Final answer:
To find the value of x that satisfies the ratio 729:x equivalent to x²:729, we set up the proportion and cross multiply, arriving at x³ = 531,441. Taking the cube root of both sides of the equation, we find x = 9.
Step-by-step explanation:
We are given that the ratio 729:x is equivalent to the ratio x²:729. To find the value of x, we can set up the proportion 729/x = x²/729.
Let's begin by cross-multiplying to solve for x:
- 729 * 729 = x * x²
- 531,441 = x³
Now we need to take the cube root of both sides to solve for x:
Therefore, the value of x that satisfies the given ratio is 9.