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zaboda42
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Simple yet challenging calc problem - please help!
http://img252.imageshack.us/i/en8t.jpg/
a searchlight is located at point A 40 feet from a wall. The searchlight revolves counterclockwise at a rate of π/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 = 10,000 lumens.
a) Find the constant of proportionality k.
b) Express L as a function of θ , the angle formed by AP and AB.
c) How fast (in lumens/second) is the strength of the light changing when θ =π/4? Is it
increasing or decreasing? Justify your answer.
d) Find the value of θ between θ =0 and θ =π/2 after which L<1000 lumens.
I was only able to do part a) the other parts are rather confusing. If anyone could help that would be greatly appreciated.
My Attempt:
a) (40)^2 + (10,000)^2 = d^2
d = 10,000
L = k/d^2
10,000 = k/(10,000)^2
k = 1E12
http://img252.imageshack.us/i/en8t.jpg/
a searchlight is located at point A 40 feet from a wall. The searchlight revolves counterclockwise at a rate of π/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 = 10,000 lumens.
a) Find the constant of proportionality k.
b) Express L as a function of θ , the angle formed by AP and AB.
c) How fast (in lumens/second) is the strength of the light changing when θ =π/4? Is it
increasing or decreasing? Justify your answer.
d) Find the value of θ between θ =0 and θ =π/2 after which L<1000 lumens.
I was only able to do part a) the other parts are rather confusing. If anyone could help that would be greatly appreciated.
My Attempt:
a) (40)^2 + (10,000)^2 = d^2
d = 10,000
L = k/d^2
10,000 = k/(10,000)^2
k = 1E12
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