Inverse Variation

There are many situations in our daily lives that involve inverse variation.

For example, the number of days required to build a bridge is varies inversely to the number of workers. As the number of workers increases, the number of days required to build would decrease.

In general, when two variables x and y are such that

xy = k where k is a non-zero constant, we say that y varies inversely with x.

In notation, inverse variation is written as

Example:

Suppose that y varies inversely as x and that y = 8 when x = 3.

a) Form an equation connecting x and y.

b) Calculate the value of y when x = 10.

Solution:

i.e. xy = k where k is a non-zero constant

a) Substitute x = 3 and y = 8 into the equation to obtain k

3 × 8 = k ⇒ k = 24

The equation is xy = 24

b) When x = 10, 10 × y = 24 ⇒ y =

Example:

Suppose that y varies inversely as x 2 and that y = 10 when x = .

a) Find the equation connecting x and y .

b) Find the value of y when x = 3.

Solution:

i.e. yx² = k

a) Substitute x = and y = 10 into the equation to obtain k

The equation is yx² =

b) When x = 3,

Example:

The force of attraction between two magnets is F Newtons. This force is inversely to the square of the distance, d cm, between the magnets.

a) Write a formula connecting F, d and a constant k.

b) When the magnets are placed at a certain distance apart, the force is 10 Newtons. What is the force when the distance is doubled?

Solution:

a)

b) The original force is 10 Newtons i.e.

If the distance is doubled then the force

Newtons

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