Question

y is inversely proportional to the cube of x. When x = 12, y = 24.(a) Find the formula for y in terms of x.

Answer 1

Since y is inversely proportional to the cube of x, this means that we can do a rule of thre for inversely proportion between y and x³. For this, we put the y values in the first column and the x³ values in the second:

y --- x³

24 --- 12³

Now, we invert either columns and put and equal sign:

$\frac{y}{24}=\frac{12^3}{x^3}$

Now, we just need to solve for y:

$y=24\frac{12^3}{x^3}=\frac{24\cdot12^3}{x^3}=\frac{41472}{x^3}$

So, the formula for y in terms of x is:

$y=\frac{41472}{x^3}$