# All Questions

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### How do I solve this bearing/direction problem?

At 2:00 PM, a ship leaves port and travels N15degreesE at a rate of 20 mph. At 2:30 PM, another ship leaves the same port and travels S75degreesW at 30 mph. How far apart are the two ships at 4:30 PM? ...
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### Functions on $K(X)$ and DVR.

In our definition a variety is an integral and separated scheme $X$ and we denote with $K(X)$ the fild of rational functions on $X$. Let $X$ be a normal variety. Let $D$ be an integral codimension-one ...
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### Sum of transformations - consequences

Well, in matrix-vector transformation, I know that if we take the composition of a transformation, like: $T(x) = A\cdot x$ and $T$ maps from $R^n$ to $R^m$ $S(x) = B\cdot x$ and $S$ maps from $R^m$ ...
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### Confused about biased coin probability

A biased coin with a probability of 0.4 showing head is tossed 4 times. a) What is the probability that the number of heads is odd? I believe the answer to a) is ...
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### When is a variety a graph?

How can I determine if a given variety is the graph of a map? For example, I know that the following variety is a 9-dimensional variety embedded in 12-dimensional a/b/c space, along with a rational ...
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### GA (Genetic Algorithm) and stochastic simulation to solve optimization in R

My problem is to solve the following optimisation problem using GA (Genetic Algorithm)and stochastic simulation. The goal is to solve the maximisation problem : \begin{equation*} \begin{aligned} ...
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### Confidence Interval, t distribution

Exam Question 40 measurements of the Boiling point of the newly developed Alloy gives 95% confidence interval $[923^\circ\mathrm C,933^\circ\mathrm C]$. you can assume that measurement error are ...
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### Properties of convergence in distribution?

If you have a random variable, W which converges in distribution to N, and another random variable X which converges in distribution to B: i) Will W multiplied by X converge in distribution to N ...
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### If $E_q=\{x\in[0,1]:\lvert x-pq^{-1}\rvert<q^{-3}\}$, why is then $m(E_q)\le q^{-2}$ ?, ($m$ is measure)

If $E_q=\{x\in[0,1]:\lvert x-pq^{-1}\rvert<q^{-3},\textit{for some$0\le p\le q$}\}$, why is then $m(E_q)\le q^{-2}$ ?, ($m$ is measure) Must it not be $m(E_q)\le 2q^{-2}$ ? Just YES or NO.
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### how to check slater condition for a constrained optimization problem?

Given any optimization problem that you suppose to solve with Lagrange by thrusting strong duality, you need to be sure the Slater Conditions. And I guess there is no algorithmic way to solve for all ...
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### Infinitely many fractions $p/q$, s.t. $\lvert x-\frac{p}{q}\rvert\le\frac{1}{q^2}$.

If $x$ is irrational, there exist infinitely many fractions $p/q$ with relatively prime $p,q$ such that $\lvert x-\frac{p}{q}\rvert\le\frac{1}{q^2}$. $\textbf{!!!I know the proof!!!!}$. ...
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### Taylor polynomial of $\sin(x)$

It is asked to construct the Taylor Polynomial $p_n$ (polynomial of order n) of the function $\sin (x)$, defined in $(-1,1)$ around 0. Also, I need to decide if $p_n$ uniformly converges to sine in ...
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### Definition of Discontinuities and example

So definition of discontinuity of some function at some point goes like this: A function $f$ is not continious at point $a$, where $a$ is an element of $D(f)$, if there exists $x$, which is an element ...
I need a result which talks about concentration of a 'random matrix' around its expected value. I need the following: $Pr(||X-E[X]|| \le \epsilon) \ge \hspace{2pt} ? \hspace{8pt}, X \in \mathbb{R}^{n ... 0answers 52 views ### Basic question about simplifying a square root I just wanted to know how to get from$\sqrt{12}$to$2\sqrt{3}$Because my buddy was teaching me math the other day and gave me a list with some basic exercises to do, one of which is to solve ... 0answers 32 views ### Formula for residence time/turnover rate with unsteady state I'm not sure this is the correct place to ask my question... but maybe someone could still help me. I'm looking for a way to calculate the residence time/turnover rate. I have the production and ... 0answers 12 views ### minimal fibrations and diagonals In the Quillen model structure on simplicial sets, if$f:X\to Y$is a minimal fibration, is the diagonal$\delta:X\to X\times_Y X$a fibration? Is a fibration$f$minimal if the diagonal$\delta$a ... 0answers 25 views ### How find this$\beta$,such$(\beta,a_{1})=1,(\beta,a_{2})=2,(\beta,a_{3})=4$Question: let$a_{1},a_{2},a_{3}$is three dimensional European space$V$is a set of standard orthogonal basis,and let$\beta\in V$,and such $$(\beta,a_{1})=1,(\beta,a_{2})=2,(\beta,a_{3})=4$$ Find ... 0answers 250 views ### How to linearize the product of two continuous variables in linear programming I have a question when I deal with a linear programming model. The situation is that: I have some constraints in the model. All the constraints are linear, except some terms, which is the product of ... 0answers 24 views ### sorted list with components in ascending order Sorry for poor translations, I'm German. I've got a homework to express following in first-order logic: "s is a list, which components are natural numbers in ascending order" Is the following ... 0answers 30 views ### Determining the Kelvin transform Find the Kelvin transform (relating to$S_1(0)$) of the harmonic function$u(x,y)=\exp(x)\cos(y)$. Here is how we defined the Kelvin transformation resp. the Kelvin transform: Consider ... 0answers 70 views ### A matrix of size$n\times n$with several properties like Markov matrices Could you find a square matrix$A=[a_{ij}]$of size$n$such that satisfies to following properties 1) For all$1\le i\le n$,$\sum_{j=1}^n a_{ij}=0$2) For all$i$,$a_{ii}<0$and for$1\le i\ne ...
For my homework I'm suppose to use the method of undetermined coefficients to derive an interpolatory quadrature formula of the form $$\int_0^{3h}f(x)dx \cong A_0f(0) + A_1f(h)+A_2f(3h)$$ To solve ...