document.write( "Question 1170538: A satellite dish is shaped like a paraboloid, with the receiver placed at the focus. It is to have a depth of 0.44 m at the vertex, with the receiver placed 0.11 m away from the vertex. What should the diameter of
\n" ); document.write( "the satellite dish be? \n" ); document.write( "
Algebra.Com's Answer #851155 by CPhill(1959)\"\" \"About 
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Let the paraboloid be represented by the equation $x^2 = 4py$, where the vertex is at the origin (0, 0) and the focus is at (0, p).
\n" ); document.write( "We are given that the receiver is placed 0.11 m away from the vertex, which means the focus is at (0, 0.11). Therefore, p = 0.11 m.\r
\n" ); document.write( "\n" ); document.write( "The equation of the paraboloid is $x^2 = 4(0.11)y$, or $x^2 = 0.44y$.
\n" ); document.write( "The depth of the dish is 0.44 m, which means when y = 0.44 m, we can find the x-coordinate of the edge of the dish.\r
\n" ); document.write( "\n" ); document.write( "Substitute y = 0.44 into the equation:
\n" ); document.write( "$x^2 = 0.44(0.44) = 0.1936$
\n" ); document.write( "$x = \pm \sqrt{0.1936} = \pm 0.44$\r
\n" ); document.write( "\n" ); document.write( "The diameter of the dish is the distance between the two x-coordinates, which is:
\n" ); document.write( "Diameter = 0.44 - (-0.44) = 2(0.44) = 0.88 m.\r
\n" ); document.write( "\n" ); document.write( "Therefore, the diameter of the satellite dish should be 0.88 m.\r
\n" ); document.write( "\n" ); document.write( "Final Answer: The final answer is $\boxed{0.88}$
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