Finding areas bounded by two equations

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5 Replies - 818 Views - Last Post: 23 November 2009 - 11:25 AM

#1 IngeniousHax

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Finding areas bounded by two equations

Posted 21 November 2009 - 07:25 PM

So i have been trying this problem for ever and I know the integra goes from -1 to 3, but I cant seem to solve for this on paper...

The equation is as follows: y = sqrt(x+1) and y = 1/2x+1/2

and I need to solve for x by setting them equal to one another
sqrt(x + 1) = 1/2x +1/2

Any ideas on how to solve this? SHould come up with (x+1)(x-3) = 0
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Replies To: Finding areas bounded by two equations

#2 poncho4all

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Re: Finding areas bounded by two equations

Posted 21 November 2009 - 08:28 PM

Well its quite simple:

Just move the sqrt to the other side of the equality and pow(1/2x + 1/2).
you would get

((1/4)x^2)+(1/2x)+(1/4)`=x+1

so after a few simple math

you see the need to use the quadratic formula with this values that are the turn out of the simple math you should have made by now

((1/4)x^2)-(1/2x)-(3/4)=0

You get two results
-1 and 3

Hope that helps

#3 IngeniousHax

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Re: Finding areas bounded by two equations

Posted 21 November 2009 - 09:23 PM

I dont think so, I tried doing that for about an hour and I would get 2+sqrt(7) and something else... even my g/f's calculator wouldnt do that formula and get 3 and -1, I mean I thank you for your asistance in trying, but I didn't get the same answers as you.

IDK we solved it by solving for x in terms of y and placing those back into the equation and it worked out.

Thanks for the try though.

#4 poncho4all

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Re: Finding areas bounded by two equations

Posted 21 November 2009 - 09:32 PM

Well just for the sake of learning ima try to type the quadratic equation as you should have in your calculator.

(-b+sqrt((b^2)-(4*a*c)))/(2*a)
and
(-b-sqrt((b^2)-(4*a*c)))/(2*a)

So with the data imputed we would have

((1/2)+sqrt(((1/2)^2)-(4*(1/4)*(-3/4)))/(2*(1/4))= 3
((1/2)-sqrt(((1/2)^2)-(4*(1/4)*(-3/4)))/(2*(1/4))= -1

Notice that -b here would become positive since - * - = + and the rest is pretty natural.

#5 IngeniousHax

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Re: Finding areas bounded by two equations

Posted 22 November 2009 - 01:44 PM

Yeah, IDK maybe I was just putting the quadratic into my calculator wrong... But either way, thanks all for the quick replies!

#6 poncho4all

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Re: Finding areas bounded by two equations

Posted 23 November 2009 - 11:25 AM