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kitteneater · Sep 20, 2008, 04:48 PM

I really need help on this problem. I have no idea how to do this.:
A rectangle is inscribed in the region enclosed by the graphs of F(x)=18-x^2 and G(x)= 2x^2- 9. It gives a picture too, but there are no points on it for the rectangle. The rectangle is vertical though, with the longest legs being parallel to the Y axis, and the shortest to the X axis.

A. Find the height of the rectangle as a function of X.
B. Find the Width of the rectangle in terms of X.
c. Write the area of the rectangle as a function of X.

I think this has to do with optimization. But how would you find the max area of a shape in parabolas if you didn't have the points of where the rectangle intersected the parabola? I've already found the vertex points of the parabolas: ) (0, 19) and 0, -9. But does that even have anything to do with the problem? I'm so freakin' confused.

galactus · Sep 20, 2008, 05:04 PM

It's a shame you can't post the picture. Is the rectangle sitting on the x-axis? Or does it extend below the x-axis? If we let x be the distance on either side of the y-axis, then the area is 2xy. Sub in y=18-x^2.

$A=2x(18-x^{2})=36x-2x^{3}$

Now, the area is in terms of x.

I am taking a leap here. It would help to see the picture.

kitteneater · Sep 20, 2008, 05:39 PM

It's not on the X axis. It sits just below. The rectangle seems like it's cut in half by the y axis too. http://s61.photobucket.com/albums/h6...nfusion012.jpg

ebaines · Sep 22, 2008, 05:46 AM

No optimization needed - they simply want you to come up with the width and height for varoius width rectangles of half-width x. The height of the rectagle is merely F(x) - G(x). For example, for x =2: F(2)-G(2) = 18-2^2 - (2*2^2 - 9) = 14-(-1) = 15. And the width is simply 2x. So now you should be able to wite the formula for the area of the rectangle.

luzcancino · Jan 14, 2009, 12:15 AM

I need help on the parabola equations how to do a equation and what vertex , focus,and directrix are and where they go on the equation

galactus · Jan 14, 2009, 07:38 AM

Originally Posted by luzcancino

i need help on the parabola equations how to do a equation and what vertex , focus,and directrix are and where they go on the equation

Google. Lots of stuff out there.

chexican · Sep 7, 2009, 09:33 PM

Yes please I need help with the same thing
STEP BY STEP

Please! And thanks