Verify that the functions: cos(ln x), sin(ln x), form a fundamental set of solutions of the DE x^2y"+xy'+y=0 on the interval (0,infinity).Form the general solution.

Acollege is planning to construct a rectangular parking lot on land bordered on one side by a highway. the plan is to use 680 feet of fencing to fence off the other three sides. what dimensions should the lot have if the enclosed area is to be a maximum?

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.

Lisa has three classes that each last 50 minutes. what is the total number of minutes of the three classes