Suppose you are at a party with 19 of your closest friends (so including you, there are 20 people there). Explain why there must be least two people at the party who are friends with the same number of people at the party. Assume friendship is always reciprocated.

If the thermal strain developed in polyimide film during deposition is given as 0.0044. assume room temperature is kept at 17.3 c, and thermal coefficient of expansion for the film and the substrate are 54 x 10^-6c^-1 and 3.3 x 10^-6c^-1respectively. calculate the deposition temperature.

Different types of steels contain different elements that alter the characteristics of the steel. for each of the following elements, explain what the element does when alloyed with steel.

The filament of an incandescent lamp has a temperature of 2000k. calculate the fraction of radiation emitted in the visible light band if the filament is approximated as blackbody