Вопрос № 1046098 - Математика

Given that . Then the value of the derivative  will be…

Given that . Then the value of the derivative  will be…

It is known that at the moment t=0 the temperature of the body was T0. Let us place it into the environment with the temperature θ and believe that at any moment of the time the body is equally warmed by volume, the temperature of the environment is constant. The rate of change of the body temperature is proportional to the desired conditions with the proportionality coefficient k>0.
Determine the correspondence between the mathematical model, describing the action of heating (T0<θ) or cooling (T0>θ) of the body, correlation of temperatures and the kind of dependence:
1. T0 <θ, the rate of change of the body temperature is proportional to the difference of the current body temperature T(t) and the environment temperature θ;
2. T0 <θ, the rate of change of the body temperature is proportional to the difference of the initial body temperature and the environment temperature;
3. T0 >θ, the rate of change of the body temperature is proportional to the difference of the current body temperature and the environment temperature;
4. T0 >θ, the rate of change of the body temperature is proportional to the difference of the initial body temperature and the environment temperature.
Mathematical models:

All infinitely differentiable functions, which obey the identity, have the appearance of…

If , then  is equal to …

Two tunnels  and  wide are connected with each other at the right angel (see Figure). Workers carry tubes of different length along these tunnels. Indicate in meters the greater length of the tube which can be carried along these tunnels in horizontal position.  (ignore the thickness of the tube).