Make $x$ the subject of the formula: [tex]y^3=\sqrt{5 x}[/tex]
Answer (1)
Square both sides of the equation: ( y 3 ) 2 = ( 5 x ) 2 which simplifies to y 6 = 5 x .
Divide both sides by 5 to isolate x : x = 5 y 6 .
Therefore, the equation with x as the subject is: x = 5 y 6 .
Explanation
Understanding the Problem We are given the equation y 3 = 5 x and we want to make x the subject of the formula. This means we want to isolate x on one side of the equation.
Squaring Both Sides First, we square both sides of the equation to eliminate the square root: ( y 3 ) 2 = ( 5 x ) 2
Simplifying the Equation Simplifying the equation gives us: y 6 = 5 x
Isolating x Now, we divide both sides by 5 to isolate x : 5 y 6 = 5 5 x
Final Answer This simplifies to: x = 5 y 6 So, x is now the subject of the formula.
Examples
In physics, you might encounter a formula relating a quantity (like velocity cubed) to the square root of another quantity (like distance). If you need to find the distance based on the velocity, you'd rearrange the formula just like we did here. For example, if y 3 represents the cube of the velocity and 5 x represents the square root of 5 times the distance, solving for x allows you to calculate the distance directly from the velocity.
