Solve each equation for the indicated variable. Round answers to two decimal places as necessary.
$-13 \sqrt[3]{B}-10=55$
Answer (1)
Add 10 to both sides: − 13 3 B = 65 .
Divide both sides by -13: 3 B = − 5 .
Cube both sides: B = ( − 5 ) 3 = − 125 .
Round to two decimal places: − 125.00 .
Explanation
Problem Analysis We are given the equation − 13 3 B − 10 = 55 and asked to solve for B , rounding the answer to two decimal places.
Isolating the Cube Root Term First, we isolate the term with the cube root of B by adding 10 to both sides of the equation: − 13 3 B − 10 + 10 = 55 + 10
− 13 3 B = 65
Isolating the Cube Root Next, we divide both sides of the equation by -13 to isolate the cube root of B :
− 13 − 13 3 B = − 13 65
3 B = − 5
Solving for B Now, we cube both sides of the equation to solve for B :
( 3 B ) 3 = ( − 5 ) 3
B = − 125
Final Answer Since we are asked to round the answer to two decimal places, we can write -125 as -125.00. Therefore, the solution is B = − 125.00 .
Examples
Imagine you're designing a refrigeration system, and the efficiency depends on the cube root of a certain parameter, B. If you know the desired efficiency and the other constants in the equation, you can solve for B to determine the required parameter value. This type of problem helps in determining the specifications for components in engineering designs, ensuring the system operates as intended. For example, if the equation − 13 3 B − 10 = 55 represents the relationship between the cooling capacity and a component's size, solving for B helps you choose the right size for the component.
