Mathematics Questions, Problems & Solutions : TransWikia.com ~ Page 189

How many ways to select 5 objects from 3 groups of 4 objects each?

Consider this problem:A question paper on mathematics consists of twelve questions divided into three parts A, Band C, each containing four questions. In how many ways can an examinee...

Asked on 11/30/2020 by ijm

1 answer

Integrate $int_{-infty}^{infty} frac{dx}{1+x^{12}}$using partial fractions

How do I integrate the improper integral $$int_{-infty}^{infty} frac{dx}{1+x^{12}}$$ using partial fraction decomposition? I am restricted to use only the principles taught in Calculus 2, which entails partial...

Asked on 11/30/2020

2 answer

Galois connection for annhilators

https://en.m.wikipedia.org/wiki/Annihilator_(ring_theory)Under the section "Category-theoretic description for commutative rings"Wikipedia states few results for galois connection for annihilator for modules.$$1. ann(ann(ann(S)))=S$$ and $$2.span(S)subset ann(ann(S))$$....

Asked on 11/30/2020

1 answer

How to compare the growth rate between $lnln n$ and $2^{lg^* n}$

Simple question, I've read in the answer sheet that the growth rate of $lnln n$ is bigger than $2^{lg^* n}$, but I can't figure out how...

Asked on 11/30/2020 by Aesop 의섭

0 answer

How do I use only NAND operators to express OR, NOT, and AND?

How do I use only NAND operators to express OR, NOT, and AND?I assume that AND would just be not NAND, but how to do the others?...

Asked on 11/29/2020 by user831636

0 answer

Showing that sum of first $998$ cubes is divisible by $999$

I've got this assignment which reads: Show that $displaystyle sum_{k=0}^{998} k^{3}$ is divisible by $999$. Now I know that a number is divisible by $999$ if the...

Asked on 11/29/2020 by Rebronja

2 answer

Choosing two points from $[0,1]$ probability

We are choosing two random points among section $[0,1]$. These create 3 sections. The sections lengths are different and called $x,y,z$. Show the sample space using $x,y$....

Asked on 11/29/2020 by ucei

2 answer

Growth of Limits of $n$-th Terms in Series

I have two divergent series when summed up to infinite $n$: $frac{1}{n}$ and $frac{2^n - 2}{2^n}$. However, in the limit of increasingly large $n$, the...

Asked on 11/29/2020

1 answer

For how many values of n, will P(n) be false?

We know that $P(2018)$ is true, then surely $P(n)$ will be true for all $n>2018$. For $n<2018$, we can...

Asked on 11/29/2020 by Asad Ahmad

2 answer

Why does $f^{(n)}(x)=sin(x+frac{npi}{2})$ for $f(x)=sin(x)$?

I'm not quite sure how does $f^{(n)}(x)=sin(x+frac{npi}{2})$ for $f(x)=sin(x)$. Taking the initial derivatives I get,begin{align}f'(x)&=cos(x)\f''(x)&=-sin(x)\f'''(x)&=-cos(x)\f^{4}(x)&=sin(x)end{align}I'm not quite understanding this relation....

Asked on 11/29/2020 by cxlim

1 answer

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