Question

. a thin plate made of iron is located in the xy-plane. the temperature t in degrees celsius at a point p(x,y) is inversely proportional to the square of its distance from the origin. express t as a function of xandy.\

Answer 1

The level of the curves are all the eclipses with the major axis.

             100                        50          1

a2 =       ------  - 1   ,   b2 =   -------  -   -----

               C                            C           2

Given that:

               100

T(x, y) = ------------

               1 + x2 + y2

This implies that the level curves of a function(f) of two variables relate to the curves with equation f(x, y) = c

where c is the constant.

                 100

        C = ------------                          ----- (1)

             1 + x2 + y2

By cross multiply

C (1 + x2 + y2) = 100

1 + x2 + y2 = 100/C

       

               100

x2 + y2= ---------  - 1                    -----(2)

                 C

From (2); let's assume that the values of c > 0 likewise c < 100, then the interval can be expressed as 0 < c <100.

Now,

(x)2           (y)2

------   +     ---------------

100            50          1

------  - 1     -------  -   -----

C                C           2

This is the equation for the  family of the eclipses centered at (0,0) is :

x2/a2 + y2/b2 = 1

             100                        50          1

a2 =       ------  - 1      b2 =   -------  -   -----

              C                            C           2

Therefore; the level of the curves are all the eclipses with the major axis:

             100                        50          1

a2 =       ------  - 1      b2 =   -------  -   -----

              C                            C           2

 and a minor axis   which satisfies the values for which 0< c < 100.

The sketch of the level curves can be see in the attached image below.

To learn more about Plane of Axis visit:

brainly.com/question/14407559

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