Card flipper: you walk into a room, and see a row of n cards. each one has a number xi written on it, where i ranges from 1 to n. however, initially all the cards are face down. your goal is to find a local minimum: that is, a card i whose number is less than or equal to those of its neighbors, xi-1 > = xi < = xi+1. the first and last cards can also be local minima, and they only have one neighbor to compare to. there can be many local minima, but you are only responsible for finding one of them. obviously you can solve this problem by turning over all n cards, and scanning through them. however, show that you can find such a minimum by turning over only o(log n) cards.

Acommercial grade cubical freezer, 4 m on a side, has a composite wall consisting of an exterior sheet of 5.0-mm thick plain carbon steel (kst= 60.5 w/m k), an intermediate layer of 100-mm thick polyurethane insulation (kins 0.02 w/m k), and an inner sheet of 5.0- mm thick aluminium alloy (kal polyurethane insulation and both metallic sheets are each characterized by a thermal contact resistance of r 2.5 x 104 m2 k/w. (a) what is the steady-state cooling load that must be maintained by the refrigerator under conditions for which the outer and inner surface temperatures are 25°c and -5°c, respectively? (b) for power saving purpose, which wall material should be increased/reduced in. thickness in order to reduce 50% of the cooling load found in part (a)? redesign the thickness of the proposed material. 177 w/m-k). adhesive interfaces between the q=575.93 w