A vessel with liquid at 18 C is placed in a cooler held at 3 C, and after 3 minutes the temperature drops to 13 C. (a) Find the differential equation satisfied by the temperature T of a liquid in the cooler at time t = 0. (b) Find the function temperature of the liquid once it is put in the cooler. (c) Find the liquid cooling constant.

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Q: Suppose you have just poured a cup of freshly brewed coffee with temperature 95°C in a room where…

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Q: The isotope thorium-234 has a half-life of 24.5 days. (a) What is the differential equation…

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Q: A thermometer is moved from a room where the temperature is 68 °F to a freezer where the temperature…

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Q: The amount y of the drug Warfarin in a patient’s body after t hours satisfies the differential…

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Q: dT -k(T - 35), where k is a positive constant. dt

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Q: The deer population of a national park has a natural growth rate of 4% per year. Each year the…

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Q: A piece of chicken is boiled until its internal temperature reaches 165 °F. The chicken is then…

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A: The complete solutions are given below

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Q: A tank contains 80 kg of salt and 2000 L of water. Pure water enters a tank at the rate 10 L/min.…

A: A tank contains 80 kg salt and 2000 L of water. Pure water enters a tank at the rate 10 L/min. The…

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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.