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#1 2006-10-28 06:19:35

Prakash Panneer
Member
Registered: 2006-06-01
Posts: 110

Help me with these problems.....

1)Find the number of  Rectangles  on the chess board.

2)The angles of  quadrilateral are in A.P . Greatest angle is double the least.  Find the angles in circular measure.

3)If A, B, C, D are angles of cylic quadrilateral then find cosA + cosB + cos C + cos D .

4)If sin  Ө + cosec  Ө  = 2 then find sin ^n (Ө) + cosec^n (Ө)


5)If  5 sin x + 12 cos x = 7 then find 5 cos x  - 12 sin x.

6)In triangle ABC ,  if  sec2 A + sec2 B =   sec2 A .sec2 B then show that triangle ABC in right angled.

7)If sec A + tan A = a then find sin A in terms of  a.

8)Find equation  of Altitude and median of triangle ABC passing through vertex ' A'  Where
A(1, 2),B(3,4), C (5,1).

9)In a mathematics class ,  20 children had forgotten their rulers and 17 had forgotten their pencils , “ Go and borrow them from some one at once”, said the teacher . 24  children left the room . Find how many children had forgotten both.

Thanks in Advance up

Last edited by Prakash Panneer (2006-10-28 06:21:26)


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#2 2006-10-28 07:24:14

All_Is_Number
Member
Registered: 2006-07-10
Posts: 258

Re: Help me with these problems.....

Prakash Panneer wrote:

1)Find the number of  Rectangles  on the chess board.

The number of rectangles that can be found on any checkerboard with dimensions n squares * m squares can be represented:

For a chess board, m=8 and n=8. Substituting these values yields:

Last edited by All_Is_Number (2006-10-29 03:01:22)


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#3 2006-10-28 11:59:26

All_Is_Number
Member
Registered: 2006-07-10
Posts: 258

Re: Help me with these problems.....

Prakash Panneer wrote:

2)The angles of  quadrilateral are in A.P . Greatest angle is double the least.  Find the angles in circular measure.

All the angles sum to 2Pi.

Clockwise, let's label the angles A, B, C, D, such that A and C are congruent small angles and B and D are congruent large angles.

A + B + C + D = 2Pi

A + B = Pi

B = 2A

3A = Pi

A = Pi/3 and  B = 2Pi/3

Last edited by All_Is_Number (2006-10-29 02:56:48)


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#4 2006-10-28 12:03:58

All_Is_Number
Member
Registered: 2006-07-10
Posts: 258

Re: Help me with these problems.....

Prakash Panneer wrote:

3)If A, B, C, D are angles of cylic quadrilateral then find cosA + cosB + cos C + cos D .

Cosines of opposite corners should be additive inverses, so the cosines of two pair of opposite angles should sum to zero also.


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#5 2006-10-28 12:07:36

All_Is_Number
Member
Registered: 2006-07-10
Posts: 258

Re: Help me with these problems.....

Prakash Panneer wrote:

9)In a mathematics class ,  20 children had forgotten their rulers and 17 had forgotten their pencils , “ Go and borrow them from some one at once”, said the teacher . 24  children left the room . Find how many children had forgotten both.

(17 + 20) - 24 = 13 students forgot both.


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#6 2006-10-29 13:06:04

krassi_holmz
Real Member
Registered: 2005-12-02
Posts: 1,905

Re: Help me with these problems.....

All_Is_Number wrote:
Prakash Panneer wrote:

1)Find the number of  Rectangles  on the chess board.

The number of rectangles that can be found on any checkerboard with dimensions n squares * m squares can be represented:

.... which is exactly:


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#7 2006-10-30 02:08:01

All_Is_Number
Member
Registered: 2006-07-10
Posts: 258

Re: Help me with these problems.....

krassi_holmz wrote:
All_Is_Number wrote:

The number of rectangles that can be found on any checkerboard with dimensions n squares * m squares can be represented:

.... which is exactly:

Interesting. How did you obtain that, if you don't mind me asking?


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#8 2006-10-30 02:14:18

Jai Ganesh
Administrator
Registered: 2005-06-28
Posts: 45,956

Re: Help me with these problems.....

Excellent work, All_is_number and Krassi!


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