The pizza place in town has a large pizza oven. Pizzas are baked in the oven until they reach a temperature of 220C and are then taken out of the oven. Detailed research has been done on how pizzas cool in this excellent pizza place and we can assume that a change in the temperature of a pizza can be described after it comes out of the oven with the following differential equation dH = k(H(t) – Hµ) dt - where H (t) is the temperature of the pizzas at time t, Hu is the temperature in the room the pizza is in after it comes out of the oven and k is a constant that we need to determine. The local bakers have also found out that three minutes after the pizza is taken out and left in a room where the temperature is 22C, the pizza has cooled by 50C. Assume that there is a risk of burns in the mouth if you bite into a pizza that is hotter than 70C. How long would it take from pizza coming out of the oven until the first bite is taken if we want to make sure no one burns in their mouth? Assume that the pizza is waiting in a place where the temperature is 22C.

The pizza place in town has a large pizza oven. Pizzas are baked in the oven until they reach a temperature of 220C and are then taken out of the oven. Detailed research has been done on how pizzas cool in this excellent pizza place and we can assume that a change in the temperature of a pizza can be described after it comes out of the oven with the following differential equation dH = k(H(t) – Hµ) dt - where H (t) is the temperature of the pizzas at time t, Hu is the temperature in the room the pizza is in after it comes out of the oven and k is a constant that we need to determine. The local bakers have also found out that three minutes after the pizza is taken out and left in a room where the temperature is 22C, the pizza has cooled by 50C. Assume that there is a risk of burns in the mouth if you bite into a pizza that is hotter than 70C. How long would it take from pizza coming out of the oven until the first bite is taken if we want to make sure no one burns in their mouth? Assume that the pizza is waiting in a place where the temperature is 22C.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

The pizza place in town has a large pizza oven. Pizzas are baked in the oven until they reach
a temperature of 220C and are then taken out of the oven. Detailed research has been done
on how pizzas cool in this excellent pizza place and we can assume that a change in the
temperature of a pizza can be described after it comes out of the oven with the following
differential equation
dH
= k(H(t) – H„)
dt
-
where H (t) is the temperature of the pizzas at time t, Hu is the temperature in the room the
pizza is in after it comes out of the oven and k is a constant that we need to determine. The
local bakers have also found out that three minutes after the pizza is taken out and left in a
room where the temperature is 22C, the pizza has cooled by 50C.
Assume that there is a risk of burns in the mouth if you bite into a pizza that is hotter than
70C. How long would it take from pizza coming out of the oven until the first bite is taken if
we want to make sure no one burns in their mouth? Assume that the pizza is waiting in a
place where the temperature is 22C.

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