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dT -k(T - 35), where k is a positive constant. dt

dT -k(T - 35), where k is a positive constant. dt

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Q42) (a) The temperature gauge of a car is giving an overheating warning and the car is stopped. At time i minutes, the temperature Tof the liquid in the radiator decreases according to the equation dT = -k(T – 35), where k is a positive constant. The initial temperature of the dt liquid in the radiator is 95°C and it cools to 70°C after 10 minutes. đT =-k(T – 35) dt (1) Show that T = 35+ Ae¨ is a solution of (ii) Find the value of A. (iii) Find the value of k , correct to 3 decimal places. (iv) How long will it take for the temperature of the radiator to cool to 40°C? Give your answer correct to the nearest minute.
Transcribed Image Text:Q42) (a) The temperature gauge of a car is giving an overheating warning and the car is stopped. At time i minutes, the temperature Tof the liquid in the radiator decreases according to the equation dT = -k(T – 35), where k is a positive constant. The initial temperature of the dt liquid in the radiator is 95°C and it cools to 70°C after 10 minutes. đT =-k(T – 35) dt (1) Show that T = 35+ Ae¨ is a solution of (ii) Find the value of A. (iii) Find the value of k , correct to 3 decimal places. (iv) How long will it take for the temperature of the radiator to cool to 40°C? Give your answer correct to the nearest minute.
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