<SYSTEM_TASK:>
Solve the following problem using Python, implementing the functions described below, one line at a time
<END_TASK>
<USER_TASK:>
Description:
 def satisfy(self, *requirements):
 """ Checks whether the given requirements are satisfiable within the given execution context Parameter --------- requirements : list(Requirement) List of requirements to check whether they are satisfiable """

        versions = []
        for req_range in requirements:
            try:
                version = self._detected_versions[req_range.name]
            except KeyError:
                try:
                    version = req_range.requirement.detect_version()
                except ArcanaRequirementNotFoundError as e:
                    if self._fail_on_missing:
                        raise
                    else:
                        logger.warning(e)
                except ArcanaVersionNotDetectableError as e:
                    if self._fail_on_undetectable:
                        raise
                    else:
                        logger.warning(e)
                else:
                    self._detected_versions[req_range.name] = version
            if not req_range.within(version):
                raise ArcanaVersionError(
                    "Detected {} version {} is not within requested range {}"
                    .format(req_range.requirement, version, req_range))
            versions.append(version)
        return versions