Question

Estabon poured himself a hot beverage that had a temperature of 205F then set it on the kitchen table to cool. The temp of the kitchen ws a constant 71F. If the drink cooled to 182 F in 3 min, how long will it take to cool to 105 F???

Answer 1

@AlexandervonHumboldt2

Answer 2

@Luigi0210

Answer 3

hint y = m x + b
y is the hot temp m is the drop in temp per min and b is the temp of the room

Answer 4

Doesnt this problem pertain to newton's law of cooling?

Answer 5

rate of cooling?
do you know the formula?

Answer 6

hi :D

Answer 7

nu ;-;

Answer 8

d theta/dt

Answer 9

newtons law of cooling: rate of change of temprature of a body is proportional to difference between its temprature and surrounding temperature

Answer 10

perfect :)

Answer 11

\(T_b\): temperature of beverage
\(T_k\): temperature of kitchen=71

\[\frac{dT_b}{dt}=-k(T_b-T_k)\]

Answer 12

substitute \(T_k\) ; solve the differential equation for \(T_b\)

Answer 13

annnd im still confused lol

Answer 14

you have to solve that equation by using "seperation of variables"

Answer 15

\[\frac{dT_b}{dt}=-k(T_b-71)\]

Answer 16

\[\frac{dT_b}{(T_b-71)}=-kdt\]

Answer 17

integrate both sides