y is inversely proportional to d^2. When d = 10, y = 4. d is directly proportional to x^2. When x = 2, d = 24. Find a formula for y in terms of x. Give your answer in its simplest form.

Inversely proportional means proportional to one over, so the first bit tells us y = a/d^2, where a is number we don't know yet that connects y and d. To find it we need some example values of y and d, which we get in the question. When d=10, y=4, and we can substitute this into out equation: 4 = a/100. This is a simple algebra expression and you can solve it for a by multiplying both sides of the equation by 100. This gives you a=400. We can do exactly the same thing for the next bit of the question involving d and x. d = bx^2, 24 = 4b, b=6.We now have two equations, y = 400/d^2 and d = 6x^2. The question has asked for y in terms of x, so we don't want d to appear at all in the final answer. We can make d disappear by substituting for d - we replace the d in the first equation with what the second equation tells us d is the same as. y=400/(6x^2)^2. The question also wants us to simplify so we expand the brackets and cancel the fraction to give y= 25/(2x^4).