Search found 264 matches
- Sat Jul 17, 2021 4:11 pm
- Forum: Junior Level
- Topic: Memorable Year
- Replies: 1
- Views: 6636
Re: Memorable Year
Sudipta noticed that his birth year $1978$ is a memorable year in which two number of two sides are $19$ and $78$. The sum of this two number is $97$ which is it's middle number. Now it is $2018$. How many years will Sudipta wait for the next memorable year? Source : Gonitzoggo, Link: https://gonit...
- Sat Jul 17, 2021 3:30 pm
- Forum: Test Forum
- Topic: Number Theory
- Replies: 1
- Views: 8257
Re: Number Theory
If you want to post about programming or other computer science related topic, you should post here . For number theory, post here . Every odd number is difference of two squares, $2n+1=(n+1)^2-n^2$ Every even number that's divisible by $4$ is difference of two squares, $4n=(n+1)^2-(n-1)^2$. Every n...
- Sat Jul 10, 2021 2:27 am
- Forum: Algebra
- Topic: sqrt of sqrt
- Replies: 1
- Views: 4966
Re: sqrt of sqrt
Calculate $2\sqrt{2\sqrt[5]{2\sqrt[8]{2\sqrt[11]{2 \cdots}}}}$ \begin{equation} \begin{split} 2\sqrt{2\sqrt[5]{2\sqrt[8]{2\sqrt[11]{2 \cdots}}}}&=2^{1+\frac12+\frac1{2\cdot5}+\frac1{2\cdot5\cdot8}+\frac1{2\cdot5\cdot8\cdot11}+\cdots} \end{split} \end{equation} Here, let \begin{equation} \begin{spli...
- Sat Jul 10, 2021 12:32 am
- Forum: Computer Science
- Topic: Wanna start programming
- Replies: 5
- Views: 14041
Re: Wanna start programming
Read Tamim Shahriar Subeen's "Computer programming" book.Asif Hossain wrote: ↑Fri Jul 09, 2021 3:35 pmNeed some suggestions
1.What is the best way to learn and excel at it?
2.What are some beginners book or resource to start with?
3.Planning to start with C as our intermediate syllabus also includes it.
- Tue Jun 29, 2021 4:06 pm
- Forum: National Math Olympiad (BdMO)
- Topic: BdMO National 2021 Primary Problem 2
- Replies: 1
- Views: 4774
Re: BdMO National 2021 Primary Problem 2
Let $t_A,t_B,t_C$ be the time (in minutes) is takes to fill the pool using faucets $A,B,C$ respectively. So, in $1$ minute, $A,B,C$ fills the fraction of $\frac1{t_A},\frac1{t_B},\frac1{t_C}$ of the whole pool respectively. Therefore, we have, $\frac1{t_A}+\frac1{t_B}+\frac1{t_C}=\frac1{100}\cdots\c...
- Tue Jun 29, 2021 3:49 am
- Forum: Junior Level
- Topic: Logical Puzzle that gives Headache
- Replies: 0
- Views: 38492
Logical Puzzle that gives Headache
$Alice$ and $Bob$ both choosed a secret number and secretly tells the numbers to $Charlie$. Then they had the following conversations between them (which is not secret) : $Charlie$ : Both of you have choosen a positive integer and one of them is $2$ more than the other. $Alice$ : I don't know $Bob$'...
- Tue Jun 29, 2021 3:25 am
- Forum: Junior Level
- Topic: Computing Value of a Functional Equation
- Replies: 1
- Views: 5569
Re: Computing Value of a Functional Equation
A Function $f(x)$ is such that for any integer $x$, $f(x) + x f(2-x) = 6$ . Compute $-2019 f(2020)$ $f(x)+xf(2-x)=6\cdots\cdots(1)$ Replacing $x\mapsto2-x$ gives, $f(2-x)+(2-x)f(x)=6\cdots\cdots(2)$ Multiplying $x$ with $(2)$ and subtracting that from $(1)$ gives us, $f(x)-(2x-x^2)f(x)=6-6x$ $\Righ...
- Sat Jun 26, 2021 11:48 pm
- Forum: Physics
- Topic: A Comeback Post (Assignment related)
- Replies: 7
- Views: 73587
Re: A Comeback Post (Assignment related)
Acceleration is the second derivative of position with respect to time. The position of the object is given by, $y(t)=v_0t-\frac12gt^2$ $\Rightarrow y''(t)=-g$ Some confusion is arising that since the object was moving upwards, there should be an upward force acting on that object, and the gravitat...
- Fri Jun 25, 2021 8:21 pm
- Forum: College / University Level
- Topic: Maybe not as hard as you see
- Replies: 8
- Views: 20807
Re: Maybe not as hard as you see
Does this matches your reasoning? I highly doubt if "rotating the rectangle and keeping it's side tangent to the loop" is a continuous action or not. . The word "tangent" here is somewhat inappropriate since the curves is not necessarily smooth. In that case, I am referring to a line that contains ...
- Fri Jun 25, 2021 8:08 pm
- Forum: Physics
- Topic: A Comeback Post (Assignment related)
- Replies: 7
- Views: 73587
Re: A Comeback Post (Assignment related)
Acceleration is the second derivative of position with respect to time. The position of the object is given by, $y(t)=v_0t-\frac12gt^2$ $\Rightarrow y''(t)=-g$ Some confusion is arising that since the object was moving upwards, there should be an upward force acting on that object, and the gravitati...