y is inversely proportional to d² - Edexcel - GCSE Maths - Question 14 - 2018 - Paper 1

Since d is directly proportional to x², we can write: $d = mx^2$ for some constant m.

Given that when x = 2, d = 24, we can substitute these values to find m: $24 = m(2^2)$ $24 = 4m$ Dividing both sides by 4 gives: m = 6.

Therefore, we can express d in terms of x as: $d = 6x^2$

To find y in terms of x, we can substitute the expression for d into the equation for y: $y = \frac{400}{d^2}$ Substituting d: $y = \frac{400}{(6x^2)^2}$ Simplifying this gives: $y = \frac{400}{36x^4}$ This further simplifies to: $y = \frac{100}{9x^4}$ Thus, the final formula for y in terms of x is: $y = \frac{100}{9x^4}$