It rains when the relative humidity is above 100%. If relative humidity is given by 200 - 3*(x + 5)^2, where x is the number of days after 1st of Jan how many days in the year does it rain.

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The relative humidity in the city is modeled by the function H(x) = 200 - 3*(x + 5)^2 where x is the number of days after 1st of January. It rains when H(x) is greater than 100.

Solving H(x) > 100 gives:

200 - 3*(x + 5)^2 > 0

=> 200 > 3*(x + 5)^2

=> (x + 5)^2 < 200/3

=> x + 5 < `sqrt(200/3)` and x + 5 > `-sqrt(200/3)`

=> x < 3.16 and x > -13.16

Rounding the two solutions, it rains in the city for x < 3 and x > -13. It rains in the city on 2 + 1 + 12 = 15 days.

**It rains in the city for 15 days in a year.**

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