You have 700 sq ft of plywood to make the stage floor. Use A^-1(x) to find the dimensions of both the runway and the main part of the stage.

main stage is a rectangle and runway is a square. length of the main stage is 3x o f the runway, the width of the main stage is 2x the length of the runway.
A^-1(x)= square root of 1/7 y.
the question is, what are the dimensions of both the runway and the main part of the stage? Thank You!

well, what does x represent?

its the inverse of A(X) = 7x^2

I don't mean the formula. I mean, in the original problem, what was the variable x defined to be?

Answer that, and you have answered your problem.

To find the dimensions of both the runway and the main part of the stage, we need to solve the given equation A^-1(x) = √(1/7)x, where x represents the area of the stage floor (which is 700 sq ft in this case).

First, substitute the value of x into the equation: A^-1(700) = √(1/7)(700).

Calculate the square root of (1/7)(700): √(1/7)(700) = √100 = 10.

So, A^-1(700) = 10. This means that the area of the stage floor can be represented as 10 units.

Next, let's denote the dimensions of the runway as r x r, where r represents the side length of the runway, and the dimensions of the main part of the stage as 3x x 2x, where x represents the side length of the runway.

Since the area of a square is simply the side length squared, we can determine the side length of the runway using the equation r^2 = x, where r represents the side length of the runway.

Now substitute the value of A^-1(x) = 10 into the equation: 10^2 = x.

Solve for x: 100 = x.

So, the side length of the runway is x = 100.

Since the length of the main stage is 3 times the length of the runway, and the width of the main stage is 2 times the length of the runway, we can determine the dimensions of the main stage.

The length of the main stage is 3x = 3(100) = 300, and the width of the main stage is 2x = 2(100) = 200.

Therefore, the dimensions of the runway are 100 ft x 100 ft, and the dimensions of the main part of the stage are 300 ft x 200 ft.

Note: Please note that there was a minor error in the provided equation A^-1(x). It should be A^-1(x) = √(1/7)x, not A^-1(x) = √(1/7)y.