Solve each equation for the indicated variable. Round answers to two decimal places as necessary.
$-2 \sqrt[3]{C}+19=15$
Answer (1)
Subtract 19 from both sides: − 2 3 C = − 4 .
Divide both sides by -2: 3 C = 2 .
Cube both sides: C = 8 .
The solution is C = 8 .
Explanation
Problem Analysis We are given the equation − 2 3 C + 19 = 15 and we want to solve for C .
Isolating the Cube Root Term First, we subtract 19 from both sides of the equation to isolate the term with C : − 2 3 C + 19 − 19 = 15 − 19
− 2 3 C = − 4
Isolating the Cube Root Next, we divide both sides by -2 to isolate the cube root: − 2 − 2 3 C = − 2 − 4
3 C = 2
Solving for C Now, we cube both sides of the equation to solve for C : ( 3 C ) 3 = 2 3
C = 8
Final Answer Since the solution is an integer, no rounding is necessary. Therefore, the solution is C = 8 .
Examples
Imagine you are designing a cubic container, and you know that a certain expression involving the cube root of its volume must equal a specific value. Solving the equation allows you to determine the exact volume (C) of the container needed to meet the design requirements. This type of problem is useful in engineering and design, where precise calculations are essential for creating functional and efficient products.
