Calculus problem help please

[Jellyjook]

Many physical quantities are connected by inverse square laws, that is, by power functions of the form f(x) = kx⁻².
In particular, the illumination of an object by a light source is inversely proportional to the square of the distance from the source. Suppose that after dark you are in a room with just one lamp and you are trying to read a book. The light is too dim and so you move halfway to the lamp. How much brighter is the light?

I'm completely clueless on this one... Any ideas?

 

[stapel]

Many physical quantities are connected by inverse square laws, that is, by power functions of the form f(x) = kx⁻².
In particular, the illumination of an object by a light source is inversely proportional to the square of the distance from the source. Suppose that after dark you are in a room with just one lamp and you are trying to read a book. The light is too dim and so you move halfway to the lamp. How much brighter is the light?

I'm completely clueless on this one... Any ideas?

Hint: Use what you learned back in algebra about variation equations.

 

[Jellyjook]

Hmm..someone tried helping me with this and I don't understand the thought process of this problem..I know what the answer should be, but I don't know how to get to it.

 

[DrPhil]

Many physical quantities are connected by inverse square laws, that is, by power functions of the form f(x) = kx⁻².
In particular, the illumination of an object by a light source is inversely proportional to the square of the distance from the source. Suppose that after dark you are in a room with just one lamp and you are trying to read a book. The light is too dim and so you move halfway to the lamp. How much brighter is the light?

I'm completely clueless on this one... Any ideas?

What part of "inversely proportional to the square of the distance" do you not understand? Don't try to make the question more difficult than it is. You just have to figure out the meaning of that phrase. [The phrase is also repeated as an algebraic formula.]

 

[Jellyjook]

I just don't understand the initial thought process for this kind of problem. That's why I sometimes struggle in math.

 

[DrPhil]

I just don't understand the initial thought process for this kind of problem. That's why I sometimes struggle in math.

I first read through to find the "?" so I know what is being asked for: "How much brighter is the lamp?"

Then read it again, finding whatever I need to know about "brightness." At this point I usually translate English to Algebra, but really you can solve this just by knowing a few English words:

inverse

proportional

square

distance

If you don't understand the English, the relationship of intensity to distance was also presented in the language of Algebra:

\(\displaystyle f(x) = \dfrac{k}{x^2}\)

If the distance \(\displaystyle x\) is reduced by half, what happens to the inverse of the square of \(\displaystyle x\)? You should be able to answer that in either English of Algebra.

 

[stapel]

Hmm..someone tried helping me with this and I don't understand the thought process of this problem..I know what the answer should be, but I don't know how to get to it.

You could try following the link in the first reply, and studying a few of the lessons on "variation equations" that are listed there. :lol: