y is inversely proportional to d² When d = 10, y = 4 d is directly proportional to x² When x = 2, d = 24 Find a formula for y in terms of x - Edexcel - GCSE Maths - Question 14 - 2018 - Paper 1

We know that when d = 10, y = 4. Plugging these values into the equation:

$4 = \frac{k}{10^2}$

This simplifies to:

$4 = \frac{k}{100}$

Multiplying both sides by 100 gives:

$k = 400$

Now substituting k back into the original equation for y:

$y = \frac{400}{d^2}$

Since d is directly proportional to x², we can write:

$d = mx^2$

where m is another constant. We know that when x = 2, d = 24:

$24 = m(2^2)$

This simplifies to:

$24 = 4m$

Thus, we find:

$m = 6$

Hence, we have:

$d = 6x^2$

Substituting d back into the equation for y gives:

$y = \frac{400}{(6x^2)^2}$

This simplifies to:

$y = \frac{400}{36x^4}$

Finally, reducing this expression results in:

$y = \frac{100}{9x^4}$