20 points find the area under one arch of a cycloid described by the parametric equations x = 3(20 - sin 20) and y = 3( i - cos 20). use 0 and π for the limiting values of θ .

Rockwell hardness of pins of a certain type is known to have a mean value of 50 and a standard deviation of 1.1. (round your answers to four decimal places.) (a) if the distribution is normal, what is the probability that the sample mean hardness for a random sample of 8 pins is at least 51?

Does the point (1, sqrt 7) lie on circle shown.

1. are the corresponding angles congruent 2. find the ratios of the corresponding sides 3. is triangle jkl congruent to triangle rst? if so what is the scale factor