PROPORTION

Inverse proportion

Y is Inversely proportional to x

Y varies inversely as x

x

kY

Inverse proportion

Y is inversely proportional to the square of x

Y varies inversely as the square of x

2x

kY

Inverse proportion

Y is inversely proportional to the square root of x

Y varies inversely as the square root of x

x

kY

1

If y is inversely proportional to the square of x and

y = 2 when x = 3, find

(i) y when x = 12

(ii) x when y = 0.5

2

The Pressure P of a given mass of gas varies

inversely as the volume V.

When P = 250 N/m2, V = 4 m3.

a) Find the volume when the pressure is 400

N/m2

b) Find the pressure when the Volume is 20 m3.

3

Example

The force F between two magnets is inversely

proportional to the square of the distance x

between them. If F = 9 when x = 2, find F when x

= 3.

4

Example

The Force of attraction F between two magnets

varies inversely as the square of the distance d,

between them. When the magnets are 3cm apart the

force of attraction is 12 newtons.

How far apart are they if the attractive force is 18

newtons?

5

Example

The life expectancy of a rat varies inversely as the

square of the density d of poison distributed

around the home.

When the density of poison distributed is 1 g/m2

the life expectancy is 50 days.

How long will he survive if the density of poison is

5 g/m2?

6

Example

y is inversely proportional to the square of x.

When y = 3, x = 2

Find the value of y when x = 4

7

Example

y is inversely proportional to the square root of x.

When y = 10, x = 4.

Find the value of y when x = 25.

8

Example

y is inversely proportional to the cube of x.

When y = 18, x = 3.

Find the value of y when x = 6.

9

Example

The illumination, L, provided by a torch is inversely

proportional to the square of the distance, d, from

the torch.

When L = 2, d = 10.

(a) Find an equation expressing L in terms of d.

(b) Find the value of L when d = 2.

(c) Find the value of d when L = 8.

10

ExampleM and G are positive quantities.M is inversely proportional to G.When M = 90, G = 40.Find the value of M when G = M.

11

Example

y is inversely proportional to the square root of x.

When x = 16, y = 2

What is the value of y when x = 0.25?

12

Example

In a circuit, the resistance, R ohms, is inversely

proportional to the current, I amps.

When the resistance is 12 ohms, the current in the

circuit is 8 amps.

(a)Find an equation connecting R and I.

(b)Find the current when the resistance in the circuit

is 6.4 ohms.

13