Use trigonometric substitution to evaluate the integral below. Give the restriction on , show all work, and be scrupulously careful about all of your notation. Everything you write means something. ∫ 3√ 2 − 1 , > 1

On a cm grid, point p has coordinates (3,-1) and point q has coordinates (-5,6) calculate the shortest distance between p and q give your answer to 1 decimal place

Are the corresponding angles congruent? explain why or why not.

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?