The change in temperature of the coffee, when an insulated bottle containing coffee was shook for a few minutes.

Question

Suppose that the temperature at a point x, y, z in space is given by T(x,y,z)=80/1+x2+2y2+3z2, where T=°c and x,y,z in metres. In which direction does the temperature increases fastest at the point (1,1,-2). What is the maximum rate of increase.

Answer 1

Question

Chapter 11, Problem 15CQ

To determine

The change in temperature of the coffee, when an insulated bottle containing coffee was shook for a few minutes.

Expert Solution & Answer

Trending nowThis is a popular solution!

See solution

Check out sample textbook solution

Students have asked these similar questions

Suppose that the temperature at a point x, y, z in space is given by T(x,y,z)=80/1+x2+2y2+3z2, where T=°c and x,y,z in metres. In which direction does the temperature increases fastest at the point (1,1,-2). What is the maximum rate of increase.

Two blocks, A and B, are made of the same material. Block A has dimensions l x w x h = L X 2L X L and Block B has dimensions 2L X 2L X 2L. If the temperature changes, what is (a) the change in the volume of the two blocks, b) the change in the cross-sectional area l x w, and (c) the change in the height of the two blocks?

We know from Newton's Law of Cooling that the rate at which an object warms up is proportional to the difference between the ambient temperature of the room and the temperature of the object. The differential equation corresponding to this situation is given by y' = k(M – y) where k is a positive constant. The solution to this equation is given by y = M + (yo – M)e-kt , where yo is the initial temperature of the object. Suppose your Thanksgiving turkey is kept at a temperature of 40 degrees Fahrenheit until it is put into a 350 degree Fahrenheit oven. It takes 2 hours for the turkey to warm up to a safe eating temperature of 165 degrees Fahrenheit. Find the values of yo, M, and k, for this situation, rounding your answers to 3 decimal places. Yo= M = k= Regardless of your answers above, suppose the k value in this situation is k = 0.3. Find the initial rate of increase of the turkey's temperature as soon as it is placed in the oven. Round to 3 decimal places. degrees per hour.