amaths - Ans.fyi 參考答案

amaths

2007-11-09 2:45 am

1.the curve Ax^2 +Bxy +Cy^2= 16,where A, B, C are constants, passes through the points R(2根3, 1) and S(-2根3, 1).
a) show that B=0.
b) if the slope of the curve at R is -根3/2, find A, C.
Ans: a=1,c=4
2.a wire of 6m in lingth is cut into two pieces. one piece is bent into a circle, the other piece into a square. find the length of the side of the square if the sum of the areas of the circle and the square is max.
Ans=0

回答 (1)

Gabriella Montez

2007-11-09 3:49 am

✔ 最佳答案

1a) A ( 2sqr3 )^2 + B ( 2sqr3 )( 1 ) + C ( 1 )^2 = 16

12A + 2Bsqr3 + C = 16 --- ( 1 )

A ( -2sqr3 )^2 + B ( 2sqr 3 )( - 1 ) + C ( 1 )^2 = 16

12A - 2Bsqr3 + C = 16 --- ( 2 )

( 1 ) - ( 2 ):

4Bsqr3 = 0

So B = 0

b) The curve: Ax^2 + Cy^2 = 16 --- ( 3 )

By differentiation,

2Ax + 2Cy dy/dx = 0

dy/dx = -Ax / Cy

-sqr3 / 2 = -2Asqr3 / C

C = 4A --- ( 4 )

Put ( 4 ) into ( 3 ),

Ax^2 + 4Ay^2 = 16

12A + 4A = 16

A = 1

C = 4A = 4 ( 1 ) = 4

So A = 1, C = 4.

2) For Q2, plx refer to my previous ans.

http://hk.knowledge.yahoo.com/question/?qid=7007071503856

參考: My Maths Knowledge

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