F4 Maths Variation

a)
z = kx2
.......y
6 = k(62)
.........3
k = 1
......2
so...z = (1/2)x2
.................y
b)
z = (1/2)x2
.........y
z = (1/2)42
......(2/3)
z = 12
c)
let z' be the new value of z
z' = (1/2)(1.12x)2
..........1.12y
z' = (1/2)1.2544x2
...........1.12y
z' = 1.2544 x (1/2)x2
.......1.12............y
z' = 1.2544z
........1.12
percentage change = (( 1.2544 - 1) / 1) * 100% = 12%
.....................................1.12

2007-06-19 14:38:46 補充：
jointly 係指一齊z=hx^2 同 z=k/y 一齊睇咪就係 z=kx^2/y lawk 係一個 constant而且由於係 jointlyk 就一定等如 h如果你分開左佢地就會更加麻煩

a)
z = kx^2/y, k is constant
6 = k(36)/3,
k = 1/2

z = x^2/(2y)

b)
z = 4^2/(4/3) = 12

c)
{ (1.12)x^2 / [ (2)(1.12)y ] - x^2/(2y) } / [ x^2/(2y) ] * 100%
= 0
no change in z

2007-06-19 14:16:50 補充：
錯左少少, c part square 少左 1.12,睇返上面一個高手 noman, 佢啱

Given that z varies jointly as x2 and inversely as y, z=6 when x=6 and y=3.
a) Express z in term of x and y
z = kx2 / y
當 z = 6，x = 6，y = 3，則
6 = k62 / 3
k = 1/2
所以
z = x2 / 2y
b) Find the value of z when x=4 and y=2/3
因
z = 42 / 2(2/3)
z = 12
c) Find he percentage change in z when x and y are both increased by 12%.
x = (1 + 12%)xo
y = (1 + 12%)yo
代入
z = x2 / 2y
z = (1.12xo)2 / 2(1.12yo)
z = 1.12(xo2 / 2yo)
z = 1.12zo
所以增加了
1.12 zo - zo = 0.12 zo
增加了 12%
Please show steps.