# Tagged Questions

Homework questions are welcome as long as they are asked honestly, explain the problem, and show sufficient effort. Please do not use this as the only tag for a question. For the answers on homework questions, helpful hints or instructions are preferred to a complete solution. Please do not add ...

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### (Improved; Kindly assist )CSI Forensic Maths

In a square room with 7 m-long sides, five people have shot at random people. They all had two bullets and killed two people in the crowd. Other people in the room were not hurt. CCTV recordings show ...
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### What is $\lim\limits_{k \to 0}{f(k) = 2 + k^{\frac{3}{2}}\cos {\frac{1}{k^2}}}$

Just want to check this one: I got: $$\displaystyle \lim_{k \to 0}{f(k) = 2} \;+\; \lim_{k \to 0}{k^{\frac{3}{2}}\cos {\frac{1}{k^2}}}$$ Since $\lim\limits_{k \to 0}\cos{\frac{1}{k^2}} = 0$, using ...
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### Successes or failures in a row

Let random variable $X$ be defined as the number of independent Bernoulli(p) trials required until we observe either two successes or two failures in a row. Find $P(X=n)$ for $n=2,3,4, \ldots$ Then ...
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### prove that the set of rational numbers is not connected on the real line

Could someone help me through this problem? Prove that the set of rational numbers is not connected on the real line
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### help me prove that a matrix with a trivial nullspace must always be invertible

I'm proving that $A^tA$ will be positive definite iff $A$ is invertible. I guess that there are ways to show this with determinants, eigenvectors. But I've just gone with positive definites must ...
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### Solving geodesic problems with Euler-Lagrange equation

This is the question: Problem B.1 Two cities - Tel-Aviv, Israel and SanDiego, CA - have the same latitude 32 ◦ N, but, diﬀerent longitudes: Tel-Aviv is 34 ◦ E and San-Diego is 117 ◦ W. What is the ...
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### How to approach this combinatorics programming question?

This question is asking for the pseudocode mainly: Design an algorithm that would play "Word Game." In Word Game an English word is supplied, then one is supposed to form as many words that ...
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### Linear algebra - Dual, functionals

Given three functionals $f_1(p) = \int_0^1 p(t)\,dt$ $f_2(p) = \int_0^2 p(t)\, dt$ $f_3(p) = \int_0^{-1} p(t)\, dt$ defined on $V = P_2$, the space of all polynomials over $\mathbb R$ of degree ...
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### Probability that a coin lands on tails an odd number of times when it is tossed $100$ times

A coin is tossed 100 times , Find the probability that tail occurs odd number of times! I do not know the answer, but I tried this, that there are these $4$ possible outcomes in which tossing of ...
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### Find the different equivalence classes of this relation on A and show their connection to a partition of A.

Define a relation $R$ on the set $A = \{n \mid n \in \mathbb{N} \textrm{ and } 0 < n < 14\}$ such that $R$ is an equivalence relation on $A$. (You can either define a property on $A$ or simply ...
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### How to find $h'(x)$, if $h(x) = f(g(x))$.

Let $f'(x) = \sqrt{3x + 4}$ and $g(x)=x^2-1$. Find $h'(x)$, if $h(x) = f(g(x))$. I know that $g'(x) = 2x$, but I don't know how to do further. The answer is $h'(x) = 2x \sqrt{3x^2 + 1}$.
I am stuck with a homework problem which is about the modelling of tumor growth by ODEs. The function $A(t)$ is the amount of drugs in the patients blood. During some intervals (namely, $(n,n+\tau)$, ...