The surface of a spherical conductor of radius a is kept at a temperature of u(φ)=300k+50k cos(φ). the temperature inside is governed by the laplace equation. find an expression for the temperature everywhere inside the sphere. evaluate the temperature at the center of the sphere.

The surface of a spherical conductor of radius a is kept at a temperature of u(φ)=300K+50K cos(φ). The temperature inside is governed by the Laplace equation. Find an expression for the temperature everywhere inside the sphere. Evaluate the temperature at the center of the sphere.

see below

Step-by-step explanation:

a. Has a slope of 2 and passes through (10,17)

Using the slope intercept form

y = mx+b  where m is the slope and b is the y intercept

y = 2x+b

Substitute the point into the equation

17 = 2(10)+b

17 = 20+b

Subtract 20 from each side

17-20 =b

-3 =b

y = 2x-3

b. passes through (1,-4) and (2,-5)

First find the slope

m= (y2-y1)/(x2-x1)

   = (-5- -4)/(2-1)

  = (-5+4)/(2-1)

  = -1/1

  = -1

Using the slope intercept form

y = -x+b

Substitute a point into the equation

-4 = -1(1) +b

-4 = -1+b

Add 1 to each side

-3 = b

y = -x+3