# Video: Pack 1 β’ Paper 1 β’ Question 13

Pack 1 β’ Paper 1 β’ Question 13

02:20

### Video Transcript

The table shows a set of values for π₯ and π¦. The variable π¦ is inversely proportional to the cube of π₯. Find an equation for π¦ in terms of π₯.

If two items are inversely proportional to one another, we can say π¦πΌ one over π₯. This symbol πΌ is just our way of saying is proportional to. So π¦ is proportional to one over π₯. We can then form this equation: π¦ is equal to π over π₯. In this case though, π¦ is inversely proportional to the cube of π₯. So we write π¦ is proportional to one over π₯ cubed. Our equation, therefore, becomes π¦ is equal to π over π₯ cubed.

You might have noticed that we have a table of values linking π₯ and π¦. At this stage, we can use any one of these pairs of numbers to help us calculate the value of the constant π. Since this is a noncalculator paper, letβs choose the simplest numbers possible. When π₯ is two, π¦ is equal to five over four. Substituting these values into our equation gives us five over four is equal to π over two cubed. To work out the value of π, we multiply both sides of the equation by two cubed or eight. π is therefore equal to 40 over four, which is equal to 10. We mustnβt forget to substitute our new value of π back into the original equation. π¦ is therefore equal to 10 over π₯ cubed.

Find the value of π¦ when π₯ equals 10. We now have an equation linking π₯ and π¦. Weβre asked to find the value of π¦ when π₯ equals 10. So itβs a simple matter of substituting π₯ equals 10 into that equation to find π¦. π¦ is therefore equal to 10 over 10 cubed. 10 cubed is 1000, giving us a value of π¦ equals one over 100 or 0.01. Remember as long as our answer is a fraction in its simplest form, we donβt need to work out as a decimal, unless specifically told to. π¦ is equal to one over 100.