Two sc tips.

Astronomers at the Palomar Observatory have discovered a distant supernova explosion, one that they believe is a type previously unknown to science. E.    they believe to be of "Believe x to be y." => In the context of this sentence, the infini­tive to be is more appropriate than the limited present-tense is in referring to an event that occurred long ago but has been discovered only recently.

People tend to overestimate the amount of energy used by equipment, such as lights, that are visible and must be turned on and off and underestimate it when used by other equipment. -> Karim will overestimate the number when used by a grade. => This sentence is wrong because it nonsensically menas that Karim is used by grade.   when used by: à Nonsensically suggests that  the people are used by equipment.       When used by/if used by retains the subject of the verb.