document.write( "Question 1208127: A right triangle has one vertex on the graph of y = 9 - x^2, x > 0 at (x,y) another at the origin, and the third on the positive x-axis at (x,0). Express the area A of the triangle as a function of x. \n" ); document.write( "

Algebra.Com's Answer #846325 by ikleyn(52858) $\"\"$ $\"About$

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\n" ); document.write( "A right triangle has one vertex on the graph of y = 9 - x^2, x > 0 at (x,y) another at the origin,
\n" ); document.write( "and the third on the positive x-axis at (x,0). Express the area A of the triangle as a function of x.
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document.write( "Three given points are (0,0) (the origin), (x,0) and (x,9-x^2) with x > 0.\r\n" );
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document.write( "They form a right-angled triangle with the right angle at x-axis.\r\n" );
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document.write( "Notice that 2 cases are possible.\r\n" );
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document.write( "    (1)  0 < x < 3.    Then the triangle is in quadrant I.\r\n" );
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document.write( "    (2)  3 < x < .  Then the triangle is in quadrant IV.\r\n" );
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document.write( "In any case, the legs of this triangle are x units and |9-x^2| units (absolute value).\r\n" );
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document.write( "    At x= 3 the triangle is degenerated; so it is a special case, \r\n" );
document.write( "    which does not fit to the problem's formulation.\r\n" );
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document.write( "So, the area of this triangle is  A(x) = , x > 0, x =/= 3.     ANSWER\r\n" );
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