Calculus QUEST

[maeveoneill]

Can you please help me, I am stuck on the following two questions.

An object is moving away from the light source at a rate of 4 units/s. Find the rate of change of the intensity of illumination when it is 2 unit from the light source.

A balloon is rising at a rate of 200m/min. For every 500 m increase in height the air pressure causes the radius to increase 2 cm. Find the rate of increase of the volume when the radius is 10 m.

 

[tkhunny]

Do you have a model for illumination? Normally, that would be inversely proportional to the distance from the light source. (or is that the SQUARE of the distance? I forget.) You'll need that model (formula) in order to get started.

Do you know some Standard Gas Laws? Temperature, Volume, and Pressure relate to each other. Volume of a sphere can be written as a function of the radius. You'll need these formulations in order to get started.

 

[maeveoneill]

you dont need any extra information. for the second questoin the air pressure has nothing to do with it. wahts important is the rising rate 200m.min and that for every 500m the radius increased by 2cm. ahh yea thats about as much as i know. help please!

 

[stapel]

you dont need any extra information.

What is one to differentiate for the first exercise, without information on the light-intensity formula?

Eliz.

 

[Gene]

I would assume the light, L(umens) is illuminating the inside of a sphere.
The a(rea) = 4*pi*r².
If the object has an area A the l(ight) on the object is
l = LA/a = LA/(4*pi*r²)
dl/dr = -2LA/(4*pi*r³)
dr/dt=4
dl/dt=da/dr*dr/dt=-2*LA/(pi*r³)

******************

Volume = (4/3)*pi*r^3
dV/dr = 4*pi*r²
dr/dt=2cm/500m*200m/min = .008m/min
dV/dt=dV/dr*dr/dt=.032*pi*r² m³/min