Solve each equation for the indicated variable. Round answers to two decimal places as necessary.
$\frac{\sqrt[3]{B}}{-9}$
Answer (2)
Multiply both sides of the equation by -9: 3 B = − 9 × □ .
Cube both sides of the equation: B = ( − 9 × □ ) 3 .
Simplify the expression: B = − 729 × ( □ ) 3 .
The solution for B is: B = − 729 × ( □ ) 3 .
Explanation
Understanding the Problem We are given the equation − 9 3 B = □ , where □ represents an unknown value. Our goal is to solve for B .
Isolating the Cube Root To isolate the cube root of B , we multiply both sides of the equation by − 9 :
3 B = − 9 × □
Cubing Both Sides To solve for B , we cube both sides of the equation: ( 3 B ) 3 = ( − 9 × □ ) 3 B = ( − 9 × □ ) 3 B = ( − 9 ) 3 × ( □ ) 3 B = − 729 × ( □ ) 3
Final Solution Therefore, the solution for B is: B = − 729 × ( □ ) 3 Since the value of □ is unknown, we leave the answer in terms of □ .
Examples
Imagine you are designing a cube-shaped container, and you know that a certain fraction of the cube root of its volume is related to another variable. Solving for the volume (B) in terms of that variable ( □ ) allows you to determine the exact size of the container needed. This type of problem is useful in engineering, physics, and architecture, where understanding relationships between variables is crucial for design and calculations.
To solve − 9 3 B = x for B , multiply both sides by -9 to get 3 B = − 9 x . Then cube both sides resulting in B = − 729 x 3 . This method systematically isolates the variable B .
;
