Search found 75 matches
- Sun Feb 09, 2014 11:22 am
- Forum: National Math Olympiad (BdMO)
- Topic: BdMO National Higher Secondary 2008/9
- Replies: 4
- Views: 3902
Re: BdMO National Higher Secondary 2008/9
Someone..?
- Sun Feb 09, 2014 9:46 am
- Forum: Junior Level
- Topic: Acute angled circular
- Replies: 13
- Views: 10014
Re: Acute angled circular
Yes it is, but give an explanation if possible. There are $$C(7,3)-7-14=14$$ acute angled triangle. If we count the obtuse angled triangles then we have 2 case. First place points $$A,B,C,D,E,F,G$$. Then we have 2 types of obtuse angled triangle: $$ABC$$ type and $$ABD$$ type. We have $$7$$ triangl...
- Fri Feb 07, 2014 10:51 pm
- Forum: Secondary Level
- Topic: I have a confusion in a problem of series .
- Replies: 4
- Views: 3853
Re: I have a confusion in a problem of series .
$$1+57+56+56= 170$$
- Fri Feb 07, 2014 10:47 pm
- Forum: Secondary Level
- Topic: I have a confusion in a problem of series .
- Replies: 4
- Views: 3853
Re: I have a confusion in a problem of series .
I think the ans is $$170$$
- Fri Jan 31, 2014 11:57 pm
- Forum: National Math Olympiad (BdMO)
- Topic: BdMO National 2013: Junior 6
- Replies: 12
- Views: 8860
Re: BdMO National 2013: Junior 6
আমারও ১ আসছিল। গুনে গুনে করসিলাম
- Fri Jan 31, 2014 2:32 pm
- Forum: Secondary Level
- Topic: n divides 2^(n-1)+3^(n-1)
- Replies: 8
- Views: 5607
Re: n divides 2^(n-1)+3^(n-1)
How would you cancel power?Thanic Nur Samin wrote:Canceling the powers we get $$2\equiv3(mod n)$$
Substracting 2 gives us $$0\equiv1(mod n)$$
Am I making a mistake?
$$5^2\equiv3^2(mod16)$$
which tells
$$5\equiv3(mod16)$$
but it's impossible.
- Fri Jan 31, 2014 1:53 pm
- Forum: National Math Olympiad (BdMO)
- Topic: Junior 2006/3
- Replies: 5
- Views: 3229
Re: Junior 2006/3
Can also be done without using anything.
$$b=m-a$$
$$ab=a(m-a)=am-a^2$$
$$=\frac{m^2}{4} -a^2+ 2\frac{m}{2}a-\frac{m^2}{4}$$
$$=\frac{m^2}{4}- (a-\frac{m}{2})^2$$.
So, ab will be maximum if
$$a-\frac{m}{2}=0$$
$$a=\frac{m}{2}$$.
$$b=m-a=\frac{m}{2}$$
$$b=m-a$$
$$ab=a(m-a)=am-a^2$$
$$=\frac{m^2}{4} -a^2+ 2\frac{m}{2}a-\frac{m^2}{4}$$
$$=\frac{m^2}{4}- (a-\frac{m}{2})^2$$.
So, ab will be maximum if
$$a-\frac{m}{2}=0$$
$$a=\frac{m}{2}$$.
$$b=m-a=\frac{m}{2}$$
- Sat Jan 25, 2014 3:44 pm
- Forum: Secondary Level
- Topic: Angle and Sides
- Replies: 0
- Views: 1825
Angle and Sides
In $$ \triangle ABC$$, $$2 \angle A= 3 \angle B$$. Suppose that $$BC = p, AC = q, AB = r$$. Determine a triangle with positive integer side lengths $$p, q, r$$ and positive area that satisfies $$(p^2-q^2)^2 + p^3r +pq^2 r= r^2q$$.
- Thu Jan 16, 2014 3:28 pm
- Forum: Divisional Math Olympiad
- Topic: Rangpur Secondary 2012/10
- Replies: 1
- Views: 2115
Rangpur Secondary 2012/10
Consider the infinite sequence $$a_0, a_1, a_2, a_3 $$which follows the
given relations
$$\frac{1}{a_0}=2$$
$$\frac{1}{a_n}=\frac{1}{a_{n+1}}+\frac{1}{a_{n+2}}+\frac{1}{a_{n+3}} + ............$$ .
What is the value of $$a_{2012} ?$$
given relations
$$\frac{1}{a_0}=2$$
$$\frac{1}{a_n}=\frac{1}{a_{n+1}}+\frac{1}{a_{n+2}}+\frac{1}{a_{n+3}} + ............$$ .
What is the value of $$a_{2012} ?$$
- Thu Jan 16, 2014 2:35 pm
- Forum: Divisional Math Olympiad
- Topic: Sirajgonj Secondary 2013/8
- Replies: 1
- Views: 2155
Sirajgonj Secondary 2013/8
For an injective function $$f:R \rightarrow R$$, $$f(x + f(y)) = 2012 + f (x + y) $$ then $$f (2013)=?$$