Y varies directly as the square of x and y=96 when x=4. Find the value of x when y=24
We can use the formula for direct variation, which states that y varies directly as the square of x can be written as:
y = kx^2
where k is the constant of variation. To find the value of k, we can use the given information that y=96 when x=4:
96 = k(4^2)
96 = 16k
k = 6
Now we can use this value of k to find x when y=24:
24 = 6x^2
4 = x^2
x = ±2
Since x must be positive (as it represents a length), the value of x is 2. Therefore, when y=24, x=2.