### 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¦πΌ one over π₯. This symbol πΌ 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, letβs 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 mustnβt 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¦. Weβre asked to find the value of π¦
when π₯ equals 10. So itβs 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 donβt need to work out as a decimal, unless
specifically told to. π¦ is equal to one over 100.