Question

a^2 varies bc, b^2 varies d, c^2 varies b, d^2 varies ac and abcd varies k. so k=?​

Answer 1

i) Since A varies inversely as B  

Therefore A ∝ 1/B or, A = k ∙ 1/B ………………. (1), where k = constant of variation.  

Given A = 2 when B = 10.  

Putting these values in (1), we get,  

2 = k ∙ 1/10  

or, k = 20.  

Therefore, the law of variation is: A = 20 ∙ 1/B……………... (2)  

When B = 4, then from (2) we get, A = 20 ∙ ¼ = 5.  

Therefore, A = 5 when B = 4.  

(ii) Since, x ∝ y²

Therefore, x = m ∙ y² ……………… (1)  

where m = constant of variation.  

Given x = 8 when y = 4.  

Putting these values in (1), we get,  

8 = m ∙ 42 = 16m  

or, m = 8/16  

or, m = 1/2

Therefore the law of variation is: x = ½ ∙ y² ………….. (2) When x = 32, then from (2) we get,  

32 = 1/2 ∙ y²  

or, y² = 64  

or, y = ± 8.  

Hence, y = 8 or, - 8 when x = 32.