3.1 H) Direct & Inverse Proportion – Square or Cube
If we had two variables (x & y) that were in direct proportion to one another, the notation and the general equation would be:
a) Form an equation for j in terms of n.
b) Find the value of j when n is 3.
c) Find the value of n when j is 900.
Part a
Part a asks us to form an equation for j in terms on n. The general equation for this question is:
Part b
Part b asks us to find the value of j when n is 3. We do this by subbing n as 3 into the general equation.
Part c
Part c asks us to find the value of n is when j is 900. We do this by subbing in j as 900 into the general equation.
We want to find the value of n (make n the subject). The first step to achieve this is to get n2 by itself. At the moment, we have 25n2 and we are able to get just n2 by dividing both sides of the equation by 25.
We want to find the value of n and not n2. Therefore, we need to square root both sides of the equation.
Therefore, when j is 900, n is 6.
Let’s remind ourselves of the notation and general formula for inverse proportion. If y was inversely proportional to x, the notation and general formula would be:
Let’s now have an example. w is inversely proportional to z3. When w is 108, z is 2.
a) Form an equation for w in terms of z.
b) Find the value of z when w is 13.5.
c) Find the value of w when z is 3.
Part a
The question tells us that w is inversely proportional to z3. The notation and general equation for this would be:
Part b
Part b asks us to find the value of z when w is 13.5. We are able to do this by subbing in w as 13.5 into the general equation.
We want to find the value of z. Currently we have z3 on the denominator of a fraction, which is far from ideal. Therefore, the first step should be to bring the z3 up from the denominator of the fraction/ get rid of the denominator. We are able to do this by multiplying both sides of the equation by z3 (we get rid of the denominator of a fraction in an equation by multiplying both sides of the equation by the denominator).
The next step in finding the value of z is to get z3 by itself. Currently we have 13.5z3. We can get just z3 by dividing both sides of the equation by 13.5.
We want to find the value of z and not z3. Therefore, we cube root both sides of the equation.
Part c
Part c asks us to find the value of w when z is 3. We are able to do this by subbing in z as 3 into the general equation.
Direct and inverse proportion questions involving squares, cubes and roots are not too dissimilar to the normal direct and inverse proportion questions. The only difference is that a square, cube or root is involved, and this results in there being some more steps in the working. Providing you are carful with these types of questions, you should find them ok after you have tried a few questions. There are quite a few questions like this in the quiz, so it is definitely worth giving the quiz a go.