K G(S) = S(S+20)(S+20) A unity feedback system with is operating at 20% overshoot. Design a compensator to decrease the settling time by a factor of 2 without affecting the percent overshoot and do the following: 1. Evaluate the uncompensated system's dominant poles, gain and settling time 2. Evaluate the compensated systems dominant poles and settling time. 3. Evaluate then compensators poles and zero. Find the required gain.

23. Consider a simple economy with just two industries: farming and manufacturing. Farming consumes 1/2 of the food and 1/3 of the manufactured goods. Manufacturing consumes 1/2 of the food and 2/3 of the manufactured goods. Assuming the economy is closed and in equilibrium, find the relative outputs of the farming and manufacturing industries.

Explain the differences between Gaussian elimination and Gauss-Jordan elimination.

For the following scenarios for a population: 1) Construct a dynamic model by writing down a difference equation both in the updating function form (N(t+1)=f(N(t))N(t+1)=f(N(t))) and the increment form (N(t+1)−N(t)=g(N(t))N(t+1)−N(t)=g(N(t))) and specify the time step; 2) find the solution of the linear difference equation with a generic initial value and check that it satisfies the difference equation by plugging the solution into your equation (in either form); 3) plug in the given initial value and predict the future. Zombies have appeared in Chicago. Every day, each zombie produces 3 new zombies. Suppose that initially there is only one zombie, how many zombies will there be in 7 days? Suppose hunters kill 50 deer in a national forest every hunting season, while the deer by themselves have equal birth and death rates. If there are initially 500 deer in the forest, predict how many there will be in 5 years. The number of infected people in a population grows by 8% per day and…