Solve each equation for the indicated variable. Round answers to two decimal places as necessary.
[tex]$A^3+14=266$[/tex]
Answer (2)
Subtract 14 from both sides of the equation: A 3 = 266 − 14 = 252 .
Take the cube root of both sides: A = 3 252 .
Calculate the cube root: A ≈ 6.316359597656378 .
Round to two decimal places: 6.32 .
Explanation
Understanding the Problem We are given the equation A 3 + 14 = 266 and asked to solve for A , rounding the answer to two decimal places.
Isolating the Term with A First, we isolate the term with A by subtracting 14 from both sides of the equation:
A 3 = 266 − 14
Simplifying the Equation Next, we simplify the right side of the equation:
A 3 = 252
Taking the Cube Root Now, we take the cube root of both sides of the equation to solve for A :
A = 3 252
Calculating the Cube Root and Rounding Calculating the cube root of 252, we find that A ≈ 6.316359597656378 . Rounding this to two decimal places, we get A ≈ 6.32 .
Final Answer Therefore, the solution to the equation A 3 + 14 = 266 , rounded to two decimal places, is A ≈ 6.32 .
Examples
Imagine you're designing a cubic container for a product and need it to hold a specific volume. If you know the desired volume (in this case, related to the number 252), solving an equation like A 3 = 252 helps you determine the necessary side length ( A ) of the cube. This ensures your container meets the volume requirements, which is crucial in packaging, storage, and transportation industries. Understanding how to manipulate and solve such equations is fundamental in engineering and design.
To solve the equation A 3 + 14 = 266 , you first isolate A 3 to find that A 3 = 252 . Then, taking the cube root gives you A ≈ 6.32 when rounded to two decimal places.
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