please show work ## Newton's Law of Heating and Cooling: Ice Cream Making ProcessNewton's heating-cooling law states that the rate of change in the temperature, $ H $, is proportional to the difference between the object and the surrounding temperature. Let $ H(t) $ be the temperature of the object being cooled and $ S $ be the surrounding temperature. **Example Scenario:**An ice cream maker works by cooling the milk, cream, and sugar mixture in 32 degrees ice, while stirring until the ice cream is "frozen" at 33 degrees. If the ingredients are placed in the ice cream maker at 70 degrees, it takes 2 hours to make the ice cream.**Objective:**Write and solve the differential equation which describes the temperature of the ice cream over time.**Possible Solutions:**Choose the correct differential equation:- $ \circ $ $ H(t) = 32 + 38e^{-2.819t} $- $ \circ $ $ H(t) = 32 + 38e^{-1.819t} $- $ \circ $ $ H(t) = 32 - 38e^{1.819t} $- $ \circ $ $ H(t) = 32 + 38e^{1.819t} $**Explanation:**Here, the equation $ H(t) $ represents the temperature $ H $ of the ice cream mixture at any time $ t $ in hours. The constants in the equation are derived based on the initial and surrounding conditions described. Solving this differential equation will provide the function that predicts how the temperature of the ice cream mixture changes over time.**Determining the Correct Function:**To find the correct solution, we will need to consider the initial conditions (ice cream mixture at 70 degrees and the surrounding ice at 32 degrees). The correct differential equation model often follows the form laid out by Newton's Law and takes into account these initial temperature conditions to find the function describing temperature $ H(t) $.

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Newton's heating-cooling law states that the rate of change in the temperature, H, is proportional to the difference between the object and the surrounding temperature. Let H(t)be the temperature of the object being cooled and S be the surrounding temperature. An ic cream maker works by cooling the milk, cream, and sugar mixture in 32 degree ice, while stirring until the ice cream is "frozen" at 33 degrees. If the ingredients are placed in the ice cream maker at 70 degrees, it takes 2 hours to make the ice cream. Write and solve the differential equation which describes the temperature of the ice cream over time. O H(t) = 32 + 38e-2.819t O H(t) = 32+38e-1.819t O H(t) = 32 – 38e1.819t O H(t) = 32 +38e1.819t

Newton's heating-cooling law states that the rate of change in the temperature, H, is proportional to the difference between the object and the surrounding temperature. Let H(t)be the temperature of the object being cooled and S be the surrounding temperature. An ic cream maker works by cooling the milk, cream, and sugar mixture in 32 degree ice, while stirring until the ice cream is "frozen" at 33 degrees. If the ingredients are placed in the ice cream maker at 70 degrees, it takes 2 hours to make the ice cream. Write and solve the differential equation which describes the temperature of the ice cream over time. O H(t) = 32 + 38e-2.819t O H(t) = 32+38e-1.819t O H(t) = 32 – 38e1.819t O H(t) = 32 +38e1.819t

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.

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please show work

## Newton's Law of Heating and Cooling: Ice Cream Making Process

Newton's heating-cooling law states that the rate of change in the temperature, $ H $, is proportional to the difference between the object and the surrounding temperature. Let $ H(t) $ be the temperature of the object being cooled and $ S $ be the surrounding temperature.

**Example Scenario:**
An ice cream maker works by cooling the milk, cream, and sugar mixture in 32 degrees ice, while stirring until the ice cream is "frozen" at 33 degrees. If the ingredients are placed in the ice cream maker at 70 degrees, it takes 2 hours to make the ice cream.

**Objective:**
Write and solve the differential equation which describes the temperature of the ice cream over time.

**Possible Solutions:**
Choose the correct differential equation:

- $ \circ $ $ H(t) = 32 + 38e^{-2.819t} $

- $ \circ $ $ H(t) = 32 + 38e^{-1.819t} $

- $ \circ $ $ H(t) = 32 - 38e^{1.819t} $

- $ \circ $ $ H(t) = 32 + 38e^{1.819t} $

**Explanation:**
Here, the equation $ H(t) $ represents the temperature $ H $ of the ice cream mixture at any time $ t $ in hours. The constants in the equation are derived based on the initial and surrounding conditions described. Solving this differential equation will provide the function that predicts how the temperature of the ice cream mixture changes over time.

**Determining the Correct Function:**
To find the correct solution, we will need to consider the initial conditions (ice cream mixture at 70 degrees and the surrounding ice at 32 degrees). The correct differential equation model often follows the form laid out by Newton's Law and takes into account these initial temperature conditions to find the function describing temperature $ H(t) $.

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