maths f4

a) z=kx^2/y where k is a constant

2=k(8^2)/4
16k=2
k=1/8

Therefore z=x^2/(8y)


b)
i) x-2y-z=0
From a): z=x^2/(8y)
x-2y-x^2/(8y)=0
8xy-16y^2-x^2=0
x^2-8xy+16y^2=0
(x-4y)^2=0
x-4y=0
x=4y

Hence, z=x^2/(8y)=(4y)^2/(8y)=2y

Therefore x:y:z=4y:y:2y=4:1:2


ii) x:z=4:2=2:1
i.e. x/z=2
(2x)/(2z)=2
Therefore the increase of z is 2, if x is increased by 2.


2011-05-28 13:30:30 補充：
b)
ii) x:z=4:2=2:1
i.e. x/z=2

Suppose when x is increased by 2, x becomes X and z becomes Z.
Then X=x+2 and X/Z=2

X/Z=2
(x+2)/Z=2
Z=(x+2)/2=x/2+1=z+1

Therefore the increase of z is 1, if x is increased by 2.

2011-05-28 13:35:13 補充：
z隨x的平方而正變和隨y而反變，其中x，y和z為正數。當x=8和y=4時，z=2。
a) 以x和y表示z。
b) 假設x-2y-z=0，
i) 求 x:y:z
ii) 若x增加2，求z的增加。