<PRE><B>Question 71149</B>
A, B are two light source 100m apart. A is twice as strong as B. P is a point between A, B. Intensity of illumination varies inversely as the square of the distance from the light source. Find the length of AP so that the point P is the darkest 
:
I am going to try to solve this graphically. Arbitrarily assign a value of 200 at
10 ft from A and 100 at 90 ft from A, or 10 ft from B. 
:
The x axis from 1 to 10 represents 100 meters (10 meters per unit of x)
:
Let y = light intensity
:
I came up with the following equation: y = (200/x^2) + (100/(10-x)^2)
:
Graphing this:
{{{ graph( 300, 200, -2, 10, -10, 60, (200/x^2)+(100/(10-x)^2)) }}}
:
you can see the minimum intensity occurs between 5 and 6 which is between 50 and
60 meters from A. About 56 meter from A to p would be the darkest.
:
Sorry I messed this up the first time, hope this helps
 </PRE>