Which of the following is the mathematical equivalent of the following Java expression: h = (4.0 * a * b - Math.pow(b, 2)) / c;

The expression in question is ( h = \frac{4.0 \cdot a \cdot b - \text{Math.pow}(b, 2)}{c} ). To understand the correct mathematical equivalent, it is essential to parse the components of the Java expression clearly.

Firstly, ( \text{Math.pow}(b, 2) ) calculates ( b^2 ), which is crucial for correctly representing that part of the equation mathematically. Therefore, the expression simplifies to ( h = \frac{4ab - b^2}{c} ).

Looking at the options, the correct form retains the structure of the original equation: both the numerator and denominator are clearly defined.

In the choice that is correct, ( 4ab - b^2 ) is enclosed in parentheses, indicating that the entire expression ( 4ab - b^2 ) is considered as a single entity before division by ( c ). This grouping is vital to preserving the intended order of operations, ensuring that the computation is done in the same sequence as in the Java expression.

Hence, the choice reflects the need for clarity in mathematical expressions, particularly when those expressions involve multiple operations, ensuring that calculations adhere to