Question

Given that a varied inversely as b, and b varies directly as the square of c, and a=1 when c=3 find the value of a when c=1/3

Answer 1

Answer:

81

Step-by-step explanation:

When two variables have direct variation, as one variable increases the other variable increases or as one variable decrease, the other decrease. While for an inverse variation, as one variable increase, the other variable decrease or as one variable decrease, the other variable increase.

Given that a ∝ 1/b. Also b ∝ c².

Hence if k is the constant of proportionality, we have:

a ∝ 1 / c²

a = k / c²

When a = 1, c = 3, hence:

1 = k / 3²

k = 1 * 3²

k = 9

Therefore:

a = 9 / c²

When c = 1/3

a = 9 / (1/3)²

a = 9 / (1² / 3²)

a = 9 / (1 / 9)

a = 9 * 9

a  = 81