18. A mechanical or electrical system is described by the differential equation y + ω2y = f(t). Find y if f(t)= 1,0 a separately, remembering that f(t) = 0 for t > a. Show that 8>< 1 (1−cosωt), t: 1 [cosω(t−a)−cosωt], t>a. ω2 Sketch the motion if a = 1 T where T is the period for free vibrations of the system;

Atechnician compares repair costs for two types of microwave ovens (type i and type ii). he believes that the repair cost for type i ovens is greater than the repair cost for type ii ovens. a sample of 6767 type i ovens has a mean repair cost of $79.79$⁢79.79. the population standard deviation for the repair of type i ovens is known to be $19.18$⁢19.18. a sample of 5555 type ii ovens has a mean repair cost of $75.24$⁢75.24. the population standard deviation for the repair of type ii ovens is known to be $21.40$⁢21.40. conduct a hypothesis test of the technician's claim at the 0.050.05 level of significance. let μ1μ1 be the true mean repair cost for type i ovens and μ2μ2 be the true mean repair cost for type ii ovens. step 2 of 4 : compute the value of the test statistic. round your answer to two decimal places.