As shown in figure,a search light is located at point a, 40 ft from a wall. The search light revolves counterclockwiseat a rate of pi/30 radians per second. At any point b on the wall,the strength of the light L, is inversely proportional to the square of the distance d from a: That is, at any point on the wall, l= k/d^2. At the closest point p, l =10000 lumens.

A) Find the constant of proportionality k.
B) Express l as a function of theta, tthe angle formed by line AP and line AB.
C) How fast in lumens per second is the strength ofthe light changing when theta equals pi/4? Is it increasing

Question

As shown in figure,a search light is located at point a, 40 ft from a wall. The search light revolves counterclockwiseat a rate of pi/30 radians per second. At any point b on the wall,the strength of the light L, is inversely proportional to the square of the distance d from a: That is, at any point on the wall, l= k/d^2. At the closest point p, l =10000 lumens.

A) Find the constant of proportionality k.
B) Express l as a function of theta, tthe angle formed by line AP and line AB.
C) How fast in lumens per second is the strength ofthe light changing when theta equals pi/4? Is it increasing