Question

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.

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
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...
The temperature T in a metal ball is inversely proportional to the distance from the center...
The temperature T in a metal ball is inversely proportional to the distance from the center of the ball, which we take to be the origin. The temperature at the point (1, 2, 2) is 130°. (a) Find the rate of change of T at (1, 2, 2) in the direction toward the point (3, 1, 4). (b) Show that at any point in the ball the direction of greatest increase in temperature is given by a vector that points...
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.
show that L: x=-1+t , y=3+2t ,z=-t and the plane P : 2x-xy-2z=-3 are parallel then...
show that L: x=-1+t , y=3+2t ,z=-t and the plane P : 2x-xy-2z=-3 are parallel then find the distance btween them
Imagine the xy plane, the xz plane, and the yz plane all made of metal and...
Imagine the xy plane, the xz plane, and the yz plane all made of metal and soldered together at the intersections. A single point charge Q is located a distance d from each of the planes. Sketch the configuration of image charges you need to satisfy the bound- ary conditions. What is the direction and magnitude of the force that acts on the charge Q?
(a) Find an equation of the plane tangent to the surface xy ln x − y^2...
(a) Find an equation of the plane tangent to the surface xy ln x − y^2 + z^2 + 5 = 0 at the point (1, −3, 2) (b) Find the directional derivative of f(x, y, z) = xy ln x − y^2 + z^2 + 5 at the point (1, −3, 2) in the direction of the vector < 1, 0, −1 >. (Hint: Use the results of partial derivatives from part(a))
A box consists of five grounded metal plates at x=0,x=a,y=0,y=b and z=0. The other plate located...
A box consists of five grounded metal plates at x=0,x=a,y=0,y=b and z=0. The other plate located at z=c is held at a constant potential V0. Find the potential inside the box.
Suppose ?(?,?)=??f(x,y)=xy, ?=(−4,−4)P=(−4,−4) and ?=3?+2?v=3i+2j. A. Find the gradient of f. ∇?=∇f=  ?+i+  ?j Note: Your answers should...
Suppose ?(?,?)=??f(x,y)=xy, ?=(−4,−4)P=(−4,−4) and ?=3?+2?v=3i+2j. A. Find the gradient of f. ∇?=∇f=  ?+i+  ?j Note: Your answers should be expressions of x and y; e.g. "3x - 4y" B. Find the gradient of f at the point P. (∇?)(?)=(∇f)(P)=  ?+i+  ?j Note: Your answers should be numbers C. Find the directional derivative of f at P in the direction of ?v. ???=Duf= D. Find the maximum rate of change of f at P. E. Find the (unit) direction vector in which the maximum rate...
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.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT