document.write( "Question 1167082: a flashlight is shaped like a paraboloid so that if its bulb is places at then focus, the light rays from the bulb will then bounce off the surface in a focused direction that is parallel to the x-axis. if the paraboloid has a depth of 1.8 inches and the diameter on its surface is 6 inches, how far should the light source be placed from the vertex \n" ); document.write( "

Algebra.Com's Answer #851397 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "a flashlight is shaped like a paraboloid so that if its bulb is places at then focus,
\n" ); document.write( "the light rays from the bulb will then bounce off the surface in a focused direction
\n" ); document.write( "that is parallel to the x-axis. if the paraboloid has a depth of 1.8 inches
\n" ); document.write( "and the diameter on its surface is 6 inches, how far should the light source be placed from the vertex
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\n" ); document.write( "\n" ); document.write( "        It is a standard problem of this kind. The feature is\r
\n" ); document.write( "\n" ); document.write( "        that in this problem the symmetry line is parallel to x-axis,\r
\n" ); document.write( "\n" ); document.write( "        while usually in such problems the symmetry line is parallel to y-axis.\r
\n" ); document.write( "\n" ); document.write( "        So, I will adapt a standard solution to this case.\r
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document.write( "For solving such problems, write an equation of the parabola in the cross-section\r\n" );
document.write( "in the form\r\n" );
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document.write( "    x = .    (1)\r\n" );
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document.write( "The advantage of writing in this form is the fact that then \"p\"\r\n" );
document.write( "is the distance from the parabola vertex to its focus.\r\n" );
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document.write( "So, now our task is to find value of \"p\" from the given data.\r\n" );
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document.write( "The fact that \"the paraboloid has a depth of 1.8 inches \r\n" );
document.write( "and the diameter on its surface is 6 inches\"\r\n" );
document.write( "means that x = 1.8 meters at y = 6/2 = 3 inches.\r\n" );
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document.write( "So, we substitute this data into equation (1), and we get\r\n" );
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document.write( "    1.8 = .\r\n" );
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document.write( "It gives\r\n" );
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document.write( "    p =  = 1.25 = 1 inches.\r\n" );
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document.write( "Thus, the light source should be placed 1 inches from the vertex.    ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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