Guys Is My Professor Ok??? 💀

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28. You are at a club, doing calculus, when no one understands what you are doing, so you go home depressed, eat a half gallon of ice-cream, and wash it down with a fifth of vodka. You then realise you have no ice-cream, go to the store, and buy 20 pints. You now have a tub of ice cream containing 20 pints. However, you now also have a tub of ice cream with a unique property. The rate at which it melts is not only proportional to the temperature difference between the ice cream and the room temperature but also inversely proportional to the cube of the volume of the remaining ice cream. The differential equation describing the melting process is given by = - k(I- 25, where V is the volume of ice cream in pints, tis time in minutes. T is the temperature of the ice cream in degrees Celsius, and k is a positive constant. The initial temperature of the ice cream is 18°C, and the initial volume is 25 pints. After 5 minutes, the volume of the ice cream has decreased to 20 pints. Determine the the value of the constant k. 1562⠝ • 1539 • 1526 • 1549¼ © 15698/ V (5) =26 SV3 dU = - 5 k (+ -251/(V3)) 1 E 4 (284 = - KS (+ 14 +25) +C 5 = 15625