y varies directly as the square of x. When x = 2, y = 40. Find x when y = 640.

Are you sure that shouldn't say y=4?

@jen no it shouldnt

To find the value of x when y = 640, we can use the direct variation formula.

In this case, the direct variation formula is y = kx^2, where k is the constant of variation.

We are given that when x = 2, y = 40. We can use this information to find the value of k.

Substituting the given values into the formula:
40 = k(2^2)
40 = 4k

To find the value of k, divide both sides of the equation by 4:
k = 40 / 4
k = 10

Now that we have the value of k, we can substitute it into the direct variation formula:
y = 10x^2

To find the value of x when y = 640, we can rearrange the formula:
640 = 10x^2

Divide both sides of the equation by 10:
64 = x^2

Take the square root of both sides to solve for x:
x = √64
x = ±8

The value of x when y = 640 is either 8 or -8, since we took the square root of 64.

Therefore, x can be either 8 or -8.