K, now I'll help you with the rest.

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Inverse proportion

The number of days, D, to complete a project is inversely proportional to the number of poeple, P, who work on the project.

a) The project takes 18 days to complete with 150 people working on it.

Find an equation connecting D and P

Do you remember that the equation when you had a direct proportion was

__A__=constant?

B

Well, for the inverse proportion it is something like that, specificaly A*B=constant. Now, why this? Because, supposing we now the value of the constant, if A is very big then B must be quite small so the product of both is the constant. Obviously we can do the backwards case, if B is big.

Now, if you look at the problem you can say that:

D*P=constant. We'll call it "P.I.M.P".

So:

18*150=2700. Now, P.I.M.P=2700.

Then, the equation that connects D and P will be:

__D__=2700

P

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Simplification

Rationalise 1

[square root] 6

When you've got something like this, the last thing you want is a square root in the lower part of the fraction, right? So, how do we get rid of it? The answer is pretty simple: you can multiply by a certain number in the upper and lower part of the fraction. For example:

__1__ *

__3__=

__3__2 3 6

__3__ and

__1__ are the same right?

6 2

Now, as I said before, you gotta multiply the fraction by a number in both parts of it. And that number has got to be sqrt(6), because:

sqrt(6)*sqrt(6)=sqrt(6*6)=sqrt(36)=6.

(NOTE: Technically, sqrt(36) can be -6 or 6, because -6*-6=36 and 6*6=36, but in general terms when you work with this kind of exercises you just use the positive term, 6).

The result of this exercise would be:

__sqrt(6)__6

In another note, what if the teacher asks you to rationalise

__1__ ?

sqrt(1-sqrt(x))

We do the same thing: multiplying in the upper and lower part of the fraction by sqrt(1-sqrt(x)) we get:

__sqrt(1-sqrt(x))__1-sqrt(x)

Now, how do we get rid of that evil square root? This is the time when you gotta remember this thing:

A^2-B^2=(A + B )*(A - B )

because:

(A + B )*(A - B )=A^2+AB-AB-B^2= A^2 -B^2.

With that case it's just the same thing, with A=1 and B=sqrt(x). So, instead of multiplying for a square root or something like that, you multiply in both parts of the fraction for 1+sqrt(x), and you get the following:

__sqrt(1-sqrt(x)) * (1+sqrt(x))__1-x

Problem solved!

I hope this has been of any help. If you've got any more questions, just ask

**Edited by jpalz, 09 November 2005 - 02:47 AM.**