If (x^3+y^6) is positive, which of the following must be true?

Previous response was incorrect

Since adding positive numbers yields a positive result. For this expression to be positive, both terms must be positive.

1. \((x^3)\): If \((x^3)\): is negative, then \((x^3 + y^6)\) will not be positive no matter whatever the value of \((y^6)\). Hence, \((x^3)\) must be positive.
2. \((y^6)\): must be positive.

Let's evaluate the options:

A. \((x^3)\) is positive: Already established.
B. \((y)\) is positive: Not completely true. For example, if \((y)\) is negative but raised to an even power (i.e. \((y^6)\)), it will still yield a positive.
C. \((x^3)\) is negative: Contradict A, not true .
D. We know that \((x^3)\) and \((y^6)\) are positive, but this doesn't guarantee the signs of \((x)\) and \((y)\) themselves. For example, \((x)\) could be negative and \((y)\) could be positive, satisfying the conditions. This statement is not true.
E. \((\lvert x^3 \rvert < y^6)\): Not true either. \((x^3) \ge (y^6) ? \color{red}\text{may be}\) depending on the specific values of \((x)\) and \((y)\).
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