(Advanced Partial Differential Equation) I don't need the exact solution, I just need you to describe how you would obtain the time dependent temperature distribution in the hollow disc. Specifically, identify the eigenfunctions in the direction and explain how you would find eigenfunctions in the direction. I am thinking to solve the Dirichlet Problem for the hollow disc, with the appropriate BCs to give an answer to that. What do you think? Thanks in advance.

/is used for a fraction 1) if x = 2/3 and y = 3/4, what is the value of (x + y) (x/y) expressed as a common fraction? 2) what is the least positive integer greater than 1 that leaves a remainder of 1 when divided by each of 2, 3, 4, 5, 6, 7, 8, and 9? 3) the ponde family's powerjet pumps 420 gallons of water per hour. at this rate, how many gallons of water will it pump in 45 minutes? 4) kim's insurance company pays 80% of the cost of all prescription medication she purchases in a year beyond the first $250 worth of prescriptions. her prescriptions for this year cost a total of $570. how many dollars of this amounts will kim's insurance company pay?

Express in the simplest form: (x^2+9x+14/x^2-49) / (3x+6/x^2+x-56)

Solve this riddle: i am an odd number. i an less than 100. the some of my digit is 12. i am a multiple of 15. what number am i?