Solve each equation for the indicated variable. Round answers to two decimal places as necessary.
$-4 A^3=-588$
Answer (1)
Divide both sides of the equation by -4: A 3 = 147 .
Take the cube root of both sides: A = 3 147 .
Approximate the cube root to two decimal places: A ≈ 5.28 .
The solution is: 5.28 .
Explanation
Problem Analysis We are given the equation − 4 A 3 = − 588 and asked to solve for A .
Isolating A^3 First, we divide both sides of the equation by − 4 to isolate the term with A . This gives us: − 4 − 4 A 3 = − 4 − 588 A 3 = 147
Taking the Cube Root Next, we take the cube root of both sides of the equation to solve for A :
A = 3 147
Approximating the Cube Root Now, we approximate the cube root of 147 to two decimal places. The cube root of 147 is approximately 5.2776. Rounding this to two decimal places, we get 5.28. A ≈ 5.28
Final Answer Therefore, the solution to the equation − 4 A 3 = − 588 , rounded to two decimal places, is A ≈ 5.28 .
Examples
Imagine you are designing a cubic storage container and need it to have a specific volume. If you know the desired volume, you can use the cube root to find the length of each side. For instance, if you want a container with a volume of 147 cubic units, you would calculate the cube root of 147 to find the side length, which is approximately 5.28 units. This ensures your container meets the required volume specifications.
