# All Questions

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### For a tournament T of order n, let $Δ=max \{od v:v∈V(T)\}$ And $δ=min\{od v:v∈V(T)\}$ Prove that if $Δ-δ< \frac n2$, then T is strong

For a tournament $T$ of order $n$, let $Δ=max \{od v:v∈V(T)\}$ And $δ=min\{od v:v∈V(T)\}$ Prove that if $Δ-δ< \frac n2$, then $T$ is strong Here is my final attemp. Prove this by contrapositive. ...
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### Alpha and Omega limit sets (dynamical systems)

What are all the possible $α$- and $ω$-limit sets of points for the linear system of equations $x'=Ax$ given by the following matrices $A$: I guess I don't really know how to get started, Could I ...
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### determine the revenue, cost and profit functions

The demand of gloves is $$x(p)=20,000-2000p,$$ where p denotes price per pair. The total cost of $x$ pairs of gloves is $$c(x)=30,000+1.50x$$ dollars. Determine the revenue and cost functions in ...
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### Multiplying algebraic terms problem

Today I have this problem to solve (I already know the answer though, because I cheated by looking it up): The area of a rectangle is equal to x^2 + 9x + 18. If the length of one side is 2x+6 , what ...
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### Prove the condition of the score sequence make the tournament strong

Prove the theorem 4.19: A non-decreasing sequence $\pi:s_1,s_2,\ldots,s_n$ of nonnegative integers is a score sequence of a strong tournament if and only if $$\sum_{i=1}^ks_i > \binom k 2$$ for ...
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### How can I solve this equation analytically. $\sqrt{x+\sqrt{2x+\sqrt{3x…}}}-100x\sin(x)=0$

How can I solve this equation analytically. $$\sqrt{x+\sqrt{2x+\sqrt{3x...}}}-100x\sin(x)=0$$
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### Picking 3 random books probability problem

So the question is: Suppose a bookcase holds 6 chemistry, 5 math, 3 physics, and 8 computer science texts. if 3 books are selected, find the probability that none of the math texts are selected. My ...
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### Basic question: $H^1$ and $H^{0,1}$

Please could you explain why for a smooth projective variety over $\mathbb{C}$ (or - if you prefer the analytic world - compact complex manifold) $T$ we have $H^1(\mathcal{O}_T)\simeq H^{0,1}(T)$ as ...
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### Fourier Differentiation Property

I have been given this problem to solve: Define the function f(t) by $$f(t) =\begin{cases} e^{-kt},& t \geq 0 \\ 0,& \text{otherwise}\end{cases}$$ where $k > 0$ is a real number. ...
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### Fun results from modular arithmetic

I'm trying to go through various bits of neat, fun math with some junior-high-school students in my local area, and am thinking of doing a short unit on modular arithmetic/finite groups. I'm looking ...