document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=175045>Question 175045</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me on my homework. please correct my solutions and answers because i'm not sure if these are right answers.\r<BR>\n" );
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document.write( "1. 2 cars leave the same place at the same time. each car travels at a speed of 60 kph. one travels in the direction 60 degrees east of north. the other travels in the direction 45 degrees east of south. how far apart are the two cars after 30 minutes?<BR>\n" );
document.write( " My solution:\r<BR>\n" );
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document.write( "  d= distance of two cars after 30 min<BR>\n" );
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document.write( "  sin60=x/60kph         sin45=y/60<BR>\n" );
document.write( "  x=51kph               y=42.43kph<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  d=51.96kph+42.43kph<BR>\n" );
document.write( "  d=94.39kph<BR>\n" );
document.write( "  d=94.39 km/1hr x 1 hr/60 min x 30 min<BR>\n" );
document.write( "  my answer : d= 47.20 km\r<BR>\n" );
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document.write( "2. 2 ships leave a big port at the same time. the first ship travels N 30 degrees W at 20 kph. the other heads toward N 15 degrees E at 25 kph. how far apart will they be in 3 hours?<BR>\n" );
document.write( "  sin30=x/20 kph         sin15=y/25<BR>\n" );
document.write( "  x=10                   y=6.47\r<BR>\n" );
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document.write( "  10 kph + 6.47 kph = 16.47 kph\r<BR>\n" );
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document.write( "  16.47 km/1 hr x 3 hrs = 49.41 km\r<BR>\n" );
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document.write( "3. A regular pentagon is inscribed in a circle whose radius is 18 cm. find the perimeter of the pentagon.\r<BR>\n" );
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document.write( "I really don't know how to solve it.\r<BR>\n" );
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document.write( "   </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #130145 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=130145\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I'll convert the velocity vectors to distance vectors. Then <BR>\n" );
document.write( "I'll find the points on the x-y plane where the end up and use the distance formula<BR>\n" );
document.write( "\" One travels in the direction 60 degrees east of north.\"<BR>\n" );
document.write( "That's the same as 30 degrees N of E. In a half-hour this car<BR>\n" );
document.write( "would have gone 60 km/hr x 1/2 hr = 30 km<BR>\n" );
document.write( "The component along the y-direction is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15 ALIGN=MIDDLE  ALT=\"15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The component along the x-direction is <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15%2Fsqrt%283%29 ALIGN=MIDDLE  ALT=\"15%2Fsqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--------------------<BR>\n" );
document.write( "\" The other travels in the direction 45 degrees east of south.\"<BR>\n" );
document.write( "That's the same as 45 degrees south of east<BR>\n" );
document.write( "This car also would have gone 60 km/hr x 1/2 hr = 30 km<BR>\n" );
document.write( "The component along the y-direction is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-30%2Fsqrt%282%29 ALIGN=MIDDLE  ALT=\"-30%2Fsqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The component along the x-direction is <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30%2Fsqrt%282%29 ALIGN=MIDDLE  ALT=\"30%2Fsqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---------------------<BR>\n" );
document.write( "Now I have 2 points<BR>\n" );
document.write( "(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15 ALIGN=MIDDLE  ALT=\"15\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15%2Fsqrt%283%29 ALIGN=MIDDLE  ALT=\"15%2Fsqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "and<BR>\n" );
document.write( "(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30%2Fsqrt%282%29 ALIGN=MIDDLE  ALT=\"30%2Fsqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-30%2Fsqrt%282%29 ALIGN=MIDDLE  ALT=\"-30%2Fsqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "Now I use the distance formula<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+sqrt%28%2830%2Fsqrt%282%29+-+15%29%5E2+%2B+%28-30%2Fsqrt%282%29+-+15%2Fsqrt%283%29%29%5E2%29%7D%7D%0D%0A%7B%7B%7Bd+=+sqrt%28%2821.21+-+15%29%5E2+%2B+%28-21.21+-+8.66%29%5E2%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+sqrt%286.21%5E2+%2B+29.87%5E2%29 ALIGN=MIDDLE  ALT=\"d+=+sqrt%286.21%5E2+%2B+29.87%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+sqrt%2838.56+%2B+892.22%29 ALIGN=MIDDLE  ALT=\"d+=+sqrt%2838.56+%2B+892.22%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+sqrt%28930.78%29 ALIGN=MIDDLE  ALT=\"d+=+sqrt%28930.78%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+30.51 ALIGN=MIDDLE  ALT=\"d+=+30.51\"   DISABLED_style= \"max-width:90%; height:auto;\" > km </SPAN>\n" );
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