# All Questions

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### Is that possible that a inscribe angle can be greater than 90 degree

I have found a question like following: Its asked that what could be the angle x if BC is not diameter of the circle. So, my question is if it possible to be greater then 90 for an angle like x?
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### doubt regarding power of graph

could you help me in clarifying a doubt regarding how to find square of a graph g from graph g.the doubt occurs on 15th page of the document which I have shown you by the link given.the doubt is that ...
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### Solving for derivative of Frobenius norm

I am trying to solve the following objective: $\arg \min_{A,C} \|AB\|^2_F + \lambda\|C\|_1$ $\text{s.t. } D = AB + C$ where: $D,A,C \in \mathbb{R}^{d \times n}$ and $B\in \mathbb{R}^{n \times n}$ ...
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### Proving that a propositional theory of any cardinality has an independent set of axioms

This is exercise 1.2.19 from Chang & Keisler's Model Theory, which has been giving me a headache for some time now. Let $\mathscr{S}$ be a given propositional language of any cardinality (i.e. ...
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### Proof Verification: Putnam 1996 A4

PROBLEM: Suppose we have a necklace of $n$ beads. Each bead is labelled with an integer and the sum of all these labels is $n-1$. Prove that we can cut the necklace to form a string whose consecutive ...
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### Distributing Giving out Quarters Suplus and Shortage Problem

Amy, Betty, and Chloe have some quarters. Amy gives some of her quarters to Betty and Chloe, making their quarters doubled. Then Betty dos the same thing, making Amy and Chloe's quarters doubled. And ...
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### Regular Value Theorem Using Implicit Function Theorem in Calculus.

I want to prove the follwoing: THEOREM. (Regular Value Theorem.) Let $f:\mathbf R^n\to\mathbf R^m$ be a smooth function and $\mathbf a\in\mathbf R^n$ be a regular point of $f$. Let ...
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### Curves through points

An astronomer wants to determine the orbit of an asteroid about the sun. He sets up a Cartesian coordinate system in the plane of the orbit with the sun at the origin. By Kepler's law the orbit must ...
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### Issue differentiating the Lambert W function

I want to differentiate the Lambert W function (the inverse of $y = xe^x$), I didn't think it would be that difficult a problem but it's causing me some problems. I tried this method: (1.) Implicitly ...
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### Uniqueness of a real number sequence

Let ($x_n$) be a real number sequence. I'm interested in sequence(s) ($y_n$) that we can construct based on ($x_n$) with the property that every term in it is smaller than only a finite number of ...
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### Can someone explain to me in detail why the answer to number's 51 is 1/6 and 53 is 6. [on hold]

51.)limit as x approaches 4 f(x)=(sqrt(x+5)-3)/(x-4), 53.) limit as x approaches 9= f(x)=(x-9)/((sqrt x)-3)
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### How to make an expression manifestly symmetric

Believe it or not, the following expression is symmetric under the exchange of the indices $j$ and $k$, i.e. $R_{kj}=R_{jk}$: $$R_{jk}=j s_js_k-\sum_{n=1}^{\min(N-k,j)}(k-j+2n)s_{j-n}s_{k+n}$$ Where ...
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### question for recommending a good textbook in representation of quivers

I am taking representation of quivers, and the lecture notes seems not enough. So could you recommend a good textbook for this course. There is a new book "Quiver Representations, by Ralf Schiffler" ...
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### Finding all solutions to the equation $|||||x|-1|-1|-1|-1|=0$

I was presented this question by a student I was tutoring: Suppose $x \in \mathbb{R}$. Find all solutions of the equation $$|||||x|-1|-1|-1|-1|=0.$$ What I explained to the student: Given ...
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### Asymmetric Gaussian with compact support

For a genetic program, I need to generate a set of random numbers, summing to 1.0. Please visit http://www.iic.ecei.tohoku.ac.jp/~kato/papers/t.kato_spr2002a.pdf. This paper describes how an ...
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### Dummit and Foote as a First Text in Abstract Algebra

I'm wondering how Dummit and Foote (3rd ed.) would fair as a first text in Abstract Algebra. I've researched this question on this site, and found a few opinions, which conflicted. Some people said ...
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### The nullity of a square matrix with linearly dependent rows is at least one. TRUE OR FALSE

Here is the answer my textbook gives. http://imgur.com/ycCRoWK I wonder: Why does the author ask this question specifically for square matrices? Is it different for other matrices.
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### In uniform circular motion in R^2, is acceleration in the normal bundle?

In physics we learn that accleration is a vector quantity parallel to the radius and orthogonal to the velocity. With the embedding $\mathbb{S}^1 \hookrightarrow \mathbb{R}^2$ and the induced ...
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How many nonzero entries does the matrix representing the relation R on $A=\{1,2,3,\ldots,20\}$ consisting of the first $20$ positive integers have if $R=\{(a,b) \mid a >b\}$?
Suppose $f$ is a diffeomorphism.Prove that all hyperbolic periodic points are isolated. I tried using the mean value theorem using two diferents periodic points (assuming the periodic points arent ...