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 = k X Y W = k X Y 1 2

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