Evaluate the following integral over the specified region. assume (r comma theta )(r,θ) are polar coordinates. modifyingbelow integral from nothing to nothing integral from nothing to nothing with upper r startfraction da over (16 plus x squared plus y squared )squared endfraction∫∫r da 16+x2+y22; upper r equals startset (r comma theta ): 1 less than or equals r less than or equals 3 comma 0 less than or equals theta less than or equals pi endsetr={(r,θ): 1≤r≤3, 0≤θ≤π} m

Ricky takes out a $31,800 student loan to pay his expenses while he is in college. after graduation, he will begin making payments of $190.66 per month for the next 30 years to pay off the loan. how much more will ricky end up paying for the loan than the original value of $31,800? ricky will end up paying $ more than he borrowed to pay off the loan.

It is saturday morning and jeremy has discovered he has a leak coming from the water heater in his attic. since plumbers charge extra to come out on the weekends, jeremy is planning to use buckets to catch the dripping water. he places a bucket under the drip and steps outside to walk the dog. in half an hour the bucket is 1/5 of the way full. what is the rate at which the water is leaking per hour?

Abucket of paint has spilled on a tile floor. the paint flow can be expressed with the function p(t) = 6(t), where t represents time in minutes and p represents how far the paint is spreading. the flowing paint is creating a circular pattern on the tile. the area of the pattern can be expressed as a(p) = 3.14(p)^2 part a: find the area of the circle of spilled paint as a function of time, or a[p(t)]. show your work. part b: how large is the area of spilled paint after 8 minutes? you may use 3.14 to approximate pi in this problem.