document.write( "Question 730805: A cable is run from the top of a tree to a stake located 4m away from the base of the tree. the length of the cable is 1m less than twice the height of the tree. find the length of the cable. \n" ); document.write( "
Algebra.Com's Answer #446868 by ankor@dixie-net.com(22740)\"\" \"About 
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A cable is run from the top of a tree to a stake located 4m away from
\n" ); document.write( " the base of the tree.
\n" ); document.write( "the length of the cable is 1m less than twice the height of the tree.
\n" ); document.write( " find the length of the cable.
\n" ); document.write( ":
\n" ); document.write( "Let x = height of the tree
\n" ); document.write( "then
\n" ); document.write( "(2x-1) = length of the cable
\n" ); document.write( ":
\n" ); document.write( "Use pythag, a^2 + b^2 = c^2, where
\n" ); document.write( "a = 4
\n" ); document.write( "b = x
\n" ); document.write( "c = (2x-1)
\n" ); document.write( "4^2 + x^2 = (2x-1)^2
\n" ); document.write( "16 + x^2 = 4x^2 - 4x + 1
\n" ); document.write( "16 = 4x^2 - x^2 - 4x + 1
\n" ); document.write( "16 = 3x^2 - 4x + 1
\n" ); document.write( "0 = 3x^2 - 4x + 1 - 16
\n" ); document.write( "A quadratic equation
\n" ); document.write( "3x^2 - 4x - 15 = 0
\n" ); document.write( "Factors to
\n" ); document.write( "(3x + 5)(x - 3) = 0
\n" ); document.write( "the positive solution
\n" ); document.write( "x = 3 meters is the height of the tree
\n" ); document.write( "then
\n" ); document.write( "2(3) - 1 = 5 meters is the length of the cable
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "Check this 4^2 + 3^2 = 5^2 \n" ); document.write( "
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