4. A cup of coffee at temperature P cools at a rate proportional to the difference between its temperature and the surrounding temperature Po. Show that P = the cooling rate constant and A is the integral constant. A cup of coffee at 80°C is left in Ae-kt + Po , where k is a room at 20°C a) Find the cooling equation. b) It is found that after 20 minutes in the room, the temperature of the coffee has decrease by 20°C. Determine the temperature after 30 minutes

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Q: 1. What should be A for the path independent of (2,4) xy + A dx + 2Ay – x y? fip- (1,2) Moreover…

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.