Question

Consider the funtion T(x,y)=2xy-y^2(°C) which determines the temperature for a metallic circular plate centered at the...

Consider the funtion T(x,y)=2xy-y^2(°C) which determines the temperature for a metallic circular plate centered at the origin and radius = 5, Explain why there's no direction in which the rate of change of temperature in the point P(1,-1) is equals to 5°C. consider units are cm.

Math   Calculus   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Consider the vector field below: F ⃗=〈2xy+y^2,x^2+2xy〉 Let C be the circular arc of radius 1...
Consider the vector field below: F ⃗=〈2xy+y^2,x^2+2xy〉 Let C be the circular arc of radius 1 starting at (1,0), oriented counter clock wise, and ending at another point on the circle. Determine the ending point so that the work done by F ⃗ in moving an object along C is 1/2.
A metal plate is located in an xy-plane such that the temperature T at (x,y) is...
A metal plate is located in an xy-plane such that the temperature T at (x,y) is inversely proportional to the distance from the origin, and the temperature at P(3,4) is F 0 200 . Find the rate of change of T at P in the direction of i - j.
The temperature T of a flat sheet, at the point (?x, y) ?, is given by...
The temperature T of a flat sheet, at the point (?x, y) ?, is given by T (?x, y) ? ? x ^ 3 - 2xy + ? 2y ^ 22. a) Determine the rate of change of temperature in the direction of the vector v = (?2, −1) ?, from the point P (? − 1,2) ?. b) Calculate the highest rate of temperature growth from P (? − 1,2) ?, as well as the direction in which it...
The temperature on a surface can be described by the equation T(x, y, z) = 2xy...
The temperature on a surface can be described by the equation T(x, y, z) = 2xy + xy2 z + 12e 2z . Use this function to answer the following questions. Remember to clearly organize your work and indicate your final answer. (a) Find the direction you should head to achieve the greatest rate of change in temperature at any point. (b) Find the direction you should head to achieve the greatest rate of change in temperature if you are...
The temperature in degrees Celsius on the surface of a metal plate is T (x, y)...
The temperature in degrees Celsius on the surface of a metal plate is T (x, y) = 20 − 4x^(2) − y^(2) where x and y are measued in centimeters. In which direction from the point (2, −3) does the temperature increase most rapidly? What is this rate of increase in that direction? c.∗ How much greater is the rate of increase from (2, −3) in the direction of the gradient, then the rate of change in the direction of...
A circular loop of radius R1 lies in the x − y plane, centered on the...
A circular loop of radius R1 lies in the x − y plane, centered on the origin, and has a current i running through it clockwise when viewed from the positive z direction. A second loop with radius R2 sits above the first, centered on the positive z axis and parallel to the first. 1. If the second loop is centered at the point z = R1, what must the current be (direction and magnitude) in order for the net...
The temperature at a point (x, y, z) is given by T(x, y, z) = 100e^(−x^2...
The temperature at a point (x, y, z) is given by T(x, y, z) = 100e^(−x^2 − 3y^2 − 9z^2) where T is measured in °C and x, y, z in meters. (a) Find the rate of change of temperature at the point P(2, −1, 2) in the direction towards the point (5, −2, 3). (b) In which direction does the temperature increase fastest at P? (c) Find the maximum rate of increase at P.
The temperature at a point (x, y, z) is given by T(x, y, z) = 400e−x2...
The temperature at a point (x, y, z) is given by T(x, y, z) = 400e−x2 − 5y2 − 9z2 where T is measured in °C and x, y, z in meters. (a) Find the rate of change of temperature at the point P(2, −1, 2) in the direction towards the point (3, −5, 6). °C/m (b) In which direction does the temperature increase fastest at P? (c) Find the maximum rate of increase at P.
3. Consider the following two lines: x = c + t, y = 1 + t,...
3. Consider the following two lines: x = c + t, y = 1 + t, z = 5 + t and x = t, y = 1 - t, z = 3 + t. Is there a value c that makes the two lines intersect? If so, find it. Otherwise, give a reason. 4. A particle starts at the origin and moves along the shortest path to the line determined by the two points P =(1,2,3) and Q =(3,-2,-1)....
The temperature at a point (x, y, z) is given by T(x, y, z) = 10e^(− ...
The temperature at a point (x, y, z) is given by T(x, y, z) = 10e^(− 2x2 − y2 − 3z2). In which direction does the temperature increase fastest at the point (2, 1, 3)? Express your answer as a UNIT vector.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT