





import math

def       A__(		__lowerCAmelCase	,			__lowerCAmelCase ):
				if (
				    not isinstance(__lowerCAmelCase	,			(int, float) )
				    or power_factor < -1
				    or power_factor > 1
				):
								raise ValueError('power_factor must be a valid float value between -1 and 1.' )
				return apparent_power * power_factor

def       A__(		__lowerCAmelCase	,			__lowerCAmelCase ):
				if (
				    not isinstance(__lowerCAmelCase	,			(int, float) )
				    or power_factor < -1
				    or power_factor > 1
				):
								raise ValueError('power_factor must be a valid float value between -1 and 1.' )
				return apparent_power * math.sqrt(1 - power_factor**2 )


if __name__ == "__main__":
		import doctest

		doctest.testmod()













from __future__ import annotations

def       A__(		__lowerCAmelCase	,			__lowerCAmelCase	,			__lowerCAmelCase ):
				_snake_case :			Dict  						=   list(range(len(__lowerCAmelCase ) ) )
				_snake_case :			Optional[int]  						=   [v / w for v, w in zip(__lowerCAmelCase	,			__lowerCAmelCase )]
				index.sort(key=lambda __lowerCAmelCase : ratio[i]	,			reverse=__lowerCAmelCase )

				_snake_case :			float  						=   0
				_snake_case :			list[float]  						=   [0] * len(__lowerCAmelCase )
				for i in index:
								if weight[i] <= capacity:
												_snake_case :			List[Any]  						=   1
												max_value += value[i]
												capacity -= weight[i]
								else:
												_snake_case :			Any  						=   capacity / weight[i]
												max_value += value[i] * capacity / weight[i]
												break

				return max_value, fractions


if __name__ == "__main__":
		import doctest

		doctest.testmod()






