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please show steps/calculations ! Rainfall The normal monthly rainfall at the Sea

ID: 3212132 • Letter: P

Question

please show steps/calculations !

Rainfall The normal monthly rainfall at the Seattle-Tacoma airport can be approximated by the model R = 3.121 + 2.399 sin(0.524t + 1.377) where R is measured in inches and t is the time in months, with t = 1 corresponding to January. (Source: U.S. National Oceanic and Atmospheric Administration) Determine the extrema of the function over a one period. Use integration to approximate the normal annual rainfall (Hint: Integrate over the interval [0, 12].) Approximate the average monthly rainfall during the months of October, November, and December.

Explanation / Answer

R(t)= 3.121 + 2.399sin(0.524t + 1.377)...................t belongs to [1,12].............

R(1)= 3.20...

R(12)= 3.44......

now R'(x)= 1.257cos(0.524t+ 1.377)=0.........

so t=0.37........putting this t in the R(t)..we get

r(t)= 5.52.........

so, max rainfall occurs in teh month of may....

minimum occurs in the month of january......

annual rainfall= integral((3.121 + 2.399sin(0.524t+1.377))dt)..from t=0 to 12........

which is 39.72...............