F.4MATH 變分!!急!!!10分

設y正比於x,
a) 若x增加15%, 求y的百分改變
設y=kx , 其中k為非零常數
若x增加15%時
y=kx(1+15%)
y=1.15kx
y的百分改變
=(1.15kx - kx) / kx * 100%
=0.15 * 100%
=15%
so y增加了15%

設v正比於h開方,
b) 若v 減少5%, 求h的百分改變.
v=k開方h , 其中k為非零常數
h=(v / k)^2
若v 減少5%時
v(1 - 5%)=k開方h
h=(0.95v / k)^2
h的百分改變
=[(0.95v / k)^2 - (v / k)^2] / (v / k)^2 * 100%
= - 0.0975 * 100%
= - 9.75%
so h減少了9.75%

y 正比於x
y=kx (where k is a non zero integer)
k=Y/X

Y1 / X1=Y2 / X2
Y1 / X1=Y2 / X1(1+15%)
Y1(1.15)X1 / X1 = Y2
Y1(1.15) = Y2

Y1(1.15)-Y1
----------------- X100%
Y1
= 1.15-1
---------- X100%
1
=15%

:. Y 增加了15%



V 正比H^2

V=KH^2 (where k is a non zero integer)
K= V / ^/H

V1 / ^/H1 = V2 / ^/H2
V1 / ^/H1 = V1(0.95) / ^/H
V1 / V1(0.95) = ^/H1 / ^/H2
^/H2 = ^/H(0.95)
^/H2 = ^/H1^/(0.95)
^/H2 = ^/H1(0.975) <==(CORR TO 3 SIG FIG)

(0.975)H1 - H1
-------------------------- X100%
H1
= 0.975 - 1
---------------- X100%
1
= - 2.53%
:. H減少2.53%


因為我唔知點樣將下面果d轉做中文
(where k is a non zero integer)
(corr. 3sig fig) <===係唔係(更正到3位有效數字)
所以用住呢句先 我諗你應該知呢2句的中文的寫法吧
係上面d 式入面 / 等於 除
仲有 ^/ 者係等於開方
下面計改變百分比果度 係將個Y or H抽左出黎先變左做數字既+ - x /式
希望你明白 and 可以幫到你

let
y = kx,where k is constant
y[1] = k[(1 + 15%)x[0]]
y[1] = 1.15kx[0]
change in percentage:
{(y[1]/y[0]) - 1} x 100%
= 15%
it is increased by 15%

2)
let v = k[h]^1/2 , where k is constant
v^2 = (k^2) h
so,let v^2 = ph,where p is constant
(v[0])^2 = ph[0]
[(1 - 15%)v[0]]^2 = ph[1]
0.7225(v[0])^2 = ph[1]
change in percentage :
= {(h[1]/h[0]) - 1} x 100%
= -27.75%
it is decreased by 27.75 %