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

Step-by-step explanation:

We have to integrate the function

over the region

Let us convert into polar coordinates

x=cost : y = sint

Then we get dxdy = rdr dt

So we get the integral as

Substitute the limits to get

Answer

=

ending amount = beginning amount / (2^n)

where "n" = number of half-lives (or elapsed time / half-life)

ending amount = 50 mg / (2 ^10 / 5.3)

ending amount = 50 mg / (2 ^ 1.8867924528)

ending amount = 50 m / 3.6981210597

ending amount = 13.5203794557 mg

or about 13.5 mg remain

source:  

false

inverse variation is not exponential