The differential equation below models the temperature of an 89°C cup of coffee in a 21°C room, where it is known that the coffee cools at a rate of 1°C per minute when its temperature is 71°C. Solve the differential equation to find an expression for the temperature of the coffee at time t. (Let y be the temperature of the cup of coffee in °C, and let t be the time in minutes, with t = 0 corresponding to the time when the temperature was 89°C.) dy dt = − 1 50 (y − 21)

Step-by-step explanation:

Consider the differential equation . NOte that this fullfills the condition that the coffee cools down 1°C when y=71°C. We have the initial condition that y(0) = 89°C. Note that this is a separable differential equation, since

which leads to

. This gives us the following result

where C is a constant. Then, using the exponential function we have

which is another constant.

Given the initial condition, we have that when t=0, y = 89, then

Then, the final solution is

answer: sorry

step-by-step explanation: can you tell me pls how to find the rational of two integers

the central idea is that:

individuals should refuse to cooperate with institutions they believe unjust.

thoreau felt  that governments were more often agents of corruption than justice, even democracies, and that just because the majority feels a certain way does not make it just or correct in absolute terms. he uses the fact that slavery exists in our democracy to support this idea.

he goes on to say that, as a result, people should live true to their own internal laws regarding right and wrong, as a product of reflection and a moral life, rather than following every law that society imposes. 

step-by-step explanation: