Variations Short Question (Question 5 - 9)


Question 5:
It is given that R varies directly as the square root of S and inversely as the square of T. Find the relation between R, S and T.

Solution:
R α  S T 2


Question 6:
It is given that P varies directly as the square of Q and inversely as the square root of R. Given that the constant is k, find the relation between P, Q and R.

Solution:
P α  Q 2 R P= k Q 2 R


Question 7:
Given that P varies inversely as the cube root of Q. The relationship between P and Q is

Solution:
P α  1 Q 3 P α  1 Q 1 3


Question 8:
Given that y varies inversely as the cube of x and y = 16 when x = ½. Express y in terms of x.

Solution:
y α  1 x 3 y= k x 3 When y=16, x= 1 2 16= k ( 1 2 ) 3 16= k 1 8 k=2 y= 2 x 3


Question 9:
W varies directly with X and inversely with the square root of Y. Given that k is a constant, find the relation between W, X and Y.

Solution:
W α  X Y W =  kX Y W =  kX Y 1 2