You need to ship n packages across the country using trucks. each package i has a weight wi, and each truck can hold a total weight of m. you want to make the shipment using as few trucks as possible. more formally, given n packages with weights w1, , and numbers m and k, is there a way to ship the packages using ktrucks where the total weight carried by each truck is at most m? prove that this problem is np-hard. then, find a greedy algorithm that uses at most twice as many trucks as optimal. provide a proof.

Shafts are machine elements that are used to a) carry axial loads b) direct shear loads c) transmit power d) rotate at constant speed e) none of the above circular and square shafts subjected to the same torque under the same circum behave a) the same way b) almost the same way

What is a monomer? how do they form a ploymer from the view point of chemical bonding?

Afoot bridge is made as a simple deck, 4 m long, with a cross section 2 m (wide) and 20 cm thick, and made of wood. the deck is supported at the two ends. the maximum load allowable on the bridge is 10 tons, provided it is uniformly distributed on the deck. to sense this load, a strain gauge is placed at the center of the bridge and its resistance is monitored. if the sensor has a nominal resistance of 350 s2 and a gauge factor of 3.6, what is the reading of the strain gauge at maximum load? the modulus of elasticity for the wood used in the construction is 10 gpa.