The rate of change of the temperature of the coffee is given by the following differential...

The rate of change of the temperature of the coffee is given by the following differential equation, where T is measured in degrees Fahrenheit and t is in minutes. The time to reach a certain temperature, T =185 F t = 4 min

dT/dt = 0.041(T – 75)

a. Use Euler's mothod with a stop size of 0.5 to estimate the temperature of coffee after 5 minutes.

b. Analyses the effect of step size on the error use of appropriate graph is recommended.

c. Find out the exact temperature of coffee solving the ordinary differential equation.

d. Compute the absolute error using the exact temperature determine in step c

ReplyForward

Solutions

Expert Solution

Amanda K answered 3 weeks ago

Next > < Previous

Related Solutions

1. Coffee temperature ~ The temperature of coffee served at a restaurant is approximately normally distributed...

1. Coffee temperature ~ The temperature of coffee served at a restaurant is approximately normally distributed with an average temperature of 160 degrees and a standard deviation of 5.4 degrees. a. What percentage of coffee servings are between 153 and 167 degrees? Final Answer: _______________________ b. What percentage of coffee is served at a temperature greater than or equal to 170 degrees? Final Answer: _______________________ c. What is the cutoff for the coolest 20% of coffee servings at this restaurant?

Newton's Law of Cooling tells us that the rate of change of the temperature of an...

Newton's Law of Cooling tells us that the rate of change of the temperature of an object is proportional to the temperature difference between the object and its surroundings. This can be modeled by the differential equation d T d t = k ( T − A ) , where T is the temperature of the object after t units of time have passed, A is the ambient temperature of the object's surroundings, and k is a constant of proportionality....

Newton's Law of Cooling is based on the principle that the rate of change of temperature...

Newton's Law of Cooling is based on the principle that the rate of change of temperature y'(t) of a body in an environment with ambient temperature A is proportional to the difference b/w the temperature y(t) of the body and the ambient temperature A, so that y'=k(A-y) for some constant k. (1) Sketch the direction field for the equation y'=K(A-y) for k=1/10 and A=70degrees. Then sketch several solution curves based on starting values of y(0) both greater than and less...

2. According to Newton’s Law of Cooling, the rate of change of the temperature of an...

2. According to Newton’s Law of Cooling, the rate of change of the temperature of an object can be modeled using the following diﬀerential equation: dT/dt = k(T-TR) where T is the temperature of the object (in ◦F), TR is the room temperature (in ◦F), and κ is the constant of proportionality. On a crime show, the detective discovers a dead body in a hotel room. (a) Write the diﬀerential equation to describe the change in temperature of the body...

Series Solutions of Ordinary Differential Equations For the following problems solve the given differential equation by...

Series Solutions of Ordinary Differential Equations For the following problems solve the given differential equation by means of a power series about the given point x0. Find the recurrence relation; also find the first four terms in each of two linearly independent solutions (unless the series terminates sooner). If possible, find the general term in each solution. (1-x)y"+xy-y=0, x0=0

Series Solutions of Ordinary Differential Equations For the following problems solve the given differential equation by...

1-A solution has a temperature change of 20 K. What is the temperature change in degree...

1-A solution has a temperature change of 20 K. What is the temperature change in degree Celsius? Flag this Question Question 2 Students used two thermometers in Thermo lab. If both thermometers consistently read temperature exactly 1.0 degree higher than the actual temperature, how does this affect the experimental molar heat of neutralization? A-It has an unknown impact on the molar heat of neutrailization. B-This will make the molar heat of neutrailization higher C-Since the temperature differences are used in...

Humid air at given : dry-bulb temperature, wet-bulb temperature and total pressure enters a drier at a given molar flow rate.

Humid air at given : dry-bulb temperature, wet-bulb temperature and total pressure enters a drier at a given molar flow rate. Using psychometric chart to estimate :relative humidity, absolute humidity, dew point temperature and humid volume of air A- volumetric flow rate entering drier?B-mass flow rate BDA entering drier?C-Ha and Hm if more mass flow rate of water is added during passing through drier?D-molar composition air leaving drier?E-percentage humidity (Hp) air entering drier?

Find the maximum rate of change of f at the given point and the direction in...

Find the maximum rate of change of f at the given point and the direction in which it occurs. f(p, q) = 3qe-p + 2pe-q, (0, 0) direction of maximum rate of change (in unit vector)

in a lab experiment to test the change in temperature of NaCl and the change in...

in a lab experiment to test the change in temperature of NaCl and the change in temperature of water: Specific heat of NaCl is 0.88 specific heat of DI water is 4.2 in the experiment, the change in temperature for the water was much greater than the change in temperature of the table salt as well as the change in energy. (when using equation E = g C × change in T) why did this occur?

Subjects