document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=344621>Question 344621</A>: <I><SPAN STYLE=\"word-break: break-all;\"> This is a calc. question; please help!\r<BR>\n" );
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document.write( "A telephone wire is to be laid from the telephone company to an island 7 mi off shore at a cost of $200,000 per mile along the shore line and $300,000 per mile under the sea.  How should the wire be laid @ the least expensive cost if the distance along the shoreline in 12 miles.  What is the cost? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #246655 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=246655\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A telephone wire is to be laid from the telephone company to an island 7 mi off shore at a cost of $200,000 per mile along the shore line and $300,000 per mile under the sea. How should the wire be laid @ the least expensive cost if the distance along the shoreline in 12 miles. What is the cost?<BR>\n" );
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document.write( "This forms a right triangle with the shore side 12 miles long and the base = 7 miles to the island.<BR>\n" );
document.write( "x = the distance along the shore from the perpendicular from the island.<BR>\n" );
document.write( "The distance on land = 12 - x miles<BR>\n" );
document.write( "The distance under water = sqrt(x^2 + 49) miles<BR>\n" );
document.write( "The cost C = 200*(12-x) + 300*sqrt(x^2 + 49) (Cost in $1000)<BR>\n" );
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document.write( "dC/dx = -200 + 300x*(x^2 + 49)^(-1/2) = 0<BR>\n" );
document.write( "3x*(x^2 + 49)^(-1/2) = 2<BR>\n" );
document.write( "3x = 2sqrt(x^2 + 49)<BR>\n" );
document.write( "9x^2 = 4x^2 + 196<BR>\n" );
document.write( "x^2 = 196/5 <BR>\n" );
document.write( "x = 2.8sqrt(5) miles for minimum cost<BR>\n" );
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document.write( "Length of cable = 12 - 2.8sqrt(5) + sqrt(88.2)<BR>\n" );
document.write( "L = 12 - 2.8sqrt(5) + 4.2sqrt(5)<BR>\n" );
document.write( "L = 12 + 1.4sqrt(5) miles total<BR>\n" );
document.write( "L =~ 15.13 miles<BR>\n" );
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document.write( "Cost = 200*(12-x) + 300*sqrt(x^2 + 49) (Cost in $1000)<BR>\n" );
document.write( "C = 2400 - 560sqrt(5) + 1260sqrt(5) = 2400 + 600sqrt(5)<BR>\n" );
document.write( "Cost =~ $3,741,641\r<BR>\n" );
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document.write( " </SPAN>\n" );
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