Direct & inverse proportion

(i) y is inversely proportional to x³. y = 0·15 when x = 6.

Use this information to write an expression for y in terms of x.

Use the expression you found in part (i) to complete the following table.

c is directly proportional to the square root of d. What happens to c if d is multiplied by 4?

Circle the correct statement below.

c is c is c is c is c is multiplied by 16 divided by 16 multiplied by 2 divided by 2 squared

In a science experiment, Jamil collects the following pairs of data values for two variables, x and y.

Also, y is inversely proportional to x, and y = 8 when x = 15.

Find the value of y when w = 25.

y is inversely proportional to the square of x.

y = 16 when x = 5.

Find an expression for y in terms of x.

Use the expression you found in part (a) to complete the following table.

Given that y is inversely proportional to x and that y = 0·2 when x = 160, find an

expression for y in terms of x.

Use the expression you found in part (a) to complete the following table.

Given that y is directly proportional to x³ and that y = 108 when x = 3,

find an expression for y in terms of x.

Use the expression you found in part (i) to complete the following table.

It is known that e is inversely proportional to f.

Describe what happens to e when f is doubled.

The wavelength of a sound wave, W metres, is inversely proportional to its frequency,

f hertz (Hz).

Richard is measuring the wavelengths of different sound waves. The wavelength is 0·5 m when the frequency is 1200 Hz.

What is the frequency when the wavelength is 10 m?

Use the expression you found in part (i) to complete the following table.

A farmer knows that the time, t, taken by goats to eat all the grass in a particular field is inversely proportional to the number of goats, g, in the field.

When there are 25 goats in the field, the time taken to eat all the grass is 36 days.

You may assume that all the goats eat grass at the same rate.

Find a formula for the time, t, in terms of the number of goats, g.

Hence, find the time taken for all of the grass to be eaten when there are 20 goats in the

field.

The farmer needs the grass to last for at least 40 days.

What is the greatest number of goats that should be allowed in the field?

The illuminance of light, I, from a lamp depends on the distance, d, from the lamp. The unit used to measure the illuminance of light is the lux.

It is known that I is inversely proportional to the square of d.

Carys has a desk lamp in her room. For her lamp, Carys measures the illuminance, I, to be 5 lux when the distance, d, is 2 m.

What is the illuminance of light from this lamp at a distance of 0·5 m?

find an expression for y in terms of x,

use the expression you found in part (a) to complete the following table.

Given that y is inversely proportional to x³ and that y = 120 when x = 2,

find an expression for y in terms of x,

use the expression you found in part (a) to complete the following table.