I had 5 questions, i wrote em up in photoshop i thought it would be easier.

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- Mar 27th 2008, 09:33 AM #1

- Joined
- Mar 2008
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- 3

- Mar 27th 2008, 10:05 AM #2
## Here is #2

we know that

$\displaystyle x-y=24 \mbox{ and } A=xy$

We want to minimize A

subbing the first into the second we get...

$\displaystyle A=(y+24)y=y^2+24y$

Since we want the minimum value we need to find the vertex of the parabola.

There are a few different ways. Since it is symmetric about its vertex the vertex is half way between its intercepts -24 and 0 so at -12

or we could use the vertex fromula

$\displaystyle y=\frac{-b}{2a}=\frac{-24}{2(1)}=-12$

Now that we know y we can solve for x

$\displaystyle x-(-12)=24 \iff x=12$

so the minimum product is $\displaystyle x \cdot y =(12)(-12)=-144$