The intersection of two or more sets, written $A\cap B$ or $\bigcap_{i\in I} A_i$, is the set of all elements contained in *all* given sets.

learn more… | top users | synonyms

0
votes
0answers
14 views

How to transform a semilattice into lattice [on hold]

I need to transform a complete semilattice according to intersection and with a unity member into a lattice. I have been researching this problem and can't understand where to start and how to resolve ...
-2
votes
0answers
24 views

Equation for intersection of two solids. [on hold]

Parametric equation $C$ for intersection of $r=2sin \theta $ and $4=x^2+y^2+z^2$
0
votes
2answers
53 views

$y=e^{-x}$ and $y=x$ point of intersection

How can I find the point of intersection of $y=e^{-x}$ and $y=x$ ? Here's the graph
0
votes
1answer
57 views

Given two points and two normals, how to find third point

I really don't know how to search for this specific question. So, I'll try my best to explain my issue. I have the point P1 (pink) and the normal vector M (white) of its line, Given an ...
-1
votes
0answers
13 views

Are the diagonals of cube subset of it?

The intersection of a cube and one of its diagonals is what? 1) This diagonal 2) two of its vertices
2
votes
1answer
44 views

Finding the point on a graph where two lines intersect?

I have the following problem: "An ant has traveled from $(4,8)$ to $(4,4)$ in $30~\text{seconds}$. A mouse located at $(-4,2)$ traveling at $10~\text{units/minute}$ wants to intercept the ant. At what ...
2
votes
1answer
47 views

How to get ellipse cross-section of an ellipsoid

I'm trying to get the major and minor radius of an ellipse which represents the cross-section of a given ellipsoid. This is particularly of interest in the field of RF propagation in terms of Fresnel ...
-2
votes
1answer
58 views

Area between $1$ and $2$ of $x^2$ and $x^{1/2}$ using integrals? [closed]

I need to find the area between $x = 1, x = 2$, between the functions $x^2$ and $x^{1/2}$. Please show all steps so I can get a better understanding! Thank you
1
vote
1answer
26 views

Area between 0,1 of x^2 and x^(1/2) using integrals? [closed]

Please show step by step so I can understand. Thank you!
0
votes
0answers
30 views

Intersection theorems for a certain type of subsets of integers modulo $N$

I've been working on something with integers modulo $N$ and have sort of hit a roadblock where I'd like to have some references. The particular problem goes as follows. We have a system $\mathcal{S}$ ...
0
votes
3answers
85 views

Possible Intersection of Intervals

Suppose there are two intervals, where one of them is fixed. Is there a way to calculate all possible intersections of the intervals as shown in the figure? ? Notice that because $a,b$ and $c$ are ...
0
votes
1answer
40 views

prove intersections of subdomains of an integral domain is a subdomain

Show that the intersection of subdomains of an integral domain D is again a subdomain of D Progress: I know that if that question were instead about the intersection of a collection of subgroups, H_i ...
0
votes
2answers
29 views

Probability - 5 card hand

Question is : You have a 5 card hand from randomly shuffled standard deck of 52 cards. P - Event that hand exactly contains one spade. Q - Event that hand exactly contains one ace. Calculate : a. ...
1
vote
1answer
34 views

Find a matrix X∈V such that U∩W=span{X}

Here is my problem. I've tried reading other people's related questions, but they're always just slightly different, I can't find one like mine and don't really know how to approach this problem. ...
-1
votes
3answers
49 views

Prove that $A \times (B \cap C) = (A \times B) \cap (A \times C)$ [closed]

How to prove that $A \times (B \cap C) = (A \times B) \cap (A \times C)$? I'm just starting relation proofs and need help starting these kinds of proofs.
-2
votes
1answer
20 views

Tangent line to intersection of cylinder and graph of function $f(x,y) = x^3 + y^3 + 2$

Find the tangent line to the intersection of the cylinder $x^2 + y^2 = 2$ with the graph of the function $f(x,y) = x^3 + y^3 + 2$ at the point $(1,\,1,\,4)$.
0
votes
1answer
44 views

Do collinear lines or overlapping collinear line segments intersect?

I am writing a function to find the intersection of a pair of lines and another function to find the intersection of a pair of line segments. The parallel case and the single point intersection case ...
1
vote
2answers
26 views

How far to move a circle along a ray so that it intersects with another circle only once?

Given two 2d circles that have intersected at two points, how do I find the distance along a ray that passes through the center of one of the circles so that when that circle is translated along that ...
0
votes
1answer
47 views

What is A intersection B'

I was answering the questions in my book and came over the question: What is A intersection B complement? I thought the answer would be shading everything EXCEPT the middle part where A and B ...
0
votes
0answers
29 views

Conical frustum tangent to two spheres

I've two spheres in cartesian space: $(x_1, y_1, z_1, r_1)$ and $(x_2, y_2, z_2, r_2)$. They don't intersect each other. I want to calculate the conical frustum tangent to these two spheres. In ...
1
vote
1answer
54 views

Coprime, commensurable integers

I really need help with proving this problem: For natural numbers k,n > 0 we define set M(k,n) = {k,2k,3k...nk}. Find out which elements are in following sets: a) M(i,n) intersection M(j,n), where ...
1
vote
2answers
21 views

Intersection of two lines and the minimum of the sum of the two.

We use a formula in my Operations Research class for finding the 'Economic Order Quantity', given the cost function (sum of Holding and Ordering costs) $$C = \frac{Q}{2}H+\frac{D}{Q}S$$ where $Q$ is ...
0
votes
1answer
32 views

how to calculate these intersections without having to count all combinations

We have the following sets: $X= {(a,b,c,d) ∈S: b< c < d},$ $Y= {(a,b,c,d) ∈S: a< c < d},$ $Z= {(a,b,c,d) ∈S: a< b < d},$ $F= {(a,b,c,d) ∈S: a< b < c},$ Where each of ...
0
votes
1answer
22 views

Calculating both points of intersection on curve $x^2 + y^2 = 16$ and a point equidistant to both when given a straight line

Given the $y$-intercept and gradient of an infinite straight line on the Cartesian plane, how can I find both points of intersection (2D vector) if the line does pass through the curve $x^2 + y^2 = ...
0
votes
1answer
20 views

Function distributing over intersection of sets

Let $\alpha : S \to T$ be one to one, and let $A$ and $B$ be subsets of $S$. Assume that $S$, $T$, $A$, and $B$ are nonempty. Show that $\alpha(A\cap B) = \alpha(A) \cap \alpha(B)$
0
votes
3answers
45 views

Find the intersection of two surfaces

I have been looking into this question : we have two surfaces : $$\big\{(x,y,z)\in \mathbb{R}^3 \mid\;\; S_1\colon\;\; x+z=1 ,\;\; S_2\colon\;\; x^2+y^2=1 \big\}$$ we need to draw or describe the ...
-1
votes
0answers
44 views

linear algebra find a line that intersects another line

question: Let L be the line with parametric equations x = 3+2t y = −5 z = −6−3t Find the vector equation for a line that passes through the point P=(−5, 5, −6) and intersects L at a point that is ...
2
votes
0answers
18 views

Explanation of solving intersection of two planes

I understand that in order to solve for intersection line of two planes, you must find the cross product of the normal vectors of each plane which will be parallel to the line of intersection. That ...
0
votes
1answer
44 views

intersection of an ellipsoid and cylindrical plane.

I need to understand if an ellipsoid and a cylindrical arc intersect, what will be the general equation of the cutted ellipse? How can I solve for that equation? I know in 3D, the equation of an ...
0
votes
1answer
33 views

Intersection of Level Curves and a Ellipse at a given angle

I am preparing for an exam and I'm going over previous administered tests. I have come across the following problem and have little idea how to tackle it. It goes as follows: Let ...
0
votes
1answer
20 views

Calculating number of students who don't study any language

According to a survey of 100 students, there are 40 students studying English, 30 studying French, and 25 studying Spanish. Inaddition, 8 students are studying English and French, 6 are ...
0
votes
1answer
34 views

What does it mean for the infinite intersection of nested sets to be empty?

$\bigcap I_i=\emptyset$ where $I_i=(0, \frac{1}{i})$ What does it mean that the infinite intersection is empty?
0
votes
1answer
23 views

line segment intersection strange results

I'm using this formula. I am getting very strange results with (1,3) to (29,17) and (6,19) to (7,8). I got an X* value of 7. When I plugged this into my intercept calculator it said they intercept at ...
0
votes
1answer
21 views

Probability Intersections

$A$ and $B$ are two events from certain probability space $\Omega$. Knowing that: $P(A)=0.6$, $P(B)=0.7 $ and $P(A\cup B)-P(A\cap B) = 0.2$ Determine $P(A\cap B)$ It says in this sheet that the ...
0
votes
2answers
24 views

Intersection points of two trignometric equations

I am studying for a SAT II Math2C and I came across this question in Barron's book. Solve $2 \sin(x) + \cos2(x) = 2 \sin^2(x) - 1$ [0<= x <= 2pi] The solution says put the equations in a ...
0
votes
0answers
31 views

Unit sphere x axis intersections

This is a problem from a vector calculus textbook, Higher Order Derivatives Consider the unit sphere S given by x^2+y^2+z^2=1. S intersects the x-axis at 2 points. Which variables can we solve for at ...
0
votes
0answers
16 views

How do I define a three space?

I'd like to take a hierarchically-modeled (vertices, lines, faces, etc) 4D object and find its intersection with three-space. In Paul Isaacson's thesis, Computer Graphic Presentation of Hypothesized ...
0
votes
2answers
91 views

Proving that the set of real numbers is a topological space.

I recently finished an activity provided by a professor where one of the questions was to prove that the set of real numbers is a topological space. The hint provided was to "consider the union of ...
0
votes
2answers
13 views

Points of intersection for two polar equations question

Why is it that when I try to find the points of intersection for $r=2$ and $r=4*\cos(2\theta)$, I only get the $\theta$ where the reference angle is $\pi/6$? There is clearly another solution between ...
1
vote
0answers
34 views

Volume of intersection between two equal cones with parallel axes

The two infinite cones (nappes) (each 45-degree wide) have parallel axes. They are oriented in opposite directions, and the top of one is inside the other, so that the common volume V is finite. How ...
1
vote
0answers
17 views

Construction of concurrent or parallel lines from a parallelogram (proof by vectors)

I have a problem with this probably easy exercise on vectors. Any help would be great. Let ABCD be a parallelogram. The line parallel to AB intersect BC and AD in points Q and S, respectively. The ...
0
votes
0answers
31 views

Find points that defines the intersection of an ellipse with a plane.

I want to test for the intersection of two ellipses $E_1$ and $E_2$ in $\mathbb{R}^3$ represented on a computer. In some sense, this isn't a hard problem: ...
1
vote
1answer
23 views

Measure on intersections of unions

Let $(X,\mathcal{A},μ)$ a measurable space and let $A_1,A_2,...∈\mathcal{A}$, assume that $\sum\limits_{j=1}^{\infty}=\mu (A_j)<\infty$ We have ...
0
votes
0answers
14 views

Measure of intersections [duplicate]

Let $(X,\mathcal{A},μ)$ a measurable space and let $A_1,A_2,...\in \mathcal{A}$, assume that $\sum^{\infty}_{j=1}\mu(A_j)<\infty$ I want to show that ...
2
votes
0answers
68 views

Prove that the two polynomials intersect each other only at a single point

Here are the polynomials: $$D^K_1(\theta)=\sum_{i=\lceil{K/2}\rceil}^K \binom{K}{i}\theta^i(1-\theta)^{K-i}$$ and $$D^K_2(\theta)=\frac{1}{2}\sum_{i=\lceil{K/2}\rceil}^K ...
1
vote
1answer
41 views

Vector Parametrization of a Hyperbolic Paraboloid and a Plane

So I need to find the intersection between a hyperboloid ($z=\frac {y^2}{b^2}-\frac{x^2}{a^2}$) and some related plane ($bx+ay-z=0$). I have tried solving for $z$ and equating the two: ...
1
vote
1answer
65 views

Determine Circle of Intersection of Plane and Sphere

How can the equation of a circle be determined from the equations of a sphere and a plane which intersect to form the circle? At a minimum, how can the radius and center of the circle be determined? ...
2
votes
1answer
32 views

Find the equation of line and finding a point in given example

The outer circle is $x^2+y^2=1$ and the smaller circle is $x^2+(y+1-r)^2=r^2$. The arclength is parameterised anticlockwise with $s=0$ at the bottom as shown. If we know $s_n$ and $s_{n+1}$ can we ...
3
votes
1answer
47 views

Longest chord inside the intersection area of three circles

I am currently working on my masters thesis in computer science and I stumbled onto a geometry problem. My goal is to compute the length of the longest possible chord inside the intersection area of ...
3
votes
1answer
18 views

Intersection problem

I am given an interval $A=(0,1)$ and $B=(1,2)$. How can I show that $A \cap B$ is an empty set? I tried to prove by contradiction by saying an arbitrary element $k\in A\cap B$ so $k \in A$ and $k \in ...