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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
Last edited by Prakash Panneer (2006-10-28 06:21:26)
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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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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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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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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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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:
IPBLE: Increasing Performance By Lowering Expectations.
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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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Excellent work, All_is_number and Krassi!
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