(1) the given curve is rotated about the y-axis. find the area of the resulting surface. y = 5 − x2, 0 ≤ x ≤ 2(2) the given curve is rotated about the y-axis. find the area of the resulting surface. y = (1/4)x2-(1/2)lnx 2 ≤ x ≤ 4

Two lines parallel to a third line are parallel to each other. always sometimes or never

Abike shop sells you a bicycle for $63 and a helmet for $21. the total cost is 150% of what the shop spent originally. how much did the shop spend originally? how much profit did the bike shop earn by selling the bicycle and helmet to you ?

The lengths of nails produced in a factory are normally distributed with a mean of 4.91 centimeters and a standard deviation of 0.05 centimeters. find the two lengths that separate the top 4% and the bottom 4%. these lengths could serve as limits used to identify which nails should be rejected. round your answer to the nearest hundredth, if necessary.