QUESTION 3(a) An object with the initial temperature To is placed in a tank of water, the temperature of which is keptat 15°C. After 25 minutes the temperature of the object is 178°C, and after 50 minutes it is 89°C.(i) Presuming that Newton's law of cooling applies, what is the initial value of To?(ii) How long does it take for the object to cool to 70°C?(b) Suppose that a radioactive metal has a half-life of 5000 years. If today, only 35 grams of a metal remains,(i) When was there 170 grams of the metal?(ii) When will there be only 19 g left of the metal?(c) Silkworms are being bred in an enclosure that holds a maximum of 750 silkworms in order to producesilk fabric. If the population grows according to the Malthusian model, with a growth constant k = 0,05when time is measured in days, how long will it take for an initial population of 50 silkworms to multiplyuntil the enclosure is full?(d) A variable R(t), t20 obeys the differential equationdRdt(R²(R²(i) Determine the equilibrium points of the model.+5R+1)(e-7) (22R-4-52-R).

(a) let the temperature of the object is T after a time x in minute according to newton's law of…

Answered: (a) An object with the initial…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

A pizza is put in an oven with a constant temperature of 230 degree Celsius. The initial temperature of the pizza was 15 degree and one hour later, it became 65 degree. How long will it take for the pizza's temperature to become 80 degree? (Feel free to use the solution we obtained for Newton's law of cooling. Notice that in this problem we are heating an object. The only difference is the constant k being positive)
Use the Newton's Method with po = 1.3 to approximate the solution of the equation cos(x-1)=-In(x - 1) within 10-3 accuracy. O a. 1.3987 b. 1.3977 O c. 1.3877 d. 1.3333 O e. 1.3900
Question 1 A tank initially holds 200 gal of brine solution containing 3 lb of salt. At t=0, another brine solution containing 3 lb of salt per gallon is poured into the tank at the rate of 6 gal / min, while the well stirred mixture leaves the tank at the same rate. Find the time at which the mixture in the tank contains 6 lb of salt. (A) 0.216 min B) 0.168 min 2.13 min D) 0.02 min
Set 2: A pork roast was taken out of a hardwood smoker when its internal temperature had reached 180 degrees Fahrenheit and it was allowed to rest in a 75 degrees Fahrenheit house for 20 minutes after which its internal temperature had dropped to 170 degrees Fahrenheit. We will assume the temperature of the roast follows Newton's Law of Cooling, T(t) = Ta +(To-Ta)e-kt, where To is the inital temperature, Ta is the ambient temperature, and k is a decay constant. ("Ambient temperature" means the temperature of the space the object is in.) (a) Find the values of To and Ta for this problem. (b) Find the value of k for this problem. Then write down the function T(t) which gives the temper- ature of the pork roast in degrees Fahrenheit as a function of time t in minutes. (c) Find the time at which the roast dropped to 160 degrees Fahrenheit.
1. Newton's Law of Cooling: At 9:00PM., a thermometer reading 70°F is taken outdoors where the temperature is 15°F. At 9:05PM., the thermometer reading is 45°F. At 9:10PM., the thermometer is taken back indoors where the temperature is fixed at 70°F. Find (a) the reading at 9:20PM. and (b) when the reading, to the nearest degree, will show the correct (70°F) indoor temperature.
12
9
Calculus II

Recommended textbooks for you

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Mathematics For Machine Technology

Advanced Math

ISBN:

9781337798310

Author:

Peterson, John.

Publisher:

Cengage Learning,

Basic Technical Mathematics

Advanced Math

ISBN:

9780134437705

Author:

Washington

Publisher:

PEARSON

Topology

Advanced Math

ISBN:

9780134689517

Author:

Munkres, James R.

Publisher:

Pearson,

SEE MORE TEXTBOOKS