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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