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MHT CET20227 Aug 2022Morning ShiftMathematicsApplication of DerivativesActual

If surrounding air is kept at 20^ C and body cools from 80^ C to 70^ C in 5 minutes, then the temperature of the body after 15 minute will be

Options

  1. A52.7^ C
  2. B51.7^ C
  3. C54.7^ C
  4. D50.7^ C

Correct answer

C. 54.7^ C

Step-by-step solution

d T d t =-k(T-20) T-20=e^ -k t+c T=20+e^c e^ -k t for t=0, T=80 e^c=60 i.e. T=20+60 e^ -k t For t=5, T=70 70=20+60 e -5 k= 5 6 i.e. T=20+60 e^ 1 5 5 6 t Now, for t=15T=20+60 e^ 15 1 5 5 6 =20+60 ( 5 6 )^3=54.7

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