Variations Short Question (Question 1 – 4)


Question 1:
It is given that y varies directly as the cube of x and y = 192 when x = 4. Calculate the value of x when y 24.

Solution:

y α x³
y = kx³
192 = k (4)³
192 = 64 k
k = 3
 
y = 3 x³
when y = – 24 
– 24 = 3 x³
x³ = – 8
x = – 2



Question 2:
It is given that y varies directly as the square of x and y = 9 when x = 2. Calculate the value of x when y = 16.

Solution:
y α x²
y = kx²
9 = k (2)²
k 9 4

y = 9 4 x 2 When y = 16 16 = 9 4 x 2 x 2 = 64 9 x = 8 3



Question 3:
Given that y varies inversely as w and x and y = 45 when w = 2 and x = 1 6 . Find the value of x when y = 15 and w = 1 3

Solution:
y α 1 w x y = k w x 45 = k ( 2 ) ( 1 6 ) k = 45 × 1 3 = 15 y = 15 w x when y = 15 , w = 1 3 15 = 15 ( 1 3 ) x x 3 = 1 x = 3



Question 4:
Given that   p α 1 q r and p = 3 when q = 2 and r = 16, find the value of p when q = 3 and r = 4.

Solution:
p α 1 q r p = k q r 3 = k ( 2 ) 16 k = 24 p = 24 q r when q = 3 , r = 4 p = 24 3 4 p = 24 6 = 4

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