Search found 134 matches
- Tue Jan 18, 2011 2:03 pm
- Forum: H. Secondary: Solved
- Topic: Dhaka Higher Secondary 2010/3 (Secondary 2010/5)
- Replies: 1
- Views: 7457
Dhaka Higher Secondary 2010/3 (Secondary 2010/5)
If $x$ is very very very small $\sin x \approx x$. An operator $S_n$ is defined such that $ S_n(x)= \sin \sin \sin \cdots \sin x$ (a total of $n$ $\sin$ operators are included here). For sufficiently large $n$, $S_n(x) \approx S_{n-1}(x)$. In that case, express $\cos (S_n(x))$ as the nearest rationa...
- Tue Jan 18, 2011 2:03 pm
- Forum: H. Secondary: Solved
- Topic: Dhaka Higher Secondary 2010/2 (Secondary 2010/9)
- Replies: 17
- Views: 21278
Dhaka Higher Secondary 2010/2
As shown in the figure, triangle $ABC$ is divided into six smaller triangles by lines drawn from the vertices through a common interior point. The areas of four of these triangles are as indicated. Find the area of triangle $ABC$.
- Tue Jan 18, 2011 1:49 pm
- Forum: H. Secondary: Solved
- Topic: Divisional MO Higher Secondary 2010
- Replies: 0
- Views: 11747
Divisional MO Higher Secondary 2010
Dhaka Divisional Mathematical Olympiad 2010 : Higher Secondary Assume, $\Phi : A \to A, A=\{0,1,2,\cdots\}$ is a function, which is defined as, \[\Phi(x) = \begin{cases} 0 \quad \text{if } x \text{ is a prime}\\ \Phi(x - 1) \quad \text{if } x \text{ is not a prime} \end{cases} \] Find \[ \sum_{x=0}...
- Tue Jan 18, 2011 1:43 pm
- Forum: H. Secondary: Solved
- Topic: Dhaka Higher Secondary 2010/1 (Secondary 2010/8)
- Replies: 3
- Views: 9461
Dhaka Higher Secondary 2010/1 (Secondary 2010/8)
Assume, $\Phi : A \to A, A=\{0,1,2,\cdots \}$ is a function, which is defined as,
\[\Phi(x) = \begin{cases}
0 \quad \text{if } x \text{ is a prime}\\
\Phi(x - 1) \quad \text{if } x \text{ is not a prime} \end{cases} \]
Find \[ \sum_{x=2}^{2010} \Phi(x)\]
(Corrected)
\[\Phi(x) = \begin{cases}
0 \quad \text{if } x \text{ is a prime}\\
\Phi(x - 1) \quad \text{if } x \text{ is not a prime} \end{cases} \]
Find \[ \sum_{x=2}^{2010} \Phi(x)\]
(Corrected)