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Mathematics-Online problems:

Interactive Problem 157: Right Triangle under a Parabola

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
The hypotenuse of the shaded right triangle is perpendicular to the parabola $ P: y = 1 - x^2$.


\includegraphics[width=1\moimagesize]{TdM_07_A1_bild1.eps}


Determine for $ x \in (0,1)$ $ $a) the minimum value for $ a \,\,$ and $ $b) the triangle having maximum area.


Answer:

$ $a)      $ a_{\operatorname{min}} =$     
$ $b)     Vertices and area of the triangle $ (a,0), (x,0), (x,y)$
$ a = $                               
$ x = $                               
$ y = $                               
         $ A_{\operatorname{max}} =$                               

(The results should be correct to 3 decimal places.)


   

(From: Mathematics Contest 2007)
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  automatically generated: 2/ 6/2018