document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=60579>Question 60579</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0495188891/algebrahomeworkh>Intermediate Algebra</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> NAVIGATION:  The paths of two ships are tracked on the same coordinate system.  One ship is following a path described by the equation 2x+3y=6, and the other is following a path described by the equation y=2/3x-3.\r<BR>\n" );
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document.write( "a.  Is there a possibility of a collision?\r<BR>\n" );
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document.write( "b.  What are the coordinates of the danger point?\r<BR>\n" );
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document.write( "c.  Is a collision a certainty?\r<BR>\n" );
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document.write( "While the answers are in the back of the book, I do not know how to get the correct answer.  Could someone help me please?  Thank you, I am going to school online and I am having difficulty.  Much thanks!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #41580 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=41580\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a) To see if there is a possibility of a collision, you could graph these two linear equations that represent the paths of the ships.<BR>\n" );
document.write( "First, get the first equation into the slope-intercept form:<BR>\n" );
document.write( "2x+3y = 6 Solve this for y by subtracting 2x.<BR>\n" );
document.write( "3y = -2x+6 Now divide both sides by 3.<BR>\n" );
document.write( "y = (-2/3)x + 2<BR>\n" );
document.write( "Now the graph of the two equations looks like:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C200%2C-5%2C5%2C-5%2C5%2C%28-2%2F3%29x%2B2%2C%282%2F3%29x-3%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C200%2C-5%2C5%2C-5%2C5%2C%28-2%2F3%29x%2B2%2C%282%2F3%29x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "As you can see, there is a possibility of a collision if the two ships continue along their respective paths.\r<BR>\n" );
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document.write( "b) The danger point is the intersection of the two lines and this can be found by solving this system of equations:<BR>\n" );
document.write( "y = (-2/3)x + 2<BR>\n" );
document.write( "y = (2/3)x - 3<BR>\n" );
document.write( "Set these two equations equal to each other and solve for x.<BR>\n" );
document.write( "(2/3)x-3 = (-2/3)x+2 Simplify and solve for x.<BR>\n" );
document.write( "(4/3)x = 5<BR>\n" );
document.write( "x = 15/4 Now substitute this into either equation and solve for y.\r<BR>\n" );
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document.write( "y = (2/3)(15/4)-3<BR>\n" );
document.write( "y = (5/2) - 3<BR>\n" );
document.write( "y = -1/2\r<BR>\n" );
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document.write( "The coordinates of the danger (collision) point are: (15/4, -1/2)\r<BR>\n" );
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document.write( "c) Is a collision a certainty? <BR>\n" );
document.write( "No, it is not.  Whether the two ships collide or not depends on their individual speeds. A collission can be avoided by appropriate adjustment of their speeds even if they do remain on the same paths as indicated on the graph.<BR>\n" );
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