z varies with x^1/3 when y is constant, and varies inversely with y^2 when x is constant.
Show z^3 varies with x^7 if x varies inversely with y.
Variation Maths DSE
2012-05-02 1:29 am
回答 (1)
2012-05-02 1:42 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"⁶) x⁷ , where (k³ / k"⁶) is a constant since k and k" is a constant.
∴ z³ propotional to x⁷ when x propotional to 1/y.
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