f.4 maths variation~

[匿名]

2012-04-27 7:24 am

it is given that z varies directly as x^(1/3) when y is constant and varies inverserly as y^2 when x is constant. show taht z^3 propotional to x^7 when x propotional to 1/y

回答 (1)

用戶2053

2012-04-27 8:02 am

✔ 最佳答案

Let z = k ∛x / y² , where k is a constant.
then z³ = k³ x / y⁶ ...... (*)
when x propotional to 1/y , let x = k" (1/y) , where k" is a constant. i.e. y = k" / x , sub. into (*) :
z³ = k³ x / (k" / x)⁶

z³ = (k³ / k") x⁷ , where (k³ / k") is a constant since k and k" is a constant.
∴ z³ propotional to x⁷ when x propotional to 1/y.

2012-04-27 00:12:30 補充：
The 2nd last line , (k³ / k") should be (k³ / k"^6) :

z³ = (k³ / k"⁶) x⁷ , where (k³ / k"⁶) is a constant since k and k" is a constant.

Sorry for my mistakes.

2012-04-28 09:42:07 補充：
z³ = (k³ / k") x⁷ should be z³ = (k³ / k"^6) x⁷

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