When the boat moves on the surface of the water the resistance force of the environment F is directl...: ответ на тест 1046096 - Математика

When the boat moves on the surface of the water the resistance force of the environment F is directly proportional to the speed v (, where  - coefficient of proportionality). At the moment of the engine shutdown the outboard motorboat is moving at a speed of 240 m/min., and 2 min. later it’s speed is equal to 120 m/min. 6 min. after the engine shutdown the outboard motorboat will be moving at a speed of ______ m/min.

When the boat moves on the surface of the water the resistance force of the environment F is directly proportional to the speed v (, where  - coefficient of proportionality). At the moment of the engine shutdown the outboard motorboat is moving at a speed of 192 m/min., and 1 min. later it’s speed is equal to 96 m/min. 8 min. after the engine shutdown the outboard motorboat will be moving at a speed of ______ m/min.

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…

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…