document.write( "Question 636919: The shell fired from the base of the hill follows the parabolic path y=-(x^2/4)+8x with distances in miles. the hill has a slope of 1/4. how far from the gun is the point of impact? \n" ); document.write( "
Algebra.Com's Answer #401296 by stanbon(75887)\"\" \"About 
You can put this solution on YOUR website!
The shell fired from the base of the hill follows the parabolic path y=-(x^2/4)+8x with distances in miles. the hill has a slope of 1/4. how far from the gun is the point of impact?
\n" ); document.write( "---
\n" ); document.write( "h(x) = (-1/4)x^2 + 8x is path of the shell where x is in seconds.
\n" ); document.write( "----------
\n" ); document.write( "y = (1/4)x is the equation of the slope of the hill.
\n" ); document.write( "---
\n" ); document.write( "Find the intersection of the shell path and the hill:
\n" ); document.write( "(1/4)x = (-1/4)x^2+8x
\n" ); document.write( "(-1/4)x^2 + (31/4)x = 0
\n" ); document.write( "Factor:
\n" ); document.write( "(-1/4)x[x - 31) = 0
\n" ); document.write( "---
\n" ); document.write( "Positive solution:
\n" ); document.write( "x = 31
\n" ); document.write( "--------
\n" ); document.write( "To figure out the slant distance sketch the shell path and the hill
\n" ); document.write( "---
\n" ); document.write( "You have a right triangle with base = 31, height = h(31) = 7.75
\n" ); document.write( "--
\n" ); document.write( "The slant distance = sqrt[31^2+7.75^2] = 31.95
\n" ); document.write( "==================================================================
\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H.\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );