i. p ∝ (1/q) … [Given]
∴ p = k × (1/q) where, k is the constant of variation.
∴ p × q = k …(i)
When p = 15, q = 4
∴ Substituting p = 15 and q = 4 in (i), we get
p × q = k
∴ 15 × 4 = k
∴ k = 60
Substituting k = 60 in (i), we get p × q = k
∴ p × q = 60
This is the equation of variation.
∴ The constant of variation is 60 and the equation of variation is pq = 60.
ii. z ∝ (1/w) …[Given]
∴ z = k × (1/w) where, k is the constant of variation,
∴ z × w = k …(i)
When z = 2.5, w = 24
∴ Substituting z = 2.5 and w = 24 in (i), we get
z × w = k
∴ 2.5 × 24 = k
∴ k = 60
Substituting k = 60 in (i), we get z × w = k
∴ z × w = 60
This is the equation of variation.
∴ The constant of variation is 60 and the equation of variation is zw = 60.
iii. s ∝ (1/t2) …[Given]
∴ s = k x (1/t2)
∴ where, k is the constant of variation,
∴ s × t2 = k …(i)
When s = 4, t = 5
∴ Substituting, s = 4 and t = 5 in (i), we get
s × t2 = k
∴ 4 × (5)2 = k
∴ k = 4 × 25
∴ k = 100
Substituting k = 100 in (i), we get s × t2 = k
∴ s × t2 = 100
This is the equation of variation.
∴ The constant of variation is 100 and the equation of variation is st2 = 100.
iv. x ∝ (1/√y) …[Given]
∴ x = k x (1/√y) where, k is the constant of variation,
∴ x × √y = k …(i)
When x = 15, y = 9
∴ Substituting x = 15 and y = 9 in (i), we get
x × √y = k
∴ 15 × √9 = k
∴ k = 15 × 3
∴ k = 45
Substituting k = 45 in (i), we get
x × √y = k
∴ x × √y = 45.
This is the equation of variation.
∴ The constant of variation is k = 45 and the equation of variation is x√y = 45.