Question

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.
Give your answer in its simplest form.

Answer 1

• y = 100 / (9x⁴)

Explanation:

y is inversely proportional to d²

• y = k/d²

When d = 10, y = 4:

• 4 = k/10²
• k = 400

y is:

• y = 400/d²

d is directly proportional to x²

• d = mx²

When x = 2, d = 24

• 24 = m*2²
• m = 24/4
• m = 6

d is:

• d = 6x²

Find a formula for y in terms of x:

• y = 400 / d² = 400 / (6x²)² = 400 / (36x⁴) = 100 / (9x⁴)