Consider the following differential equation:d2xdt2+ 3dxdt+ 2x=f(x)(1)where f(x) is the input and is a function of the output, x. Iff(x) =sin(x),linearize the differential equation for small perturbations about?

Aboat's value over time is given as the function f(x) and graphed below. use a(x) = 400(b)x + 0 as the parent function. which graph shows the boat's value increasing at a rate of 25% per year?

The sum of these consecutive integers is equal to 9 less than 4 times the least of the integer. find the three integers

Amachine that produces a special type of transistor (a component of computers) has a 2% defective rate. the production is considered a random process where each transistor is independent of the others. (a) what is the probability that the 10th transistor produced is the first with a defect? (b) what is the probability that the machine produces no defective transistors in a batch of 100? (c) on average, how many transistors would you expect to be produced before the first with a defect? what is the standard deviation? (d) another machine that also produces transistors has a 5% defective rate where each transistor is produced independent of the others. on average how many transistors would you expect to be produced with this machine before the first with a defect? what is the standard deviation? (e) based on your answers to parts (c) and (d), how does increasing the probability of an event a↵ect the mean and standard deviation of the wait time until success?