PLEASE......F.4 MATHS~~

用戶200412

2009-03-17 3:46 am

Variations

1.

The attractive force(F) between two objects varies diectly as the

product of ther masses (M1 and M2 ),and inversely as the square of

their distance (d) .If M1 and M2 are both halved and d is doubled ,

find the ratio ofthe new value of F to its original value.

2. if (x + y) varies inversely as (1/x +1/y),show that,

( a) ( x+ y) 的2次 varies directly as xy

(b) xy varies directly as (x的2次 + y的2次)

THX~~~

THX SO MUCH~~~~~~~~

回答 (1)

STEVIE-G™

2009-03-17 4:16 am

✔ 最佳答案

1)
The original value of F=k(M1)(M2)/d ,where k is real
The new value of F=k(M1/2)(M2/2)/(2d)=k(M1)(M2)/8d
the ratio ofthe new value of F to its original value
=[k(M1)(M2)/8d]:[k(M1)(M2)/d]
=1:8
2a)
if (x + y) varies inversely as (1/x +1/y)
(x+y)=k/(1/x +1/y) ,where k is real
(x+y)=k/[(x+y)/xy]
(x+y)=k(xy)/(x+y)
(x+y)^2=k(xy)---(1)
Thus ( x+ y)^2 varies directly as xy
b)
By (1)
(xy)=(1/k)(x+y)^2
(xy)=(1/k)(x^2+2xy+y^2)
(xy)=(1/k)(x^2+y^2)+(1/k)(2xy)
[1-(1/k)](xy)=(1/k)(x^2+y^2)
[(k-1)/k](xy)=(1/k)(x^2+y^2)
(xy)=[1/(k-1)](x^2+y^2)
Thus ,xy varies directly as (x^2 + y^2)

2009-03-16 20:18:05 補充：
Some mistakes in last three steps...

should be :

[1-(2/k)](xy)=(1/k)(x^2+y^2)

[(k-2)/k](xy)=(1/k)(x^2+y^2)

(xy)=[1/(k-2)](x^2+y^2)

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