Question

Solve the equation x = 4/3 πr³ for r a. r=∛3x-4π b. r = ∛3x(4π) c. r = ∛4π/3π d. r ∛4π/3π

Answer 1

To solve the equation x = 4/3 πr³ for r, multiply both sides by 3/4, then divide by π, and finally take the cube root of both sides resulting in the solution r = ∛(3x/(4π)).

Step-by-step explanation:

The student is asking to solve the equation for r when given x = 4/3 πr³. To solve for r, we need to manipulate the equation to isolate r on one side. We can do this in the following steps:

• Multiply both sides of the equation by 3/4 to get rid of the fraction on the right side: 3/4 * x = πr³.
• Next, divide both sides by π to get r³ on its own: (3/4x)/π = r³.
• Finally, take the cube root of both sides to solve for r: r = ∛((3/4)x/π).

Therefore, the correct answer is:

r = ∛(3x/(4π))