Captain Silver buried treasure on a desert island. There are only two palms on this island: a small ...: ответ на тест 1046097 - Математика

Captain Silver buried treasure on a desert island. There are only two palms on this island: a small one and a big one. They are situated at a distance of 400 m from each other. Silver told the rest of the pirates that the treasure is located at a three times greater distance from the small palm than from the big one. If L is the largest possible length of the ditch the pirates have to dig to find the treasure, then the value of the expression  is equal to…

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It is one of the largest cities in the world. It was founded three hundred years ago at the mouth Hudson River. The centre of this city is Manhattan Island. There are many skyscrapers, banks and offices of American businessmen in Manhattan. Broadway begins here; the Stock Exchange is located here. Numerous bridges link Manhattan Island with the other parts of the city.
People from almost all parts of the world live in this city. It is even called “Modern Babylon”

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 …