document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1141836>Question 1141836</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A small island is 3 miles from the nearest point P on the straight shoreline of a large lake. If a woman on the island can row a boat 2 miles per hour and can walk 3 miles per hour, where should the boat be landed in order to arrive at a town 10 miles down the shore from P in the least time? Let x be the distance between point P and where the boat lands on the lake shore. \r<BR>\n" );
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document.write( "(A) Enter a function T(x) that describes the total amount of time the trip takes as a function of the distance x. <BR>\n" );
document.write( "T(x) = \r<BR>\n" );
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document.write( " (B) What is the distance x = c that minimizes the travel time? Note: The answer to this problem requires that you enter the correct units. <BR>\n" );
document.write( "c = \r<BR>\n" );
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document.write( "(C) What is the least travel time? Note: The answer to this problem requires that you enter the correct units. <BR>\n" );
document.write( "The least travel time is : \r<BR>\n" );
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document.write( "(D) Recall that the second derivative test says that if T'(c) = 0 and T''(c) > 0, then T has a local minimum at c. What is T''(c)? <BR>\n" );
document.write( "T''(c) = <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #762596 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=762596\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A small island is 3 miles from the nearest point P on the straight shoreline of a large lake.<BR>\n" );
document.write( " If a woman on the island can row a boat 2 miles per hour and can walk 3 miles per hour, where should the boat be landed in order to arrive at a town 10 miles down the shore from P in the least time?<BR>\n" );
document.write( " Let x be the distance between point P and where the boat lands on the lake shore.<BR>\n" );
document.write( "(A) Enter a function T(x) that describes the total amount of time the trip takes as a function of the distance x.<BR>\n" );
document.write( "the distance rowed is the hypotenuse of 3 & x, and the distance walked is 10-x<BR>\n" );
document.write( "time = dist/speed<BR>\n" );
document.write( "T(x) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%283%5E2%2Bx%5E2%29%2F2%29 ALIGN=MIDDLE  ALT=\"%28sqrt%283%5E2%2Bx%5E2%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%2810-x%29%2F3%29 ALIGN=MIDDLE  ALT=\"%28%2810-x%29%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(B) What is the distance x = c that minimizes the travel time?<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-3%2C+8%2C+-2%2C+8%2C+%28%28sqrt%283%5E2%2Bx%5E2%29%2F2%29%2B%28%2810-x%29%2F3%29%29%2C+4.45%29+%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Minimum x = 2.75 mi, travel time: 4.45 hrs (green)<BR>\n" );
document.write( " Note:<BR>\n" );
document.write( " The answer to this problem requires that you enter the correct units.<BR>\n" );
document.write( "c = 2.75 mi<BR>\n" );
document.write( "(C) What is the least travel time? Note: The answer to this problem requires that you enter the correct units.<BR>\n" );
document.write( "The least travel time is : 4.45 hrs<BR>\n" );
document.write( "(D) Recall that the second derivative test says that if T'(c) = 0 and T''(c) > 0, then T has a local minimum at c. What is T''(c)?<BR>\n" );
document.write( "T''(c) =<BR>\n" );
document.write( "Actually, I don't recall this.\r<BR>\n" );
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