# Tagged Questions

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.

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### 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 ...
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### Equation for intersection of two solids. [on hold]

Parametric equation $C$ for intersection of $r=2sin \theta$ and $4=x^2+y^2+z^2$
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### $y=e^{-x}$ 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
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### 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 ...
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### 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
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### 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 ...
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### 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 ...
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### 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
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### 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!
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### 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 $\mathcal{S}$ ...
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### 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 ...
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### 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 ...
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### 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. ...
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### 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. ...
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### 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.
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### 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 $(1,\,1,\,4)$.
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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 ...