Maths problem [variations]

2009-06-28 1:50 am

if (x+y) varied directly as (x-y), then y/x is a constant,
我計黎計去都計唔到個ans, 有冇人可以話俾我聽點計?

Assume p varied directly as q^2 and inversely as r. Find the percentage change in p when q and r are both increased by 10%.
The ans. is increased by 10%. 我計黎計去都計唔到個ans, 有冇人可以話俾我聽點計?

回答 (1)

用戶9112

2009-06-28 1:57 am

✔ 最佳答案

(x+y) varied directly as (x-y)
therefore (x+y)=k(x-y) where k is a constant
x + y = kx - ky
x + y + ky - x = kx - ky +ky - x
(k+1)y = x(k-1)
y/x = (k-1)/(k+1) which is a constant

p varied directly as q^2 and inversely as r
therefore p = kq^2/r where k is a constant
when q is increased by 10% and r also by 10%, I denote the new values by p1, q1 and r1 respectively.
p1=kq1^2/r1
=k(1.1q)^2/(1.1r)
=k1.21q^2/(1.1r)
=(1.1)kq^2/r
=1.1p

Percentage change in p is (p1-p)/p x 100%
=(1.1p - p)/p x 100%
=0.1p/p x 100%
=10%

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