SOLUTION: 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

Question 71149: 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
thank you
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
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:

:
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

RELATED QUESTIONS
the intensity of illumination from a source of light varies inversely as the square of... (answered by rothauserc)

the intensity I of light varies inversely as the square of the distance D from the source (answered by rothauserc,greenestamps)

the intensity I of illumination from a light source is inversely proportional to the... (answered by ankor@dixie-net.com)

The illumination (in foot-candles) of a light source varies directly as the intensity... (answered by stanbon)

Intensity of light, measured in lux(lx) varies inversely as the square of the distance... (answered by stanbon)

At what distance from a source of light will the intensity of illumination be half as... (answered by Alan3354)

The intensity I of light varies inversely as the sqaure of the distance D from the... (answered by ankor@dixie-net.com)

The intensity of a light varies inversely as the square of the distance from the light... (answered by ewatrrr)

The intensity of light received from a source varies inversely as the square of the... (answered by Fombitz)