If x-3 is directly proportional to the square of y and x = 5 when y = 2,find x when y= 6.

(x-3)/6^2 = (5-3)/2^2

To solve this problem, let's first write down the given information:

We are told that "x - 3 is directly proportional to the square of y." We can express this relationship mathematically as:

x - 3 ∝ y^2

where ∝ represents proportionality.

Next, we are given that x = 5 when y = 2. This allows us to set up a proportion to find the constant of proportionality (k). We can write:

(x₁ - 3) / y₁^2 = (x₂ - 3) / y₂^2

Plugging in the values we know: x₁ = 5, y₁ = 2, we get:

(5 - 3) / 2^2 = (x₂ - 3) / 6^2

Simplifying:

2 / 4 = (x₂ - 3) / 36

1/2 = (x₂ - 3) / 36

Cross-multiplying:

36 * 1/2 = x₂ - 3

18 = x₂ - 3

Adding 3 to both sides:

18 + 3 = x₂

x₂ = 21

Therefore, when y = 6, x = 21.