Direct Variations (Sample Questions)


Example 1:
y varies directly to x3 and if y = 54 when x = 3, find
(a)  The value of when y = 16
(b)  The value of y when x = 4 

Solution:
Given α x³ , y = kx³
When y = 54, x = 3,
54 = k (3)³
54 = 27k
k = 2
Therefore y = 2x³
 
(a) When y = 16
16 = 2x³
x³ = 8
x = 2

(b)
When x = 4
y = 2(4)³ = 128



Example 2:
Given that p varies directly as square root of q and p = 12 when = 36, find
(a) The value of p when = 16
(b) The value of q when = 18

Solution:

p q , p = k q 12 = k 36
12 = k(6)
k = 2
p = 2 q

(a)
p = 2 q p = 2 16
p = 8

(b)   
p = 2 q 18 = 2 q 9 = q  
9² = q
q = 81

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