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# unsolved national maths contest-1995 question. watch

1. (Original post by akiromuchi)
Refer to http://sg.answers.yahoo.com/question...5150745AA35Iv4 .Why the power of number 3 is 2?
Because the number is divisible by 9, and 9 = 3^2.

(Original post by akiromuchi)
And...How can we know when to use which method of divisibility rule ?.Like the example,the divisibility rule for 23 and 11 is different?
You can't "know" which to use when, you have to guess.

(Original post by akiromuchi)
I do not understand why do we need to divide (y-2) by 10?
Having the benefit of hindsight, we know that y = 262. What's (y-2)/10 + 200? So why did they divide by 10?
2. (Original post by generalebriety)
Because the number is divisible by 9, and 9 = 3^2.

You can't "know" which to use when, you have to guess.

Having the benefit of hindsight, we know that y = 262. What's (y-2)/10 + 200? So why did they divide by 10?
Anyone can answer why is it divide by ten?
3. I have some questions here that need help...
A point p is chosen at random in a square ABCD.What is the possibility that the angle APB is obtuse?
a.1/4 b.1/3 c.3/8 d.pi /8 e.( root 3)/4

15.ABCDE is a regular pentagon.P is the point inside ABCDE such that PED
is an equilateral triangle.What is that size of angle APB?
A.72 B.84 .C.90.D.96 E.108
4. hmm for the 1st qns, using the geometrical fact that any angle subtended by the diameter of a semi circle and the third vertice on the circumference is 90degrees. Thus to get obtuse your vertice has to be nearer the diameter.
Think abt how u gona get your 90degrees first.
5. For the 2nd part the key is to use symmetry and equal lines.
have a pentagon, the point p and joined it to all the 5 vertices of the pentagon. triangles pcd and pae are isosceles. triangles abp and bcp
are congruent (side side side). note this follow from that triangle pcd and pae are congruent too. what can you tell about angle apb and bpc=).
6. (Original post by akiromuchi)
Anyone can answer why is it divide by ten?
?!

I know why they divided by ten. I'm trying to get you to work it out. Please don't be rude.
7. (Original post by OCC++)
hmm for the 1st qns, using the geometrical fact that any angle subtended by the diameter of a semi circle and the third vertice on the circumference is 90degrees. Thus to get obtuse your vertice has to be nearer the diameter.
Think abt how u gona get your 90degrees first.
Is it true if point p lies on sides of AD or BC ,then a right-angle triangle can be formed?
8. (Original post by akiromuchi)
Is it true if point p lies on sides of AD or BC ,then a right-angle triangle can be formed?
AD isn't a side. And it doesn't lie on any of the sides.
9. (Original post by OCC++)
For the 2nd part the key is to use symmetry and equal lines.
have a pentagon, the point p and joined it to all the 5 vertices of the pentagon. triangles pcd and pae are isosceles. triangles abp and bcp
are congruent (side side side). note this follow from that triangle pcd and pae are congruent too. what can you tell about angle apb and bpc=).
How we know the angle of apc if we do not know ape,epd,cpd?I know the sum of all angles is 360 degree.
10. (Original post by generalebriety)
?!

I know why they divided by ten. I'm trying to get you to work it out. Please don't be rude.
I would not ask why if i know the answer in the first place..
11. (Original post by OCC++)
hmm for the 1st qns, using the geometrical fact that any angle subtended by the diameter of a semi circle and the third vertice on the circumference is 90degrees. Thus to get obtuse your vertice has to be nearer the diameter.
Think abt how u gona get your 90degrees first.
Ok,the square ABCD is folded into half,the folded line become the diameter of circle inscribed inside the square.Angle APB where P along the folded line is 90 degrees.So,the possibility of point P is 1/2 which is half of the square ...but there is no answer?
12. (Original post by akiromuchi)
I would not ask why if i know the answer in the first place..
I gave you a hint.

Why people continue to help you is beyond me, you're so incredibly rude.
13. 1st question: AB is the diameter of the semicircle you need to draw. Then for any point x on the arc of the semicircle , what is the angle formed by axb?
What happen if the point x moved inside the semicircle? How about if x moved outside the semicircle?

2nd question : There is a way to find the interior angle of any REGULAR polygon. interior angle= [ (n-2)/n ] * 180 degrees. You get this by considering one vertice and then connecting this vertice to every other vertice. You will get (n-2) triangles and their angles all form the total interior angles of the original polygon. Now continue on your quest.=)
14. (Original post by generalebriety)
I gave you a hint.

Why people continue to help you is beyond me, you're so incredibly rude.
I do not understand why am i being so rude for you?
15. (Original post by OCC++)
1st question: AB is the diameter of the semicircle you need to draw. Then for any point x on the arc of the semicircle , what is the angle formed by axb?
What happen if the point x moved inside the semicircle? How about if x moved outside the semicircle?

2nd question : There is a way to find the interior angle of any REGULAR polygon. interior angle= [ (n-2)/n ] * 180 degrees. You get this by considering one vertice and then connecting this vertice to every other vertice. You will get (n-2) triangles and their angles all form the total interior angles of the original polygon. Now continue on your quest.=)
For the first question, i have gotten it .
But for the second one,the formula [ (n-2)/n ] * 180 degrees only apply to regular polygon.
How about the angle of isoceles triangle that we wish to find?
16. since its stated that its an equilateral triangkle, we know angle ped = pde =dep=sth.
you can find an interior angle of the pentagon by using formula, so you will for angle cde. cde-pde=cdp.
since u know pcd is an isosceles triangle , n u know angle cdp, u can find cpd.
if u draw your diagram nicely u will see that if u extend bp, it will cut de at 90 degrees, showing intuitively that there is a symmetry.
17. (Original post by akiromuchi)
I do not understand why am i being so rude for you?
I gave you a hint. You quoted me, ignored it, didn't bother to try it, and asked everyone else to spell it out for you. Do your own bloody work if you don't like the help we give you.
18. (Original post by generalebriety)
I gave you a hint. You quoted me, ignored it, didn't bother to try it, and asked everyone else to spell it out for you. Do your own bloody work if you don't like the help we give you.

I do not mean that ...It is a misunderstanding........
19. (Original post by akiromuchi)
I do not mean that ...It is a misunderstanding........
Ok... but have you tried the hint I gave you?
20. (Original post by generalebriety)
Ok... but have you tried the hint I gave you?

Frankly speaking,i still do not get why should we divide it by 10?

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