y,z)=z-x2+y2 I'm sure it has something to do with the fact that the problem...

Homework Statement Find the parametric equations for the line of intersection of two planes Homework Equations Equations for the two planes... z=x+y,-------(1) 2x-5y-z=1 -----(2) The Attempt at a Solution My answers are not correct so I guess I'm going about it the wrong way. Someone...

Problem: Prove that if an element is in the union of two infinite sets then it is not necessarily in their intersection: Proof: Have I solved it correctly?

Problem: Prove that any element in the intersection of two sets is also in their union. I am reading a proof writing book for dummies & the solution given in text is: http://tinypic.com/r/141hn7/5 http://tinypic.com/r/141hn7/5 First Question: In exam/test, is it OK if I write the...

This problem is about seismic wave propagation in a non-homogeneous layer over a halfspace. I'm not asking you to solve anything, I've already solved the problem both algebraically and in Matlab. However, the graph that I've gotten mildy surprises me. According to the graph, the seismic rays...

Homework Statement Let \vec{F}=<xy,5z,4y> Use Stokes' Theorem to evaluate \int_c\vec{F}\cdot d\vec{r} where C is the curve of intersection of the parabolic cylinder z=y^2-x and the circular cylinder x^2+y^2=36 Homework Equations Stokes' Theorem, which says that \int_c\vec{F}\cdot...

Field lines do not intersect because at their point of intersection,we would get two tangents indicating two directions of electric field at that point. Suppose the two filed lines JUST touch at a single point. wouldnt there be only a single tangent at the point??

Homework Statement Show that the circle that is the intersection of the plane x + y + z = 0 and the sphere x2 + y2 + z2 = 1 can be expressed as: x(t) = [cos(t)-sqrt(3)sin(t)]/sqrt(6) y(t) = [cos(t)+sqrt(3)sin(t)]/sqrt(6) z(t) = -[2cos(t)]/sqrt(6) Homework Equations The...

Homework Statement r(t)=(t^2+t)i+(t^3-4)j+(3-t)k r(t) hits the xy plane at the point (12,23,0). Find the angle on intersection of r(t) with the xy plane at that point. Angle= Homework Equations cosθ=(AxB)/lAllBl The Attempt at a Solution I find the answer was 0.0017 degree...

Homework Statement Let {B_j: j \in J} be an indexed family of sets. Show that \bigcup_{i \in J} B_i \subseteq \bigcap_{j \in J} B_j iff for all i, j, \in J, Bi = Bj. Homework Equations The Attempt at a Solution First show that \bigcup_{i \in J} B_i \subseteq \bigcap_{j...

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...

Sketch the 2 polar curves r = -6cos(theta), r = 2 - 2cos(theta). a. Find the area of the bounded region that is common to both curves. b. Find the length around the intersection of both curves. I got a, but I don't know what to do for b because in my calculus book it only shows how to find the...

Homework Statement Let S = {(a,b) : 0 < a < b < 1 } Union {R} be a base for a topology. Find subsets M_1 and M_2 which are compact in this topology but whose intersection is not compact. Homework Equations The Attempt at a Solution I'm not even sure what it means for an element of S to be...

Homework Statement Determine the scalar equation of the plane that contains the line of the intersection of the planes x+y+z=4 and y+z=2, if the plane is two units from the origin. Homework Equations direction of intersecting line is M = N1 × N1 The Attempt at a Solution Let y= 0...

Greetings! I am currently trying to focus my research interests before I begin applying to grad schools this coming fall. When it comes to Physics, I really enjoy Condensed Matter and everything related to it (say, Thermal Physics, Statistical Physics etc). I also took an Electronics...

Hi, Consider you are standing upright and pointing your finger at the ground. Where does the vector coming off the tip of your finger arrive when it hits ground level on the other side of the Earth? ..Think as if you were going to imperviously dig a hole through the Earth and could travel...

Hi everyone, I'm real confused and stucked about a point in applying Nyquist stability criterion... now i'll explain why. I know that it's needed to know how many times I'm wrapping the nyquist critical point (-1;0) with my plot, and I'm enough good to draw by hand a nyquist plot, but the...

Homework Statement Calculate the area of the figure given by these lines. ;x=y ;x=2y ;x+3y=1 ;x+3y=2 Homework Equations This is the intersection. http://www.wolframalpha.com/input/?i=x%3Dy%3Bx%3D2y+%3Bx%2B3y%3D1+%3Bx%2B3y%3D2...

Good afternoon! I am working on a problem, where I at some point have to find the intersection between a polytope and a hyperplan. Consider the following convex set: x2>=x1>=x4>=x3 x1+x2+x3+x4=C1 where C1 is a number. In matrixform it can be represented in the following way: A1*x<=b1...

Homework Statement There is a rod falling at a speed v that makes an angle θ with the x-axis as it falls. Is it possible for the intersection point to move faster than light as it falls. Homework Equations The Attempt at a Solution I have done the geometrical calculations and I...

Hi, I am trying to model an intersection using different rules but I am having a hard time getting the thing to work in the simplest stage. I know there is probably an easier way to do this but I am trying to do it this way: clear grid=zeros(10,10); %grid creation grid2=zeros(10,10)...

Homework Statement I have a surface given by z=x^2 - y^2 and its tangent plane at the point (x,y)=(1,1) given by z = 2x-2y. I am asked to compute the intersection of the tangent plane with the surface. The Attempt at a Solution I did the obvious and set x^2-y^2 = 2x -2y to find the x,y...

Homework Statement Please disregard, sign error corrected in the cross product Determiner the line of intersection of the following two planes. Write the parametric equations for this line. 2x+y-2z=5 3x-6y-2z=15 Homework EquationsThe Attempt at a Solution First I crossed my normal vectors...

Homework Statement At what point do the curves r1(t) = (t, 4-t, 63+t^2) and r2(s)= (9-s, s-5, s^2) intersect? Answer in the form: (x,y,z) = ____ Find the angle of intersection theta to the nearest degree. Homework Equations The Attempt at a Solution i: t=9-s j: 4-t=s-5...

Homework Statement I am given the equation of two lines that are in three space. They are in the form of (X=, Y=, Z= ). The questions wants me to prove whether or not the lines intersect. Homework Equations The equations of the lines. It gives me just the points in the equation, but it is...

intersection between x-2y+3z=11 and <1,0,-2> + t<3,-1,2> my attempted solution (59/11, -16/11, 10/11)

Homework Statement Find a vector function that represents the curve of intersection of the two surfaces: The cone z = sqrt( x^2 + y^2) and the plane z = 1+y. Homework Equations z = sqrt( x^2 + y^2) and the plane z = 1+y. The Attempt at a Solution This problem can be solved as...

Homework Statement Let A and B be two orthogonal subspaces of an inner product space V. Prove that A\cap B= \{ 0\}. Homework Equations The Attempt at a Solution I broke down my proof into two cases: Let a\in A, b\in B. Case 1: Suppose a=b. Then \left\langle a,b \right\rangle =...

My question concerns F_\sigma subsets of \mathbb{R}. An F_\sigma set is one which can be expressed as a countable union of closed sets. I have several books that state that a countable intersection of F_\sigma sets need not be an F_\sigma set (indeed, such sets have their own designation...

Homework Statement Assume V = \mathbb{R}^n where n \geq 3. Suppose that U,W,X are three distinct subspaces of dimension n-1; is it true then that dim(U \cap W \cap X) = n-3? Either give a proof, or find a counterexample.The Attempt at a Solution The question previous to this was showing that...

Hi. Here is a problem I've been trying to solve for some time now. Maybe you could help me. We have two sets \mathcal {Q} is a set of those circles in the plane such that for any x \in \mathbb{R} there exists a circle O \in \mathcal {Q} which intersects x axis in (x,0).\mathcal {T} is a set of...

Let a, b and c be three subsets of universe U with the following properties: n(A)= 63, n(B)=91, n(c)=44, The intersection of (A&B)= 25, The intersection of (A&C)=23, The intersection of (C&B)=21, n(A U B U C)= 139. Find the intersection of (A&B&C). I am told the answer is 10. I tried drawing...

how to calculate the double integral of f(x,y) within the intersected area? f(x,y)=a0+a1y+a2x+a3xy The area is the intersection of an ellipse and a circle. Any help will be appreciated, I don't know how to do this. can I use x=racosθ,y=rbsinθ to transformer the ellipse and...

Homework Statement I have two planes in R4, namely {[2, 0, 0, 1], [1, 1, 2, 0]} and {[-2, 0, 0, 1], [0, 1, -1, 0]}. Homework Equations The Attempt at a Solution Tried to row eliminate, didn't work. Tried figuring out a normal equation, but clearly that won't work in R4. Don't...

Homework Statement Use Stokes' Theorem to evaluate $$\int_{\gamma} y\,dx + z\,dy + x\,dz,$$ where ##\gamma## is the suitably oriented intersection of the surfaces ##x^2 + y^2 + z^2 = a^2## and ## x + y + z = 0## The Attempt at a Solution Stokes' says that this is equal to $$\iint_S...

Hello, I'm trying to compute the intersection point between a n-dimensional vector and a n-sphere. Do you know how to perform this? is it the same than 2 and 3 dimensions? I can't really find much information about this topic. Thank you very much,

Intersection of a sequence of intervals equals a point (Analysis) Homework Statement Let A_{n} = [a_{n}, b_{n}] be a sequence of intervals s.t. A_{n}>A_{n+1} and |b_{n}-a_{n}|\rightarrow0. Then \cap^{∞}_{n=1}A_{n}={p} for some p\inR. Homework Equations Monotonic Convergent Theorem If...

Homework Statement Suppose H and K are subgroups of G. Prove H intersect K is a subgroup of G. Homework Equations Suppose G is a group and H is a nonempty subset of G. Then H is a subgroup of G iff a,b ∈ H implies ab^-1 ∈ H. The Attempt at a Solution Suppose a and b elements of H intersect...

Homework Statement Suppose x,y \in X which is a normed linear space and x\neq y . Prove that \exists r>0 such that B(x,r) \cap B(y,r)=∅ Homework Equations Epsilon Ball B(x,r)={z \in X:||x-z||<r} The Attempt at a Solution So my attempt here is via contradiction and its not...

Let k[x,y,z,t] be the polynomial ring in four variables and let I=<x,y>, J=<z, x-t> be ideals of the ring. I want to show that IJ=I \cap J and one direction is trivial. But proving I \cap J \subset IJ has stumped me so far. Anyone have any ideas?