Explanation Determine the solution for the differential equation and use the given values to obtain the value of the engine’s cooling constant. Given: Frank’s automobile engine runs at 100℃. On a day, when the outside temperature is 21 ℃ , he turns off the ignition and notes that 5 minutes later, the engine has cooled down to 70 ℃ Calculation: The differential equation is y ' = − k ( y − 21 ) This can be written as d y ( y − 21 ) = − k d t Integration on both sides gives ∫ d y ( y − 21 ) = − k ∫ d t = > y = 21 + To determine (b) The formula for y ( t ) To determine (c) When the engine will cool to 40℃

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Question

Chapter 10.2, Problem 6E

To determine

(a)

The engine’s cooling constant, $k$

To determine

(b)

The formula for $y (t)$

To determine

(c)

When the engine will cool to 40℃

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Chapter 10.2, Problem 5E

Chapter 10.2, Problem 7E

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