Show all details. Use tables of Laplace transform and/or partial fraction expansion method to solve these problems. (Tables will take less time). Q1. Experiments were performed to understand motion of ship tied in a river. Apparatus consists of a long tank where flowing water and wave generator creates forces on the tied ship. The differential equation of motion of ship is given by: M d’x/d’t + C dx/dt + Kx = f + f2*exp(-2t) t> 0 (a) Find x(t) when M = 5.6, C = 4, K = 5, step function f = 4.6, f2 = 3, x(t=0)=1 and dx/dt (t=0)= 1 (b) Find the order of X(s) and the number of poles. Find all poles of X(s). Determine the stability of system. (c) Find damped and un-damped frequency of oscillation, steady state value of x(t) (which equals Xss) using final value theorem and form expression of x(t).

At the "no mutants allowed" country farm, every sheep has 4 legs, every chicken has two legs, and all animals have only 1 head. asked to count how many sheep and chicken are in the fields, a farm boy reports back that there are 140 feet and 50 heads. how many sheep and chicken are there? there are sheep and chicken at the farm.

The difference of two numbers is 40. find the numbers if 0.3 parts of one number is equal to 37.5% of the other one.

Carla was trying to decide what to do saturday evening. she has $100 available to spend for the evening. she has narrowed her choices down to these events: braves game, a concert of an artist she likes, or the georgia aquarium. admission to the braves game is $25, hot dogs cost $10, sodas cost $5. the concert costs $25 for admission, $20 for a souvernir t-shirt, and $10 for a soda. the georgia aquarium has the show of a lifetime with an all you can eat and drink that costs $100. carla does not want to take any driving chances, so in addition to the cost of the aquarium, she will also need to pay for her uber/lyft, which is $15 each way. which option should carla choose if she wants to spend the least? based on that choice, what then is carla's oppotunity cost? fully explain your answer in at least one paragraph.